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Volume 43 • Number 4 

IMAGING SCIENCE 

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Vol. 43, No. 4, July/Aug. 1999 i

July/August 1999 

CODEN: JIMTEG 43(4) 309–404 (1999) 

ISSN: 1062-3701 

Volume 43, Number 4 

Journal of 

IMAGING SCIENCE 

and 

TECHNOLOGY 

Official publication of IS&T—The Society for Imaging Science and Technology 

CONTENTS 

Feature Article 

309 Comparison of the Single Pixel Development of DMD (Digital Micromirror Device) and Laser Exposure Modules in 

Electrophotographic Printing 

John B. Allen and Albert B. S. Coit 

320 Particle Size Effects in Pigmented Inkjet Inks 

Alexandra D. Bermel and D. E. Bugner 

325 Investigations of Nonreproducible Phenomena in Thermal Ink Jets with Real High-Speed Cine Photomicrography 

Christian Rembe, Stefan aus der Wiesche, Michael Beuten, and Eberhard P. Hofer 

332 New Thermal Ink Jet Printhead with Improved Energy Efficiency Using Silicon Reactive Ion Etching 

Masahiko Fujii, Toshinobu Hamazaki and Kenji Ikeda 

339 Thermal Dye Transfer Printing with Chelate Compounds 

Takao Abe, Shigeru Mano, Yorihiro Yamaya, and Atsushi Tomotake 

345 Dot Allocations in Dither Matrix with Wide Color Gamut 

Ryoichi Saito and Hiroaki Kotera 

Supplemental materials—Figure 4 (in color) and Table III can be found on the IS&T website (www.imaging.org) and on the CD-ROM 

353 Symmetry Properties of Halftone Images I: Scattering Symmetry and Pattern Symmetry 

Jonathan S. Arney and Shinya Yamaguchi 

359 Symmetry Properties of Halftone Images II: Accounting for Ink Opacity and Dot Sharpness 

Jonathan S. Arney and Akio Tsujita 

365 Kubelka–Munk Theory and the Yule–Nielsen Effect on Halftones 

Jonathan S. Arney, Eric Pray and Katsuya Ito 

Contents continued 

ii 

Journal of Imaging Science and Technology

Contents continued 

371 The Free Radicals and Iron of Photographic Gelatin Doped with Na 2 

S 2 

O 3 

Yi-heng Zhang, Ji Tan, Jie Li, Tian-tang Yan, Shu-qin Yu, Si-yong Zhuang and Bi-xian Peng 

375 Calculated Properties of Sulfur Centers on AgCl Cubic Surfaces 

Roger C. Baetzold 

382 The Measurement of Diffuse Optical Densities. Part II: The German Standard Reference Densitometers 

Egbert Buhr, D. Hoeschen and D. Bergmann 

388 NIST Reference Densitometer for Visual Diffuse Transmission Density 

Edward A. Early, Christopher L. Cromer, Xiaoxiong Xiong, Daniel J. Dummer, Thomas R. O’Brian and Albert C. Parr 

398 Self-Excited Vibration Induced in Paper-Feed-Roller in Electrophotography Copy Machine 

Hiroyuki Kawamoto 

DEPARTMENTS 

iii 

Calendar 

403 Business Directory 

Calendar 

IS&T Meetings 

October 17–22, 1999—NIP15: The l5th International 

Congress on Digital Printing T echnologies, General 

Chair: Michael Lee, The Caribe Royal Resort Suites, 

Lake Buena Vista, Florida 

November 16–19, 1999—7th Color Imaging Conference— 

Color Science, Systems & Applications, cosponsored 

by the Society for Information Display; 

General Co-chairs: Jack Holm (IS&T) and Todd Newman 

(SID), The SunBurst Resort Hotel, Scottsdale, Arizona 

January 22–28, 2000—IS&T/SPIE Electronic Imaging: 

Science and Technology, General Co-chairs: John 

McCann (IS&T) and Giordano Beretta (SPIE), San Jose 

Convention Center, San Jose, California 

January 31–February 2, 2000— 11th International 

Symposium on Photofinishing Technology, General 

Co-chairs: Steven Howe and Daniel English, co-located 

with the PMA Exhibition, Las Vegas, Nevada 

March 26–29, 2000—The PICS Conference, (IS&T’s 

53rd Annual Spring Conference), General chair: Jim 

Milch, The Portland Marriott Hotel, Portland, Oregon 

September 10–14, 2000—International Symposium 

on Silver Halide T echnologies, co-sponsored by 

SPSTJ, General Co-chairs: Rene DeKeyzer, Gary House, 

Melville Sahyun, and Tadaaki Tani, Resort Hotel Mont- 

Gabriel, Montreal (St. Adele), Quebec, Canada 

October 15–20, 2000—NIP16: The l6th International 

Congress on Digital Printing T echnologies, The 

Westin Bayshore, Vancouver, B.C., Canada 

November 6–10, 2000— 8th Color Imaging Confer - 

ence—Color Science, Systems, and Applications, 

co-sponsored by the Society for Information Display, The 

SunBurst Resort Hotel, Scotsdale, Arizona 

For more details, contact IS&T at 

703-642-9090; FAX: 703-642-9094; 

E-mail: info@imaging.org; 

or visit us at www.imaging.org 

For a more complete listing of other imaging conferences 

• Visit IS&T’s website: www.imaging.org 

• See the Other Meetings column in the member 

newsletter, IS&T Reporter 

• Request a printout via e-mail: info@imaging.org or 

fax: (703) 642-9094 

Vol. 43, No. 4, July/Aug. 1999 iii

The Journal of 

Imaging Science and 

Technology CD 

Editor: Volume 40, 1996—Vivian Walworth 

Editor: Volume 41, 1997—Melville R. V. Sahyun 

The Journal of Imaging Science and 

Technology is dedicated to the advancement 

of knowledge in the imaging 

sciences, in practical applications 

of such knowledge, and in related fields 

of study. The pages of this journal are 

open to reports of new theoretical or 

experimental results and to comprehensive 

reviews. 

Vol. 40, 1996 and Vol. 41, 1997 

now available on CD 

Cost is as follows: CD-ROM 

IS&T Member $45.00 

Non-member $55.00 

Institution $100.00 

Vol. 42, 1998 and Vol. 43, 1999 

available Spring, 2000 

1999 Honors and Awards Recipients 

More information regarding IS&T awards and the nomination form Honors and Awards for 2000 

can be found on the IS&T website, http://www.imaging.org. Click on Membership, then click on Honors and Awards. 

Honorary Member 

Robert Gundlach 

Edwin H. Land Award 

Robert W. Webb 

Chester F. Carlson Award 

David S. Weiss 

Leiven Gevaert Medal 

Vitaly Belous 

Kosar Memorial Award 

Jean Fréchet 

C. Grant Willson 

Hiroshi Ito 

Bowman Award 

Jeff B. Pelz 

Fellowship 

Gary L. House 

Hiroyuki Kawamoto 

Mitsuo Kawasaki 

Robert J. Nash 

John Texter 

Journal Award (Science) 

Koichi Iino 

Roy S. Berns 

Charles E. Ives Award 

Juha Katajamäki 

Hannu J. Saarelma 

Itek Award 

Angela F. Marks 

Senior Member 

David Q. McDowell 

Service Awards 

James C. King 

Jeffrey Seideman 

Raymond Davis Scholarship 

Kishwar Ahsan 

Benjamin Spead 

iv 

Journal of Imaging Science and Technology

JOURNAL OF IMAGING SCIENCE AND TECHNOLOGY • Volume 43, Number 4, July/August 1999 

Feature Article 

Comparison of the Single Pixel Development of DMD 

(Digital Micromirror Device) and Laser Exposure Modules in 

Electrophotographic Printing 

John B. Allen and Albert B. S. Coit 

Raytheon TI Systems, Plano, Texas* 

DMD and laser exposure modules are compared with respect to the formation of a single pixel on the photoconductor . Toner 

development is assumed to neutralize the normal component of the electric field above the photoconductor at the location of the 

toner about to be developed. This field is produced by bias voltages, the single pixel latent image, and toner already developed. 

Care is taken in predicting development of the second layer of toner to assume that the latent image is on the surface of the 

photoconductor and the first layer of toner is above the surface of the photoconductor . The predicted toner development is in 

accord with the experimental data. The analysis shows that the normal component of the electric field for single pixel development 

produced by a 600 dpi DMD exposure module is stronger than the corresponding field of an 85 µm wide Gaussian pixel 

produced by a laser exposure module. Therefore, toner development resulting from the DMD exposure module is more stable, 

smaller, and more compact on the photoconductor than the toner developed image produced by the corresponding laser exposure 

module. Comparing theory with experimental data where the exposure of the photoconductor by the DMD exposure module is 

varied, suggests that toner development only begins after a threshold electric field is reached. Justification for a threshold 

behavior is given. 

Journal of Imaging Science and Technology 43: 309–319 (1999) 

Introduction 

The DMD (digital micromirror device) is a digitally controlled 

two dimensional spatial light modulator invented 

at Texas Instruments. 1,2 The idea of using a DMD in an 

exposure module of an electrophotographic printer has 

been suggested. 3–6 The DMD spatially modulates a beam 

of light with the information needed to form a desired 

print. The modulated light exposes the photoconductor 

of the electrophotographic printer. It is an optical system 

with no macroscopic moving parts such as a rotating 

polygon scanner required by a conventional laser 

exposure module. We predict the light intensity distribution 

of a single pixel on the photoconductor produced 

by a DMD exposure module and an 85 µm wide (measured 

at the 1/e 2 points) Gaussian pixel, typical of today’s 

600 dpi laser exposure module. The toner distributions 

on the photoconductor produced by the DMD exposure 

module have been experimentally measured. The exposures 

range from low to fully saturated. In order to predict 

the development of single pixels on the 

photoconductor, we extend Schein’s equilibrium theory 

of development of solid areas. 7,8 The extension accounts 

for the weakening of the field of the latent image as the 

location where the toner develops further away from the 

photoconductor surface due to the growth in height of 

Original manuscript received January 12, 1998 

* The work presented in this paper was done by the authors 

while employed at Texas Instruments, Inc., Dallas, Texas. 

© 1999, IS&T—The Society for Imaging Science and Technology 

the pile of toner comprising the pixel. The single pixel 

latent image fields weaken above the photoconductor 

due to their high spatial frequency content. Because we 

are dealing with single pixels rather than solid areas, 

the build up of charge on the carrier is not significant 

because a single pixel latent image removes much less 

toner from the carrier than a solid area latent image. 

The extended equilibrium theory closely matches the 

experiment at higher exposures. The theory predicts 

more toner to be developed than is actually observed at 

low exposures. We suggest that the deviation is due to 

the transient effect of toner being driven up into the 

magnetic bush prior to development, thus reducing the 

amount of toner available for development in the single 

pixel. This is the first time, to our knowledge, that a 

theory of electrophotographic development is able to 

semiquantitatively account for single pixel development. 

We apply the theory to compare development of a single 

pixel by a DMD and laser exposure module. 

DMD and Laser Exposure Modules . A DMD exposure 

module, depicted in Fig. 1, consists of a source of 

illumination or an illuminator, the DMD and a projection 

lens. The light from the illuminator falls on the 

DMD. The illuminator produces sufficiently uniform illumination 

to ensure that there are no artifacts in the 

final print to nonuniform illumination. The DMD consists 

of a matrix of individually addressable miniature 

mirrors called “micromirrors” as shown in Fig. 2. A 

micromirror is a square mirror that is 16 µm on the side. 

The center-to-center spacing of the micromirrors is 17 

µm. The micromirrors rotate about the diagonal shown 

309

1 

Figure 1. Schematic of the DMD exposure module. 

64 

in Fig. 3 to two discrete and stabile angular displacements 

which are +10 and –10° with respect to the plane 

of the DMD. The angular displacement of +10 ° is referred 

to as the “on” position and the angular displacement 

of –10 ° is referred to as the “off” position. The 

direction of the incident illumination upon the DMD, 

namely 20°, is chosen so that when a micromirror in 

the “on” position is illuminated, the axis of the cone of 

light reflected from the micromirror is parallel to the 

optical axis of the projection lens as shown in Fig. 3. 

When a micromirror in the “off” position is illuminated, 

the axis of the cone of reflected light from the 

micromirror makes an angle of 40° with respect the optical 

axis of the projection lens and thus is reflected 

around the lens. The projection lens images a 

micromirror in the “on” position onto the photoconductor 

forming a pixel on the photoconductor. The light from a 

micromirror in the “off” position is reflected through a 

large angle and out of the optical system and, therefore, 

no micromirror image is formed. Hence, the DMD 

is a two dimensional light switch that can selectively 

illuminate pixels on the photoconductor. The number of 

columns of micromirrors on the DMD is equal to the 

number pixels across the print, namely 7056, which for 

600 dpi, equates to 11.76 in. wide. The number of rows, 

in this case 64, is equal to the number of possible sequential 

exposures per pixel as the photoconductor drum 

turns. 

Let us compare the laser exposure module shown schematically 

in Fig. 4 with the DMD exposure module 

shown in Fig. 1. The DMD exposure module images the 

micromirrors onto the photoconductor as shown. The 

projection lens can be thought of as a pair of collimating 

lenses. The first collimating lens collimates a point 

source in the micromirror plane. The second lens focuses 

the collimated beam onto the photoconductor. The separation 

between the two lenses is not critical so long as 

the rays entering the first lens all pass through the second 

lens. The two lenses are generally placed as close 

together as possible in a single unit to form the projection 

lens. To have a high resolution imaging system, the 

diameter of the lens is made large enough to increase 

resolution due to the diffraction limit. The maximum 

diameter of the lens is limited by the geometric aberrations 

that increase as the diameter increases and the 

depth of field which decreases as the diameter increases. 

The depth of field requirements are set by the maximum 

runout of the drum. W e found the best compromise 

of these parameters to be a 1 in. diam. f/5.6 

Figure 2. Schematic of the DMD showing 7056 columns and 

64 rows of micromirrors. 

Figure 3. Sketch showing the direction of reflection of the illumination 

from a micromirror in the on and off positions. 

projection lens for a 600 dpi DMD printer . The projection 

lens magnified each micromirror so that the center 

to center spacing of the micromirror images on the 

photoconductor was 1/600 in. 

Unlike the DMD exposure module, the laser exposure 

module requires a scanner to move the focussed laser 

beam across the photoconductor. The rotating polygon 

scanner is an economically feasible and currently available 

scanner that can scan the beam fast enough for 

use in a printer. In order for the writing beam to be on a 

planar rather than a spherical surface at the photoconductor, 

it is necessary that the beam be collimated in 

the direction of scan when it falls on the rotating poly- 

310 Journal of Imaging Science and Technology Allen and Coit

Figure 4. Schematic of a laser exposure module. 

gon scanner. To attain collimation, the laser beam is 

focussed in the focal plane of collimating lens 1 as shown 

in Fig. 4. The beam is reflected by the scanner and is 

focussed by collimating lens 2 onto the photoconductor. 

Like the DMD exposure module, the laser exposure 

module has a projection lens that can be thought of as a 

pair of collimating lenses. Unlike the DMD exposure 

module, a rotating polygon scanner must be inserted 

between the two components of the projection lens in 

order to scan the laser beam across the photoconductor. 

In the scanning system configured as shown in Fig. 4, 

the height of the rotating polygon scanner must at least 

equal the diameter of the projection lens so that all of 

the light entering the lens is scanned. If a 1 in. diam. 

f/5.6 lens analogous to the imaging lens in the DMD exposure 

module were used, the height of the rotating 

polygon scanner would have to be at least 1 in. This 

would result in a large and expensive polygon scanner. 

The height restriction of the polygon scanner can be 

overcome 13 by placing a cylindrical lens after collimating 

lens 1 in Fig. 4 to focus the laser beam in the cross 

scan direction onto the face of the scanner. A second cylindrical 

lens is placed before collimating lens 2 to image 

the scanner face in the cross scan direction onto the 

photoconductor. As pointed out by Holland, 13 this arrangement 

also reduces distortion due to scanner 

wobble. Apertures or masks can be placed in the focal 

plane of the focussing lens to alter the Gaussian distribution 

of the laser beam and increase its spatial frequency 

content. However the scanner and optics must 

be designed to pass the increased spatial frequency content 

onto the photoconductor. It is clear that multiple 

addressing or the exposure of an adjacent pixel affect 

the final toner distribution of a given pixel for either a 

laser or DMD exposure module. However , only single 

isolated pixels are treated here and adjacent pixel effects 

and the formulation of screens are beyond the scope 

of this particular study. 

The salient difference between the DMD and the laser 

exposure module is that the DMD exposure module 

requires no scanner and therefore the diameter and 

hence the resolution of the projection lens is not limited 

by the scanner aperture. The problems of preserving 

single pixel spatial frequency content in the presence of 

an aperture restricting rotating polygon scanner and the 

jitter and wobble included with that scanner are nonexistent 

in DMD exposure module. 

Comparison of the Resolution of the Single Pixel 

DMD and Laser Exposure Module Images. Figure 5 

compares the single pixel image (predicted 9 and experimentally 

measured) produced by a 600 dpi DMD exposure 

module to that produced by a laser exposure module. 

The spatial intensity distribution of the laser exposure 

module image is taken to be a Gaussian function whose 

width is 85 µm (full width at 1/e 2 points). The dip in the 

center of the micromirror image results from a 3 µm hole 

in the center of the micromirror placed there for manufacturing 

reasons. The images are normalized to the same 

spatially integrated intensity, i.e., the same power in both 

beams. Note that the DMD exposure module produces a 

tighter and more intense single pixel image than does 

the laser exposure module. 

To illustrate the difference between the DMD exposure 

module and the above laser exposure module in 

terms of resolution, we reduce the aperture of the DMD 

projection lens from 1 to 0.3 in. Reduction of the aper - 

ture of the DMD projection lens from 1 to 0.3 in. results 

in a reduction of the resolving power of the lens. An 85 

µm wide laser exposure module image is shown in Fig. 

6 along with the image produced by the reduced aper - 

ture DMD exposure module. Note that the single pixel 

DMD exposure is not as compact as it is in Fig. 5. The 

single pixel image produced by the reduced aperture 

DMD exposure module is virtually identical to the single 

pixel image produced by this laser exposure module. The 

essential difference in the image produced by DMD and 

this laser exposure module is that the DMD exposure 

module is capable of producing a higher resolution single 

pixel image. 

Comparison of the Single Pixel Development of DMD ...Electrophotographic Printing Vol. 43, No. 4, July/Aug. 1999 311

Figure 5. Comparison of a single pixel image made by a 600 dpi DMD and a laser exposure module with an 85 

Gaussian beam. 

µm wide 

Figure 6. Comparison of a single pixel image made by a DMD exposure module with a reduced aperture and a laser exposure 

module with an 85 µm wide Gaussian beam. 

Computation of the Normal Component of the Electric 

Field due to the Latent Image at a Given Height 

Above the Photoconductor. We shall now compute the 

normal component of the electric field at a height h above 

the photoconductor produced by a single pixel latent image 

created by both a DMD exposure module and laser 

exposure module. We extend the air gap model shown in 

Fig. 7 and described by Schein 10 for solid area development 

to the problem of single pixel development. The 

ground plane is located at z = 0 and has a voltage equal 

to 0. The photoconductor has a thickness L and a dielectric 

K a as shown. There is a small air gap of height δ a 

with dielectric constant K b equal to unity between the 

photoconductor and the toner–carrier mix of dielectric 

constant K c . The developmental electrode resides at a distance 

M from the conductor. Schaffert 11 states the equations 

to find the electric field in the center layer of a three 

layer dielectric shown in Fig. 7 due to a one dimensional 

cosinusoidal charge distribution on the photoconductor. 

The relationship between the electric field and the charge 

distribution is linear implying that the relationship between 

an arbitrary charge distribution and the corresponding 

electric field can be calculated by convolving 

the charge distribution with an appropriate two dimensional 

spatial impulse response. W e shall now find the 

transfer function corresponding to this impulse response 

by applying Schaffert’s equations. 

First, we calculate the normal component of the electric 

field in the air gap due to a cosinusoidal charge density 

in the x 0 direction as shown in Fig. 8. The x 0 direction 

makes an angle θ with the x-axis. The x-axis is in the 

cross-process dimension and the y-axis is in the process 

dimension. We express the cosinusoidal charge density 

in the (x, y) coordinate system. Let the charge distribution 

σ(x 0 , y 0 ) (coulombs/m 2 ) on the photoconductor be 

given by: 

σ( x , y ) = cos( 2πfx 

) 

(1) 

0 0 0 


Figure 7. Schematic of air gap model used in the analysis. 

Figure 8. Spatial coordinates on the photoconductor used in 

the analysis. 

The factor f (cycles per meter) is the spatial frequency of 

the cosine wave. We find the potentials ( V a , V b , V c ) in the 

three regions (a, b, c) of Fig. 7 with the solution of Laplace’ s 

equation for the charge density σ(x 0 , y 0 ) as follows 11 : 

2πfz 

−2πfz 

Va 

= [ A1 

( f) e + A2 

( f) e ]cos( 2πfx0 

) 

2πfz 

−2πfz 

V = [ B ( f) e + B ( f) e ]cos( 2π fx ) (2) 

b 

1 

2 

0 

2πfz 

2 

−2πfz 

2π 

0 

V = [ C ( f) e + C ( f) e ]cos( fx ) 

c 

1 

The normal component of the electric field E bn0 in the 

air gap (region b) is obtained by differentiating V b with 

respect to z: 

2πfz 

−2πfz 

E =−2πf[ B ( f) e −B ( f) e ]cos( 2πfx 

) (3) 

bn0 1 

We now rotate the coordinate system (x 0 , y 0 ) through 

an angle θ into the (x, y) coordinate system. We obtain 

the field E bn as follows: 

2πfz 

Ebn 

= 2πf[ B1 

( f) e − B2 

( f) e ]cos[ 2πfxcos( θ) 

+ 

(4) 

2πfysin( θ)] 

2 

−2πfz 

Now make the following definitions: 

so that E bn becomes: 

fx 

= f cos( θ) fy 

= f sin( θ) 

2 2 (5) 

ρ = f + f 

x 

y 

2πρz 

−2πρz 

Ebn 

= 2πρ[ B1 

( ρ) e − B2 

( ρ) e ]cos( 2πfxx+ 

2πfyy) (6) 

By definition from Eq. 6, the transfer function H na (f x , 

f y ) relating the normal component of the electric field to 

the two dimensional charge density on the 

photoconductor is: 

2πρz 

−2πρz 

Hna( fx , fy 

) = 2πρ[ B1 

( f) e −B2 

( f) e ] 

With respect to Fig. 7, we can apply the following 

boundary conditions to obtain B 1 (ρ) and B 2 (ρ): 

0 

(7) 

1. The voltage at z = 0 is zero and the voltage at z = M 

is V 0 

. 

2. The potential is continuous across the dielectric 

boundary. 

3. The change in the normal component of electric 

displacement at a dielectric boundary is equal to the 

charge density at the boundary. 

Theory of Toner Distribution of Single Pixels on 

the Photoconductor. We extend Schein’s theory of 

solid area development to predict the development of 

single pixels. In that theory, Schein 10 compares the forces 

attracting the toner to the photoconductor and the forces 

attracting the toner to the carrier. Schein assumes that 

development occurs if the forces attracting the toner to 

the photoconductor exceed the forces attracting the toner 

to the carrier taking into account the build up of charge 

on the carrier bead. The build up of charge on the car - 

rier does not significantly restrict development of single 

pixels because the amount of toner removed from a carrier 

by a single pixel is much less than the toner removed 

by a solid area. We extend Schein’s approach to 

include the degradation of the electric field produced 

by a single pixel latent image as development occurs 

further from the photoconductor. The first layer of toner 

senses the electric field at a height above the photoconductor 

approximately equal to the radius of the toner 

which is four µm for eight µm diameter toner. The second 

layer of toner senses the field at a height above the 

photoconductor that is approximately the toner radius 

above the first layer, or 12 µm above the photoconductor. 

The single pixel latent image field has high spatial frequency 

content and therefore weakens as the height 

above the photoconductor increases. As the pile of toner 

becomes higher, the latent image field weakens and the 

force of the already developed toner strengthens thus 

terminating further development. 

Calculations of Single Pixel T oner Distributions 

for DMD and Laser Exposure Modules. We predict 

and compare the toner distributions for single pixel development 

produced by both DMD and laser exposure 

modules at an exposure of 0.0021 J/m 2 . We assume that 

the DMD exposure module images 16 µm micromirrors 

on 17 µm centers imaged to 1/600 in. at the photoconductor 

surface. We assume that the laser exposure module 

creates an 85 µm wide Gaussian beam at the 1/e 2 

points at the photoconductor surface. We also assume 8 

µm toner particles and a high sensitivity photoconductor. 


Figure 9. Comparison of the normal components of the E-fields for a DMD and the assumed laser exposer module at height of 4 

microns above the PC. 

Figure 10. Comparison of the normal components of the E-fields for a DMD and the assumed laser exposer module at height of 

12 microns above the PC. 

Figure 9 compares the normal component of the latent 

image electric field at a height of 4 µm above the 

photoconductor where development of the first layer of 

toner occurs for both the DMD and laser exposure modules. 

Similarly, Fig. 10 compares the normal component 

of the latent image electric field at a height of 12 µm 

above the photoconductor where development of the second 

layer of toner occurs for both exposure modules. Note 

that fields produced by the DMD exposure module are 

stronger and more concentrated than the fields produced 

by the laser exposure module. In addition, the top of 

the electric field produced by the DMD exposure module 

is flat as shown in Fig. 9. The flat top is a result of 

the hole in the micromirror as described earlier and 

and will promote uniform toner development. Figure 11 

compares the image on the photoconductor of a micromirror 

with and without a hole present. The image of 

the hole is apparent. Figure 12 compares the normal 

component of the electric field at 4 µm above the 

photoconductor resulting from the im ages shown in 

Fig. 11. Note that flat top is present in the electric 

field created by micromirror with the hole present. 

The hole in the micromirror creates an object for 

the projection lens that has higher spatial frequency 

content than the object created by the micromirror with 

no hole. Hence image of the micromirror with the hole 

has higher spatial frequencies than the micromirror 

without the hole as is apparent from Fig. 1 1. Because 

the transfer function relating the micromirror image to 

the normal component of the electric field is lowpass, 

the field produced by the micromirror with the hole also 

has higher spatial frequencies i.e., a flat rather than a 

rounded top. 

Figures 13 and 14 show the predicted toner distribution 

in the first two layers of toner for the DMD and 

laser exposure module pixels, respectively. Each square 

corresponds to the space taken by an 8 µm toner particle. 

The development of the first layer is predicted by 

computing the net electric field sensed by the toner particle 

at its center, namely, 4 µm above the photoconductor 

for an 8 µm toner diameter. The net electric field consists 

of the bias field and the latent image field. The 


Figure 11. Comparison of the single pixel intensity distribution on the PC produced by a micromirror with and without a hole. 

Figure 12. Comparision of the normal component of the electic field of a single pixel produced by a micromirror with and without 

a hole. 

Figure 13. Location of toner particles on the photoconductor 

in the first and second layers of the DMD pixel. Each square 

corresponds to one toner particle. The solid squares represent 

the x and y location of the toner particles in both the first and 

second layers. The crosses represent the location of toner particles 

in the first layer only. 

Figure 14. Location of toner particles on the photoconductor 

in the first and second layers of the laser pixel. Each square 

corresponds to one toner particle. The solid squares represent 

the x and y location of the toner particles in both the first and 

second layers. The crosses represent the location of toner particles 

in the first layer only. 


Figure 15. Normal component of the electric field due to the latent image at heights above the photoconductor where development 

takes place for a single pixel 0.3 mm in diameter. 

Figure 16. Normal component of the electric field acting on the toner particles in the second and third layers of toner along a 

diameter of the 0.3 mm pixel. 

predicted development of the second layer is achieved 

in a similar manner except that the fields are computed 

at a height of 12 µm above the photoconductor and the 

repelling field of the first layer of toner is included. No 

third layer is predicted for either exposure module because 

the force repelling toner attempting to develop in 

the third layer due to the electric field of the toner in 

the first two layers exceeded the force attracting the 

toner to the photoconductor . The predicted developed 

area of the first layer of the DMD pixel is 50% of the 

predicted area of the laser pixel. The second layers are 

comparable in size. The DMD developed pixel is smaller 

with steeper sides than the laser produced pixel. This 

is in accord with our observations. 

Predictions Using Extended Equilibrium Theory 

of Toner Distributions in Solid Areas. We applied 

the extended equilibrium theory of development to solid 

areas of diameter 0.3 mm and 2.0 mm. Figure 15 depicts 

the latent image field as a function of displacement 

across the 0.3 mm pixel at the heights above the 

photoconductor where toner development takes place. 

Note that the reduction in field strength as height above 

the photoconductor increases and is less severe for the 

0.3 mm area than the single pixel case depicted in Figs. 

9 and 10. The field created by the large area has a lower 

spatial frequency content than the field created by the 

single pixel and hence degrades less as the height of 

the photoconductor increases. Figure 16 shows the total 

field acting on the toner at locations where the second 

and third layers are formed. The field acting on the 

toner is the sum of the attracting latent image field and 

the repelling field of previously developed toner. Because 

the field is positive for the second and third layers, toner 

development will take place in the first three layers. 

The field acting on the fourth layer was entirely negative 

and hence no fourth layer is developed. Figure 17 

describes the latent image field as function of displacement 

across the 2.0 mm solid at the heights above the 

photoconductor where toner development takes place. 

The drop off of the field strength as the height above 

the photoconductor is increased, is even less than that 

incurred by the 0.3 mm solid area. Figure 18 shows the 

net field acting at the locations above the photoconductor 


Figure 17. Normal component of the electric field acting on the toner particles in the second to the third layers of toner along a 

diameter of the 2 mm pixel. 

Figure 18. Normal component of the electric field acting on the toner particles in the second to the third layers of toner along a 

diameter of the 2 mm pixel. 

where the second and third layers will develop. Two complete 

layers and a portion of a third layer around the 

edges of the area develop. The field acting on the fourth 

layer was negative across the pixel so that no fourth 

layer was formed. The development of toner in the large 

pixels representing solid areas in the limit, shown in 

Figs. 16 and 18, is consistent with the experiment. 

Measurements of Single Pixels. We carried out 

halftoning experiments to investigate the properties of 

single pixels formed by DMD exposure modules. The 

measurements were made on the image evaluation 

breadboard (IEB), which is a custom designed testbed. 

The IEB is an optical bench that holds all of the electrophotographic 

subsystems, including the DMD exposure 

module. All subsystems are cantilevered for easy access, 

and can be mounted at various locations around the 

photoconductor. A CCD camera acquires the developed 

image on the photoconductor. The image is digitized and 

stored for evaluation. 

We used a two component developer and a high sensitivity 

OPC for the tests. The toner diameter was 8 µm. 

We charged the OPC to –800V and set the bias set to 

–650V. We adjusted the optics for a 600 dpi resolution 

and best focus. We measured toner concentration (TC) 

and Q/M of the developer with a blowoff device. It was 

verified that the values of TC and Q/M remained constant 

throughout the experiment. 

The test pattern used to create the single pixels consisted 

of every fourth pixel being turned on. Pixels were 

built up by gradually increasing the light intensity until 

the OPC was well into saturation. Discharge area 

development was used to develop the single pixel test 

pattern on the OPC. Images of pixels created at the various 

intensity levels were captured and stored. 

Figures 19 to 21 are sample photographs of pixels 

toned on the OPC. An example of pixels created with a 

small amount of light is shown in Fig. 19. The exposure 

was 1.1 mJ/m 2 , this corresponded to the midpoint of the 

linear region of the photoinduced discharge curve. An 

example of pixels created with an intermediate amount 

of light is shown in Fig. 20. In this case exposure was 

2.2 mJ/m 2 . The pixel diameter is on the order of 60 µm. 

This corresponds to the optimum 600 dpi dot size. An 


Figure 19. Single pixels created with small amount of light. 

Mean diam. = 40 µm. 

Figure 21. Single pixels created with large amount of light. 

Mean diam. = 73 µm. 

Figure 20. Single pixels created with intermediate amount of 

light. Mean diam. = 60 µm. 

example of pixels created with a large amount of light 

is shown in Fig. 21, where exposure was 4.5 mJ/m 2 , 

which is well into the saturation region of the OPC. The 

pixel diameter is on the order of 73 µm. 

Figure 22 compares the experimentally measured 

pixel diameter with the predicted diameter . The predicted 

diameter is taken to be the diameter of the first 

layer of toner. The distribution of the first layer of toner 

was predicted in the same manner as in Figs. 13 and 

14. A toner particle is developed if the net electric field 

sensed by the toner at its center i.e., at a height of 4 

µm above the photoconductor for the first layer , attracts 

the toner to the photoconductor . Note that the 

predicted diameter is greater than the experimentally 

measured diameter at the low exposures. At higher 

exposures, the curves are somewhat closer together . 

We suggest that this deviation from theory at lower 

exposure pixels may be explained by the following reasoning. 

Prior to the development of a single pixel, the 

magnetic brush passes over areas of the photoconductor 

with no exposure. The bias electric field in these 

areas prevents development and drives the toner up 

into the brush. When the brush passes over the por - 

tion of the photoconductor exposed as a single pixel, 

the lack of toner at the interface of the brush and the 

exposed photoconductor reduces the amount of toner 

developed. At high exposures, the field of the latent 

image is strong enough to pull more toner down the 

brush to be developed. No attempt is made in this study 

to model this effect. Jen and Lubinsky 12 discuss the 

transient effects in development of a line. This effect 

is the source of the well known trailing edge and leading 

edge deletion of magnetic brush development. 

The experimentally observed pixels can be interpreted 

in terms of a threshold on the electric field computed at 

the center of the toner in the first layer which is 4 µm 

above the photoconductor for our experimental data. If 

at a given location on the photoconductor the field is 

greater than the threshold, we declare toner development 

at that location. If the field is less than the threshold, 

no toner is developed. Figure 23 depicts the 

prediction of single pixel diameter using two thresholds. 

The threshold at a field value of 3.21 × 10 6 V/m 

matches the data at high exposures and the threshold 

at a field value at 1.23 × 10 7 V/m matches the data at 

low exposures. 

Conclusions 

We have analytically compared the single pixel performance 

of both DMD and laser exposure processes for a 

600 dpi printer assuming an 85 µm wide Gaussian exposure 

for the laser exposure module. The salient difference 

between the two exposure processes is that the 

DMD exposure module is a static system and requires 

no rotating polygon scanner as does the laser exposure 

module. The rotating polygon scanner restricts the optical 

aperture and introduces distortions due to jitter 

and wobble. The images produced by the DMD exposure 

module had higher resolution than the laser exposure 

module. The increased resolution translates into 

smaller and sharper single pixel images on the 

photoconductor, the presence of stronger fringe fields, 

and tighter and more compact developed pixels with a 

DMD exposure module. 

We formulated a theory to explain the experimental 

observations that is an extension of Schein’ s equilibrium 

theory for solid area development to the problem 

of single pixel development. The extension is the inclusion 

of the weakening of the latent image field as the 

layers of developed toner grow further away from the 

photoconductor surface. We applied the extended equilibrium 

theory to compare the single pixels produced 

by the DMD and laser exposure modules. This is the 

first time, to our knowledge, that a theory of electrophotography 

is able to semiquan-titatively account for 

single pixel development. The model predicts larger pixels 

than observed at lower exposures. Inclusion of the 

transient effects of toner movement in the magnetic 

brush will likely have to be included to make the model 

complete. 


Mean Diameter [µm] 

Figure 23. Prediction of pixel diameter using two thresholds. 

Figure 22. Comparison of experimentally measured and analytically 

predicted pixel diameters. 

Acknowledgment. The authors would like to thank Dr. 

W. E. Nelson, TI Fellow, for his support and encouragement 

without which this article could not have been 

written. The authors also wish to thank Dr . Lawrence 

B. Schein, consultant, for his encouragement and his 

many thoughtful suggestions and comments made to the 

authors which greatly enhanced the article. 

References 

1. L. J. Hornbeck and W. E. Nelson, Bistable Deformable Mirror Device, 

Technical Digest on Spatial Light Modulators and Applications Lake 

Tahoe, NV 8: , OSA, Washington, DC, 1988, p. 107. 

2. L. J. Hornbeck, Deformable-Mirror Spatial Light Modulators, Proc. SPIE 

1150, 86 (1989). 

3. W. E. Nelson and L. J. Hornbeck, Micromechanical Spatial Light Modulator 

for Electrophotographic Printers, SPSE’s Fourth International Congress 

on Advances in Non-Impact Printing Technologies, IS&T, 

Springfield VA, 1988, p. 427. 

4. W. E. Nelson, and R. L. Bhuva, Digital Micromirror Device Imaging Bar 

for Hardcopy, Proc. SPIE 2413, 130 (1995). 

5. W. E. Nelson, Tutorial on Optical Printheads, IS&T’s Eleventh International 

Congress on Advances in Non-Impact Printing Technologies, IS&T, 

Springfield VA, 1995. 

6. W. E. Nelson, in Digest IEEE/LEOS 1996 Summer Topical Meetings, 

Optical MEMS and Their Applications IEEE, Piscataway, NJ, 1996, paper 

WC3. 

7. L. B. Schein, Photogr. Sci. Eng. 19, 255 (1975). 

8. L. B. Schein and K. J. Fowler, J. Imaging Technol. 11, 295 (1985). 

9. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York, 

1968, p. 113. 

10. L. B. Schein, Electrophotography and Development Physics, Laplacian 

Press, San Jose, 1992, p. 125. 

11. R. M. Schaffert, The Nature and Behavior of Electrostatic Images, 

Photogr. Sci. Eng. 6, 385 (1962). 

12. S. Jen and A. R. Lubinsky, Model for the Magnetic Brush Development 

of Line Images, Electrophotography, Fourth International Conference, 

IS&T, Springfield, VA, 1981, p. 239. 

13. W. D. Holland, Tutorial on Optical Printheads, IS&T’s Tenth International 

Congress on Advances in Non-Impact Printing Technologies, IS&T, 

Springfield, VA, 1994, p. 75ff. 



Particle Size Effects in Pigmented Ink Jet Inks 

Alexandra D. Bermel and D. E. Bugner 

Eastman Kokak Company, Imaging Research and Advanced Development, Rochester, New York 

Eastman Kodak Company has recently announced breatkthrough nanoparticulate ink technology which represents an improvement 

in both dye-based and pigment-based inks. These ultrafine pigmented inks exhibit average particle size approximately one 

order of magnitude smaller than other commercially available pigmented ink jet inks. In this article, we will discuss the effects 

of colorant particle size on reliability, image quality, and durability in an ink jet printing system. Comparisons will also bemade 

to conventional dye-based inks. 


Introduction 

Until recently, those involved in the business of producing 

large format ink jet prints have had to choose between 

two different types of ink sets depending on 

requirements of the intended application. For the highest 

image quality applications, dye-based inks have been 

preferred, but for signage applications where durability, 

especially lightfastness, is required, pigmented inks 

have become a very popular option. In addition to image 

quality limitations, such as inferior color gamut and 

differential gloss, pigmented inks have also exhibited 

poorer reliability than dye-base inks, presumably caused 

by large pigment particles or agglomerates clogging the 

channels and/or nozzles of the ink jet heads. 

With the launch of the new Kodak Professional Large 

Format 2000 series printer, there is no longer a need to 

choose between dyes and pigments. This value proposition 

is made possible by a breakthrough in pigmented 

ink technology, which yields pigment particle sizes that 

are approximately one-tenth the size of other manufacturers’ 

pigmented inks. In theory, inks containing these 

pigment particles with average particle sizes of 50 nm 

or less, should show improved image quality and improved 

printhead reliability (i.e., less nozzle clogging) 

when compared to inks containing significantly larger 

particles. The purpose of this study was to determine 

the effect of pigment particle size on various ink properties 

and printing performance attributes. Specifically, 

this study considered the effects of pigment particle size 

on dispersion stability, optical density, color gamut, 

gloss, and lightfastness. The effects of pigment particle 

size were evaluated for cyan, magenta, and yellow inks. 

Additional studies are underway to quantify the effect 

of pigment particle size on printhead jetting reliability. 

Materials 

In this study, cyan, magenta, and yellow pigments were 

used. The cyan is a Kodak proprietary siloxane-bridged 

aluminum phthalocyanine obtained from the Synthetic 

Chemicals Division of Eastman Kodak Company . 1 The 

magenta pigment is pigment red 122 (PR 122), a 

quinacridone-type pigment obtained from Sun Chemica l 

Company as Sunfast Magenta 122. The yellow is pigment 

yellow 74 (PY 74), a non-benzidine yellow obtained 

from Clariant Chemical Company as Hansa Brilliant Yellow 

5GX-03. Sodium N-methyl-N-oleoyl taurate (OMT) 

was obtained from Rhone-Poulenc and was purified by 

the Synthetic Chemicals Division of Kodak. Diethylene 

glycol (DEG) and glycerol were obtained from Acros 

Chemical Co. and Aldrich Chemical Co., respectively. 

Methods 

The pigments were milled using a variation of the process 

described by Czekai and Bishop. 2 The milling formulations 

for the cyan, magenta, and yellow pigments, 

respectively, were 21, 20, and 20 wt% pigment, 13, 6, 

and 2.5 wt% OMT , with the balance being de-ionized 

water. For each pigment, particle size was monitored 

as a function of milling time, and two cuts were chosen 

with differing particle size distributions. The smaller 

cut will be referred to as “small” cyan, magenta or yellow, 

and the larger cut will be referred to as “large” cyan, 

magenta or yellow. 

Inks were prepared from the different particle size 

fractions by adding the pigment concentrate with stir - 

ring to a mixture of deionized water , DEG, and glycerol. 

The final cyan, magenta, and yellow ink 

formulations are given in Table I. 

TABLE I. Cyan, Magenta, and Yellow Ink Formulations 

Color Wt% Pigment Wt% OMT Wt% DEG Wt% Glycerol 

Original manuscript received September 8, 1998 


Cyan 2.25 1.35 7.95 12.05 

Magenta 2.60 0.78 10.80 7.20 

Yellow 2.25 0.28 6.36 9.64 

320

Figure 1. Cyan inks incubated at 60°C: PSD vs. time. 

Figure 3. Yellow inks incubated at 60°C: PSD vs. time. 

TABLE II. Particle Size Distributions for the Cyan Inks of this 

Study along with Several Commercially Available Pigmented 

Cyan Inks 

Ink D 10 (nm) D 50 (nm) D 95 (nm) D 100 (nm) 

Small cyan 13 16 89 204 

Large cyan 49 122 267 486 

Commercial A 54 108 356 688 

Commercial B 57 98 178 344 

Commercial C 86 145 223 289 

TABLE III. Particle Size Distributions for the Magenta Inks of 

this Study along with Several Commercially Available Pigmented 

Magenta Inks 

Figure 2. Magenta inks incubated at 60°C: PSD vs. time. 

Pigment particle size distributions (PSDs) were measured 

on a Leeds and Northrup Microtrac-UP A 150 

ultrafine particle size analyzer. To simulate the effect 

of shipping and handling, the inks were subjected to a 

“freeze/thaw” test. This test involves holding the inks 

for 24 hr at –20 °C, then for 24 hr at 60 °C, measuring 

particle size, and repeating this cycle four times. 

Samples were examined for sediment and then shaken 

prior to sampling for the PSD measurements. Shelf-life 

of the inks was evaluated by incubating samples of inks 

at several temperatures and evaluating them for sediment, 

filterability, and PSD as a function of time. 

For image quality and lightfastness evaluations, the 

inks were loaded into a Hewlett-Packard model 51626A 

printhead and printed onto Kodak Ektajet 50 semigloss 

paper MW8, resin-coated photo paper. Optical density 

and color gamut were determined by previously disclosed 

methods. 3 Gloss was measured on a BYK Gardner 

microgloss meter acccording to ASTM D523. Lightfastness 

was evaluated by exposing targets comprising several 

printed densities ranging from D-min to D-max with 

a 50 klux Xenon source filtered with window glass. 

4 

Optical densities were measured before and after differing 

lengths of exposure, and lightfastness is expressed 

as the percent retained optical density, corrected 

for D-min. 

Results 

The particle size distributions for the large and small 

cyan, magenta, and yellow inks are given in T ables II, 

III, and IV. Also included in the tables are the PSDs of 

several commercially available pigmented inks. It 

should be noted that the commercially available cyan 


Small magenta 9 11 55 122 

Large magenta 46 100 201 344 

Commercial A 67 146 326 688 


Commercial C 188 335 749 1375 

TABLE IV. Particle Size Distributions for the Yellow Inks of this 

Study along with Several Commercially Available Pigmented 

Yellow Inks 


Small yellow 9 11 37 122 

Large yellow 33 73 173 344 

Commercial A 67 146 326 688 


Commercial C 82 148 254 409 

inks all appear to contain copper phthalocyanine as the 

cyan pigment. In the tables, the columns labeled D n 

represent 

the size of the particles at the nth percentile of 

the distribution. Thus, the column labeled D 50 

is typically 

referred to as the average or mean particle size of 

distribution, and D 100 

is the size of the largest particles 

in the distribution. Table V shows the effect of freeze/ 

thaw cycling on the particle size (D 50 

and D 95 

) of the cyan, 

magenta, and yellow inks, respectively. Figures 1, 2 and 

3 show the effect of incubating the inks at 60°C on the 

pigment particle size. 

Figure 4 compares the reflection spectra of the large 

and small inks. Table VI summarizes the effect of particle 

size on optical density and gloss, and T able VII 

compares the color gamut achieved with the small inks 

to that achieved with the large inks. In Table VIII, the 

Particle Size Effects in Pigmented Inkjet Inks Vol. 43, No. 4, July/Aug. 1999 321

TABLE V. The Effect of Four Freeze/Thaw Cycles on the Inks of 

this Study 

Ink Initial D 10 Final* D 50 Initial D 95 Final* D 95 

Large cyan 122 114 267 243 

Small cyan 16 14 89 80 

Large magenta 99 102 196 195 

Small magenta 13 12 68 60 

Large yellow 73 65 173 208 

Small yellow 11 14 37 87 

*Final: after four freeze/thaw cycles; 1 cycle = 24 hr at –20°C then 24 hr at 

+60°C 

TABLE VI. A Comparison of Optical Density and Gloss for the 

Inks of this Study 

Ink Optical density 60° gloss 

Small cyan 2.08 65 

Large cyan 1.23 72 

Small magenta 2.22 96 

Large magenta 1.76 85 

Small yellow 2.00 113 

Large yellow 1.67 93 

Figure 4. A comparison of reflection spectra for the small and 

the large cyan, magenta, and yellow pigmented inks. 

TABLE VII. A Comparison of Color Gamut for the Inks of this 

Study 

Ink combination 

Color gamut 

Large cyan, large magenta, large yellow 53,390 

Small cyan, small magenta, small yellow 70,728 

TABLE VIII. Effect of Increasing Pigment Concentration in Large 

Cyan Ink 

Pigment Size Wt% pigment Optical density Color gamut* 

Large 2.25 1.28 59,838 

Large 3.00 1.73 67,963 

Large 3.50 1.68 65,897 

Large 4.00 1.63 65,119 

Small 2.25 2.07 70,728 

*The small magenta and small yellow inks were used in combination with the 

indicated cyan inks for the gamut calculations. 

Figure 5. Reflection spectra of large cyan ink containing 3.5% 

pigment (dashed) and small cyan ink containing 2.25% pigment 

(solid). 

effects of increasing the pigment concentration in the 

large cyan ink on the optical density and the color gamut 

are presented. Figure 5 compares the reflection spectrum 

of the small cyan ink at 2.25% pigment concentration 

with the large cyan ink containing a higher pigment 

concentration. In Fig. 6, the lightfastness results for the 

yellow inks are compared. 

Discussion 

Historically, the inks developed for the first commer - 

cially successful thermal drop-on-demand ink jet printers 

employed off-the-shelf dyes as colorants. Dyes are 

colorants that are soluble in the solvent(s) or vehicle 

used to make the ink. Each molecule of the dye is sur - 

rounded by the solvent(s) and is separated from other 

dye molecules. For applications requiring weatherability, 

especially lightfastness, pigmented inks have become 

increasingly popular. In contrast to dyes, pigments are 

colorants that are essentially insoluble in the ink 

solvent(s). It is important to note that the lightfastness 

Figure 6. Yellow lightfastness data: % retained density after 

8 weeks exposure to 50 Klux high-intensity daylight. 

322 Journal of Imaging Science and Technology Bermel and Bugner

properties of pigments vary; some are extremely 

lightfast, while others fade as quickly as dyes. 

Pigmented inks are normally prepared in a two-step 

process. In the first step, a mixture of pigment and water 

is milled or otherwise mechanically sheared in the 

presence of a dispersant or stabilizer. During this step, 

the clumps of as-received pigment particles are broken 

down into their primary particles. The primary particles 

become coated with the dispersant molecules and are 

thereby stabilized against re-aggregation and/or settling. 

The pigment concentrate thus produced is then 

diluted in a second step to a working strength ink by 

addition of co-solvents, called humectants, and other 

addenda, such as surfactants or biocides. Commercially 

available pigmented inks produced by this method generally 

result in average particle sizes in the range of 

100–200 nm, with particle size distributions often extending 

to greater than 400 nm. 

By using a new type of milling process, we have been 

2 

able to produce inks with much finer particles. Comparisons 

of inks produced by this process with commercially 

available pigmented inks have revealed several 

noticeable advantages to the smaller particle size distributions. 

However, there are many other differences 

between the commercially available inks and inks produced 

by this process, such as the pigment, dispersant, 

and humectant types and levels, so that it becomes difficult 

to isolate specific particle size effects on the various 

performance attributes. By preparing two inks with 

virtually identical chemical compositions, differing only 

in their particle size distributions, we hoped to better 

understand which attributes are strongly affected by 

pigment particle size. 

Our goal was to prepare a set of cyan, magenta, and 

yellow inks with PSDs comparable to those being offered 

with the Kodak Professional 2000 series printers (“small 

inks”), and, for comparison, a set of cyan, magenta, and 

yellow inks with average particle sizes approximately 

ten times larger than the small inks (“large inks”). The 

large inks were designed to simulate other manufacturers’ 

commercially available inks. Tables II, III, and IV 

indicate that we achieved that goal. 

The first requirement of a pigmented ink is for the 

pigment dispersion to be stable (i.e., no significant 

change in PSD) over a reasonable range of temperatures 

and times. Two types of studies were carried out to 

evaluate dispersion stability; freeze/thaw cycling and 

Arrhenius testing. 5 Freeze/thaw cycling, as defined 

above, is essentially a “shipping and handling” simulation. 

The effect of freeze/thaw cycling on D 50 and D 95 for 

the cyan, magenta, and yellow inks is shown in Table V. 

The data indicate that the freeze/thaw cycling had 

essentially no effect on the particle size of the large and 

small magenta and cyan inks. In addition, the optical 

density of a D-max patch printed with each magenta 

and cyan ink, before and after freeze/thaw cycling, exhibited 

essentially no change as a result of the treatment. 

The data indicate that there was some growth in 

the yellow inks as a result of the freeze/thaw testing. 

This growth was not observed in yellow inks that were 

stored at room temperature for up to one year . The 

growth is most apparent in the larger fractions of the 

small yellow ink. 

Arrhenius testing is a tool for estimating shelf-life 

for formulations that are sensitive to time and temperature. 

The basic concept is to measure the rate of a given 

phenomenon, in this case particle size growth, at three 

or more temperatures. For well-behaved systems with 

a single mechanism of degradation, these data can be 

used to estimate an energy of activation for the process, 

which, in turn, allows one to calculate the time, or shelflife, 

at any temperature within the range tested, that 

the dispersion will remain stable. Figures 1 and 2 show 

the effect of incubating the cyan and magenta inks at 

60°C. As shown in Figs. 1 and 2, there was no significant 

particle growth in the large and small cyan and 

magenta inks over reasonable times at 60°C. Additional 

studies indicated no particle growth in the cyan and 

magenta inks for temperatures up to 80°C. Thus, as was 

the case with freeze/thaw cycling, there does not appear 

to be an effect of particle size on shelf-life for the magenta 

and cyan inks. 

In Fig. 3, the effect of incubating the yellow ink at 

60°C is presented. For both the small and large yellow 

ink, the D 50 value remains constant throughout the experiment. 

However, significant growth is observed in the 

D 95 value initially in the incubation period for both small 

and large inks, then the particles grow more slowly. 

Evaluation of the large particles using scanning electron 

microscopy indicates that large particles are not 

agglomerates of small particles, but rather they are 

plate-like in appearance. This suggests that the pigment 

is ripening with time. It appears that both large 

ink and small ink undergo the ripening phenomenon , 

which appears to be a property of this pigment type, 

and is not due to particle size effects per se. We are 

currently evaluating how to prevent ripening in this 

pigment dispersion. 

The image quality attributes that we evaluated with 

respect to particle size included optical density , gloss, 

and color gamut. Figure 4 indicates that the maximum 

optical density achieved using the large inks is significantly 

lower than the maximum optical density that can 

be achieved using the small inks. The lower densities 

result in a significant reduction in color gamut (T able 

VII). In theory, increasing the pigment concentration in 

the large ink should increase the optical density and 

improve the color gamut. This was done with the large 

cyan ink, and the results are given in T able VIII. The 

pigment concentration of the large cyan ink was increased 

from the standard level for the small cyan pigment 

of 2.25%, to 3.00%, 3.50%, and 4.00%. The data 

indicate that increasing the pigment concentration of 

the large cyan ink does increase the optical density; 

however, it is not possible to achieve as high an optical 

density or as large of a color gamut with the large pigment 

as with the small pigment. In addition, when the 

pigment concentration was increased to 4.00% severe 

imaging artifacts, i.e., banding, were observed, which 

resulted in a decrease in optical density and the resulting 

color gamut. This is attributed to the fact that the 

cartridges are not designed to fire such high concentrations 

of pigment. In Fig. 5, it is also apparent that another 

effect of increasing the pigment concentration is 

to broaden the absorption curve of the ink, which is undesirable 

and will reduce color gamut. 

As expected, 6 the gloss levels of the small magenta 

and yellow inks were higher than the gloss levels of the 

corresponding large magenta and yellow inks. However, 

the large cyan ink exhibited a slightly higher gloss value 

than the small cyan ink at an angle of 60°. This observation 

was also confirmed at 20° and 85° viewing angles 

as well. This unexpected observation is currently under 

investigation. 

One of the concerns with using pigmented inks in ink 

jet systems has been that the color gamut would not be 

acceptable. However, as demonstrated above, the use of 

very small pigment particles results in a color gamut 

Particle Size Effects in Pigmented Inkjet Inks Vol. 43, No. 4, July/Aug. 1999 323

that approaches the best color gamuts achieved with 

dye-based inks (i.e., 76,000). 

After having determined that the use of small pigment 

particles is required to achieve an acceptable color 

gamut, it was important to investigate the claims 7 that 

pigmented inks containing very small pigment particles 

would exhibit poorer lightfastness than inks containing 

larger pigment particles. To determine the effect of 

pigment size on lightfastness, step wedges of all the inks 

were printed with densities ranging from D-min to D- 

max. The large and small cyan and magenta inks were 

exposed for 16 wk to a high-intensity Xenon source filtered 

with window glass, which is estimated to be 

equivalent to > 50 yr of indoor exposure, and none of 

the inks faded significantly. Thus for the cyan and magenta, 

there appears to be no effect of pigment particle 

size on lightfastness in the system studied. 

In Fig. 6, the results of exposing the small and large 

yellow inks for 8 wk under the same conditions are presented. 

There are several things to note in this graph. 

First, the yellow pigment used is not as lightfast as either 

the magenta or the cyan tested in this study, and a 

significant level of fade was observed for both the large 

and small pigment. Second, the large pigment appears 

to fade more than the small pigment, which is in contrast 

to the claim referenced previously. Third, the degree 

of fade was a function of the starting density of the 

image. This is particularly apparent in the data for the 

small yellow, where the high-density step retained about 

70% of its initial value, while the lower density steps 

only retained 40–50% of their initial value. 

Summary 

We have initiated a study of particle size effects in pigmented 

ink jet inks. In this study, dispersion stability, 

image quality, and lightfastness were evaluated for two 

C,M,Y sets of inks: one set containing pigment particles 

with average particle size


Investigations of Nonreproducible Phenomena in Thermal Ink Jets with 

Real High-Speed Cine Photomicrography 

Christian Rembe, Stefan aus der Wiesche, Michael Beuten, and Eberhard P. Hofer 

Department of Measurement, Control and Microtechnology, University of Ulm, Ulm, Germany 

In the ink jet printer industry the stroboscopic visualization method is a standard tool for the charactarization of printheads . 

However, this method fails for thermal ink jets owing to the existence of satellite droplets which are very critical with respect to 

print quality. This is also true for the bubble formation inside the ink chamber of the printhead. Detailed studies have shown 

that the phenomenon of satellite droplets is a nonreproducible dynamic process. Real high-speed cine photomicrography forms 

the basis of a new test setup that allows the visualization of such highly dynamic nonreproducible phenomena. This new setup 

has been used to study the ejection, the free flight, and the impact of droplets of an ink jet on print media under real printi ng 

conditions. 


Original manuscript received November 12, 1998 


Introduction 

As a result of the rapidly growing field of microsystem 

technology numerous laboratory specimens of 

microactuators have been developed, mainly at universities 

and research institutes. 1 However, only a few prototypes 

of micro devices exist that lead to industrial 

mass production. High speed visualization technique has 

supported the successful introduction of thermal ink jets 

into the market. 2–5 Curiously, there are only a few other 

examples of microdevices analyzed using photomicrography. 

6,7 This fact demonstrates the importance of high 

speed photomicrography for the analysis of dynamic 

processes in microdevices. The time durations of the 

processes in thermal ink jets are extremely short, e.g., 

the bubble life time is approximately 15 µs and the droplet 

velocity is approximately 15 m/s which is comparatively 

fast considering the fact that optical 

magnifications up to 500 have to be used to generate 

high quality droplet images. This means that the microscopic 

droplet velocity of approximately 15 m/s cor - 

responds to a macroscopic projectile flying with a 

velocity of approximately 7500 m/s. The droplet visualization 

requires extremely short exposure times to avoid 

blur. Besides the short exposure times, very short 

interframe times are necessary to depict the dynamics 

of the fluidic phenomena in thermal ink jets. T o overcome 

the technical problems in the realization of high 

exposure rates the stroboscopic visualization method is 

utilized around the world for investigation of dynamic 

processes in thermal ink jets. Only a few investigations 

have been performed with real high-speed cinematography. 

5,8 The reproducibility of the process is the condition 

for the use of the stroboscopic visualization technique. 

9 The reproducible process is repeated several 

times and each measurement is observed at a different 

delayed point of time. This procedure results in a 

pseudocinematographic sequence of images. However , 

many processes in thermal ink jets are not reproducible, 

e.g., the droplet ejection at high printing frequencies, 

the development of the bubble surface during the 

bubble growth and the generation of satellite droplets 

which have an important influence on the printing quality. 

These phenomena must be observed with real cinematographic 

visualization technique. 

Experimental Equipment 

Real high-speed cine photomicrography forms the basis 

of a newly developed advanced test setup (see Fig. 1) 

that allows the visualization of such highly dynamic 

nonreproducible phenomena. The first version of the 

setup was presented at the IS&T/SPIE International 

Symposium on Electronic Imaging in 1996. 8 The main 

part of the advanced experimental setup is the commercial 

high speed camera Imacon 468 by DRS Hadland 

Ltd. This camera is connected with the standard microscope 

Axioplan from Carl Zeiss Jena GmbH. The microscope 

images the object magnified on a fiber optic plate 

in the high-speed camera. Therefore, the beam-path in 

the microscope and the beam-path in the camera are 

uncoupled. Inside the camera, relay optics channel the 

light onto a special beamsplitter consisting of eight 

lenses and an eight-sided mirror pyramid from where it 

passes to eight CCD units. The CCD sensors which are 

arranged in a circle around the beamsplitter are amplified 

by micro channel plate units mounted in front of 

the CCD camera sensors. These intensified CCD (ICCD) 

units act as high speed shutters to determine the ultra 

short exposure time of 10 ns of the camera. Our setup 

includes eight channels, therefore, a maximum number 

325

Figure 1. Schematic of experimental test setup. 

of eight frames can be taken of one single process. The 

spatial resolution of the setup is limited by 

122 . λ 

d = 

, 

NAobj 

+ NAcon 

where λ is the wavelength, NA obj is the numerical aperture 

of the objective and NA con is the numerical aper - 

ture of the condensor . Together with the pixel size of 

the ICCD sensors, the spatial resolution of the setup 

results in d ≈ 500 nm. 

A specially designed pulsed light source fitted inside 

the lamp housing of the microscope ensures optimum 

illumination. The light source has been developed in cooperation 

with the Ernst Mach Institut of the 

Fraunhofer Gesellschaft. 10 The back mirror of the lamp 

housing images the flash tube in itself to make use of 

the reflected light for illumination also. The pulse width 

of the light source which defines the maximum time 

window, can be chosen to be 100 µs or 200 µs. This light 

source produces a luminous intensity of approximately 

50 Mcd for the 100 µs pulse length and 28 Mcd for the 

200 µs pulse length. This is sufficient to achieve exposure 

times of 10 ns with the above described approach. 

The length of the light pulse is defined by the length of 

a current pulse applied at the flash tube. A special self 

designed current supply is used to generate the current 

pulse. 10 For time windows wider than 200 µs we apply 

the continuous light source XBO 75W from Carl Zeiss 

Jena GmbH. This commercial light source is sufficient 

to realize exposure times up to 10 µs using the transmitted 

light method. For the reflected light method the 

shortest possible exposure time is 50 µs. The cameramicroscope 

combination is capable of generating high 

contrast images (256 gray levels) with exposure times 

as short as 10 ns if the pulsed light source is used for 

illumination. The setup can record a sequence of eight 

(1) 

images at frequencies as high as 100 million frames per 

second. 

A second different setup based on the stroboscopic 

principle is used for the visualization of reproducible 

events. The reproducible event is repeated with the frequency 

of a video camera (25Hz) and visualized at subsequent 

points of time, respectively. The exposure time 

of 250 ns is defined by the width of the stroboscopic 

flash. The interframe time is defined by the variation 

of the time duration between the event and the flash. 

Our pseudocinematographic setup is fully automated. 10 

The advantage of the pseudocinematographic visualization 

is the unlimited number of frames of the image 

sequence. 

The following measurements have been performed 

with the HP DeskJet 500 printhead developed in the 

11,12 

middle of the 1980s by Hewlett Packard. This 

printhead consists of 50 thermal actuators where every 

heating element has an area of 60 µm × 60 µm. With a 

pulse generator, each single actuator can be controlled 

directly by its own connection because no logical circuits 

are integrated on the microdevice. These microheaters 

transform electrical power produced by 3.3 µs long 

pulses with 6.5 W amplitude into heat. The energy diffuses 

through the passivation layers into the liquid and 

heats the lowest liquid layer up to 320 °C. After an explosive 

vaporization the accelerated liquid column over 

the heating element is ejected from the nozzle of the 

thermal actuator and forms an ink droplet with several 

satellite droplets. The colorless ink Ink Jet 23-101 R 

from Franz Büttner AG was used for all measurements. 

Bubble Generation 

Our newly developed microactuator test rig has been 

used to investigate the nucleation and the bubble growth 

in a thermal ink jet printhead. The printhead has been 

prepared for these experimental studies. T o enable a 

view inside a single thermal actuator of the printhead 

326 Journal of Imaging Science and Technology Rembe et al.

3.4 

time [µs] 

Figure 2. Two visualizations of bubble formation in a thermal ink jet printhead. The time scale starts at the beginning of the 

heating pulse. The exposure time of the images is 300 ns. 

the nozzle plate was removed and replaced by a glass 

plate. No droplet can be ejected in this closed pool ar - 

rangement. From other experiments where the nucleation 

of the vapor bubble was observed through the 

nozzle the same results follow . Therefore, we present 

the photo reproductions of the closed pool arrangement 

because these images are not distorted by the ejected 

droplet that otherwise would fly in the direction of the 

camera. Photo reproductions (see Fig. 2) prove that the 

structure of the bubble is completely different for two 

separate experiments using the same heating element 

and the same heating pulse. 

The bubble surface structure is different although the 

time point of nucleation is equal for every experiment 

carried out under unchanged conditions. The 

realcinematographic visualization allows to observe the 

nonrepoducible development of the bubble surface structure 

during the bubble expansion. An exposure time of 

300 ns has been used for this visualization with an 

interframe time of 300 ns. W e have used the reflected 

light brightfield method for this visualization. The 

Hewlett Packard standard pulse of 6.5 W and a width 

of 3.3 µs was applied to generate the bubble. The experiments 

indicate that the phase boundary of liquid 

and vapor is an unstable phenomenon because it seems 

that little disturbances and thermal fluctuations lead 

to the differences in the bubble structure. 

A simple model of the expanding vapor bubble neglects 

the surface tension and describes the vaporization as 

an endothermic reaction. Then, the phase front between 

the vapor and the superheated liquid is unstable, i.e., 

the flat interface between the two phases is not stable 

against small perturbations ζ . 13 Considering small perturbations 

of velocity v’ and pressure p’ added to the 

unperturbed functions v and p, the hydrodynamic equations 

in linearized form read as 

∂v' 

1 

div v' = 0, 

+ ( v⋅∇ ) v' = − grad p'. 

∂t 

ρ 

(2) 

In Eq. 2, the indices for liquid and vapor are suppressed 

for similarity. Without loss of generality, the unperturbed 

phase front may be traveling along the z-axis 

which is perpendicular to the heating element. Assuming 

exponential functions 

ζ = ζ 0 e i(kz–ωt) (3) 

as modes for the perturbation function which is a common 

approximation in linear perturbation theory , the 

hydrodynamic of Eq. 2 lead to positive values 

µ ⎡ 1 ⎤ 

Ω= k v ⎢ 1+µ− −1 ⎥ 

1 +µ ⎣⎢ 

µ 

(4) 

⎦⎥ 

for the frequency Ω = iω , where µ = ρ l /ρ v and ρ v and ρ l 

represent the densities for vapor and liquid respectively. 

Therefore, the perturbation (Eq. 3) will grow and hence 

the flat interface between the two phases is not stable 

and the phenomenon of bubble structure generation is 

a nonreproducible event. Consequently, the necessity of 

the realcinematographic visualization method for the 

investigation of the development of the bubble structure 

versus time is required for the experiment. 

It is an interesting question if the differences of the 

bubble surface results only from statistical influences, 

e.g., thermal fluctuations. If this is the case the differences 

in the structure should disappear after averaging 

the images of a set of single experiments. W e have averaged 

the images of 99 bubble surfaces visualized at 

the same timepoint to check this assumption. The result 

can be seen in Fig. 3 for three different heating 

elements. Although the bubble surfaces are different for 

two separate experiments using the same heater the 

averaged images of the bubbles show a characteristic 

structure for each single heating element. The procedure 

has been performed by averaging the values of 

every pixel, and it results in the same characteristic 

Investigations of Nonreproducible Phenomena in Thermal Ink Jets ...Photomicrography Vol. 43, No. 4, July/Aug. 1999 327

Figure 3. Structures of bubble surfaces after the averaging of 99 images for three different heating elements. 

Figure 4. Break up of the liquid column into several satellite droplets. 

Figure 5. The ink jet of a thermal ink jet printer after the averaging of 80 images of the same time point. 

structure if the averaging is repeated with 99 new measurements. 

The visualizations were performed with the 

pseuodocinematographic setup, setting the interframe 

time to zero. The averaging was performed after the 

single frames were saved on hard disk. 

Although the surface of the vapor bubble is unstable, 

the averaged images of the bubble structure are char - 

acteristic for every heater . This leads to the assumption 

that the bubble structure is influenced by the heat 

distribution on the heating element. The roughness of 

the heater surface does not influence the nucleation behavior 

directly because the nucleation of the very thin 

liquid layer on the heater is homogeneous and can be 

described as critical phenomenon. 14,15 The nucleation 

starts if the lowest liquid layer reaches the spinodal 

limit at a temperature of approximately 320°C. Impurities 

cannot act as nuclei because the critical size of a 

bubble nucleus is approximately 1 µm. 14,15 This is more 

than the height of the vaporized liquid layer, being thinner 

than 1µm. 8 A rougher heater surface enables better 

heat transfer into the liquid and influences indirectly 

the nucleation behavior. However, the differences in the 

averaged bubble structures are caused by differences of 

the heat distribution inside the heating element. The 

procedure of the averaged images can be used for the 

characterization of the quality and the uniformity of the 

heater structure. An ideal heater should generate a 

uniform heat distribution. 

Droplet Ejection 

Using our new real cinematographic test rig we have also 

investigated satellite droplets of the liquid jet ejected from 

a thermal ink jet printhead. The break up of the liquid 

column into several satellite droplets has been visualized. 

The result is shown in Fig. 4. This visualization 

was taken with an exposure time of 250 ns and an 

interframe time of 10 µs. The first image shows the liquid 

jet 80 µs after the beginning of the heating pulse. 

Further experiments using the same thermal actuator , 

under the same conditions, result in other positions and 

velocities for the satellite droplets. Note, the velocity of 

the main droplet is the same for each experiment. 

Averaging 80 images of satellite droplets taken with 

the pseudocinematographic setup shows a gray line of 

dots (see Fig. 5). The single images used in the averag - 


Figure 6. Integration of the prepared ink jet printer in the new test rig. 

ing procedure were taken 110 µs after the beginning of 

the heating pulse with an exposure time of 250 ns. This 

experiment clearly demonstrates the nonreproducibility 

of the break up of the liquid jet. The reason is that small 

disturbances 16 r(t,z,ϕ) = R 0 + ε 0 e σt e i(kz+mϕ) (5) 

and small physical differences in the experiment lead to 

the instability of the jet. In Eq. 5, z denotes the direction 

of the cylindrical liquid column, ϕ the angle of the cylindrical 

coordinates, r(t,z,ϕ) the radius of the cylindrical 

liquid column, R 0 is the constant radius of the liquid column 

without disturbances, and ε 0 the amplitude of the 

disturbances. The wave number k of the disturbances in 

z-direction is a real variable and m is an integer. A cylindrical 

liquid column is unstable if any solution of the disturbances 

r(t,z,ϕ) with σ > 0 for any values for k and m 

exist. The formula for σ for an incompressible liquid jet 

was derived first by Lord Rayleigh 17 

σ 

2 

m 

T kR I' m( kR ) 2 

= 1−m 

−( kR0 ) 2 (6) 

R ρ I ( kR ) 

0 0 

0 2 m 0 

( ) 

with T the surface tension, ρ the density, I m (x) the modified 

Bessel functions of the first kind of order m for a 

purely imaginary argument, and I′ m (x) = dI′ m (x)/dx the 

derivative of I m (x) respect to the argument x. From Eq. 

6 it is apparent that 

2 

σ m < 0 for all m ≠ 0 and kR0 

> 0 

σ < 0 for x > 1 and σ> 0 for 0 < x < 1. 

0 2 0 2 

Therefore, no solution of the disturbances without a 

positive solution for σ exist for axisymmetric deformations. 

In other words, the liquid jet is unstable. From 

the instability of the jet follows the nonreproducibilty 

of the event, because the instability leads to a statistical 

distribution of the positions and the velocities of the 

satellite droplets after the break up. Only the position 

of the main droplet, and for some actuators, the position 

of the last satellite droplet are reproducible. As a 

result, the formation of the satellite droplets and their 

impact on the paper has to be investigated with real 

cinematographic visualization. 

(7) 

Visualization of the Real Printing Process 

Satellite droplets can influence the print quality negatively 

if the impact of the satellite droplets is outside a 

tolerable neighborhood of the main droplet. In further 

experiments, the ejection, the free flight, and the impact 

of droplets of an ink jet on print media under real 

printing conditions have been studied. Such experiments 

are necessary for the understanding of differences in 

the quality of different printers. The knowledge of the 

physics during the printing process can be used for the 

improvement of new printer generations. 

Accounting for the nonreproducibility of the break up 

of the ink jet, the experiment has to be performed with 

realcinematographic visualization. Because the droplet 

is ejected from the moving printhead with a defined 

velocity during the printing process, the printhead has 

to be moved with the same velocity in the experiment. A 

Hewlett Packard Desk Jet 500 printer has been prepared 

for the experiment to guarantee realistic conditions 

during the experiment. We have integrated the printer 

in our new test rig to visualize the printing process, with 

real high-speed cine photomicrography . The ink jet 

printhead is moved with the original drive under the 

objective of the microscope. This feature is important 

to ensure that the velocity of the printhead is realistic. 

All unnecessary parts of the printer and the 

printhead have been removed to avoid shadows in the 

beam path and to enable the use of the brightfield transmitted 

light method for ligh ting. Although the 

printhead was fixed back to front on the printhead 

carrier there was not enough room for the condenser 

of the microscope. The light intensity is sufficient to 

achieve a exposure time of 600 ns without condenser . 

The print medium is attached opposite to the printhead. 

Normal copying paper was chosen as print medium. The 

whole arrangement is shown in Fig. 6. 

It is interesting that no specification about the real 

distance between paper and printhead can be found in 

the literature. The aim of the experiment is not the exact 

measurement of the printing process in the HP Desk 

Jet 500 printer but the demonstration of the potential of 

real high speed cine photomicrography for the characterization 

of ink jet printers. Therefore, the distance between 

printhead and paper was adjusted visually. When 

the printhead reaches the position under the objective a 

light barrier synchronizes the droplet ejection, the light 

pulse, and the recordings of the camera. The light barrier 

is fixed on the rail of the printhead to measure the 


Figure 7. Flight of a droplet ejected from the moving ink jet printhead and its impact on paper. 

time point when the printhead reaches a defined position. 

The light barrier has a 5 V output if there is no 

interruption is in the light barrier. The output is zero if 

the slide of the printhead moves between the luminescent 

diode and the phototransistor of the light barrier. 

The signal of the light barrier with respect to time and 

the length of the slide, 2.2 mm has been used to determine 

the velocity of the printhead as 0.68 m/s. The 

printhead generates a trigger signal if it meets the light 

barrier to synchronize the high speed camera. The delay 

generator in the camera synchronizes the shootings, 

the flash, and the droplet ejection. 

The prepared printer is attached to a table adjustable 

in height to enable the adjustment of the sharpness of 

the image of the ejected droplet. After this adjustment, 

the delay between the trigger signal of the light barrier 

and the exposures are varied. The droplet is ejected 

under the objective of the microscope if the droplet is 

imaged in the middle of the camera sensor . Then, the 

arrangement is completely adjusted and the visualization 

of the printing process under real conditions can be 

performed. Figure 7 shows the flight of a droplet ejected 

from the moving ink jet printhead and its impact on the 

print medium. An exposure time of 600 ns and an 

interframe time of 20 µs were used for this visualization. 

The printhead moves from right to left. The visualization 

shows that the main droplet does not penetrate into the 

paper immediately. Because of the inertial impulse the 

ink jet is also tilted towards the direction of the moving 

printhead. Therefore, the impact of the satellite droplets 

is outside the neighborhood of the main droplet. Because 

of the penetration of the ink into the paper this does 

not influence the print quality negatively . The dot of 

the main droplet is bigger than the sprinkled area on 

the paper which can be seen on the image sequence in 

Fig. 7. 

Conclusions 

In this article, the potential of the realcinematographic 

visualization method for investigation and character - 

ization of thermal ink jet printers is demonstrated. Our 

new test rig is described and the realcinematographic 

visualization of the bubble generation, the break up of 

the liquid jet and the impact of the jet on a print medium 

is presented for the first time. This article shows 

that unstable phenomena lead to nonreproducible 

events. Nonreproducible events have to be investigated 

with real high-speed cinematograhy . The aim of this 

article is the demonstration of the necessity of the real 

high-speed cine photomicrography for the characterization 

of nonreproducible processes in microdevices. Future 

research is directed towards studying the 

phenomena in micro fluidic devices, e.g., the flow behavior 

inside a thermal ink jet printhead. 

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DeskJet printer chassis and mechanism design, Hewlett Packard 

Journal, 67 (October 1988). 

13. L. D. Landau and E. M. Lifshitz, Hydrodynamics, Pergamon, New 

York, 1982. 

14. S. aus der Wiesche, C. Rembe and E. P. Hofer, Boiling of superheated 

liquids near the spinodal: 1 general theory, Heat and Mass 

Transfer, 35 (1999). 

15. S. aus der Wiesche, C. Rembe and E. P. Hofer, Boiling of superheated 

liquids near the spinodal: 2 application, Heat and Mass Transfer, 

35, 25 (1999). 

16. S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Dover 

Publications Inc., 1981. 

17. Lord Rayleigh, On the instability of jets, Proc. Lond. Math. Soc. 10, 

pp. 4–18, (1879). 



New Thermal Ink Jet Printhead with Improved Energy Efficiency 

Using Silicon Reactive Ion Etching 

Masahiko Fujii, ▲ Toshinobu Hamazaki* and Kenji Ikeda 

New Marking Development Department, Fuji Xerox Co., Ltd., Kanagawa-pref., Japan 

*Marking Device Development Department, Fuji Xerox Co., Ltd., Kanagawa-pref., Japan 

In thermal ink jet (TIJ) printhead design, in order to satisfy various market demands, it is important to consider how effectively 

the printhead transfers input energy to ejected drop performance. First, we defined energy efficiency as a ratio of ejected ink 

drop energy (the sum of kinetic and surface energy) to consuming electric energy in the heater of thermal ink jet printhead. We 

examined a method for increasing the energy efficiency in terms of printhead design, and we found that it relates with an 

inertance ratio of the rear fluid pass to the front. We proposed a new side shooter thermal ink jet printhead for improvement of 

the inertance ratio, and we tried to fabricate channels on silicon wafers by a reactive ion etching (RIE). The printhead achieved 

higher energy efficiency when compared with the conventional design and it has been proved that high energy efficiency enables 

low consuming energy or high drop energy, and other good characteristics have been also obtained by the printhead. 


Introduction 

Since personal computers have been spread widely and 

Internet environments have been prepared rapidly , 

people can get various fine images that they want from 

all over the world. In addition, because digital cameras 

have become cheaper and the pixel number of CCD has 

increased (already exceeding ‘Mega-Pixel’), we can see 

high quality images on our computers at home easily . 

As a natural desire, we want to print these images on 

paper and see them in our hands. 

Recently, most office documents have been colored to 

appeal to readers. So, the demand for producing many 

high quality color documents at high speeds has been 

increased today. 

In these situations, small, inexpensive, high image 

quality, high speed and highly reliable color printers 

have become more desirable. We believe, and it is recognized 

in the market, that thermal ink jet (TIJ) printing 

has a high potential to satisfy these demands in both 

home and office environments because ink drop ejection 

and the printing mechanism in thermal ink jet are very 

simple. 

In order to respond to the above market demands, it is 

important to consider how little energy TIJ printhead 

consumes and the high performance it offers. Namely , 

we must consider such a printhead design that can effectively 

transfer input electric energy to a desired drop 

performance. We call this transformation efficiency energy 

efficiency of TIJ printhead. If we can get high efficiency, 

we will be able to achieve low energy consumption 

Original manuscript received July 10, 1998 

▲ IS&T Member 

©1999, IS&T—The Society for Imaging Science and Technology 

to get a desired performance (drop volume), or get a high 

performance (drop velocity) at the same consuming energy. 

The former case makes the printer size smaller and 

decreases its cost. The latter can widen the variety of 

inks and decrease maintenance work load, and consequently 

achieve high image quality and high reliability. 

Energy Loss in Thermal Ink Jet and Definition of 

Energy Efficiency 

Figure 1 shows the schematic diagram of a typical side 

shooter TIJ printhead. After an electric pulse of several 

microseconds is applied to the heater, the temperature 

on the heater surface increases rapidly and reaches to 

a superheat temperature. Homogeneous nucleation occurs, 

and a vapor bubble is generated with high pressure. 

The high pressure bubble pushes ink both forward 

(to the nozzle) and backward (to the reservoir). The 

pushed ink overcomes surface tension of the meniscus 

and forms an ink drop. 

In this process, when electric energy supplied from the 

power source is changed to ink drop energy , a great 

amount of energy loss occurs. The energy losses can be 

classified by physical phenomena or locations where they 

occur: 

1. Electric loss in electrode and driver (IR drop): 

electric energy changes only partially into heat due 

to the resistance of electrode and driver. 

2. Thermal transfer around the heater: 

heat generated at the heater layer is transferred not 

only to the upper , but also to the lower and side 

directions. 

3. Bubble generation: 

not all of the energy transferred to the interface of 

heater surface and ink contributes to bubble 

generations and growth. 

332

Nozzle 

Ink Drop 

(5) 

Channel Substrate 

Front pass 

Rear pass 

(4) 

Bubble (3) 

Ink flow 

Inlet 

Reservoir 

Electrode2 

Ink Meniscus 

t p 

Electric Pulse 

(2) 

Heater 

Electrode1 

Heater Substrate 

Driver 

Id 

R (1) 

R 

h R 3 

1 

V d 

R 2 Electrode2 

Power Source 

Figure 1. Schematic diagram of a typical side shooter TIJ 

printhead. The number desginates the order in which phenomena 

occur or the locations where energy losses occur in the drop 

ejection process. 

4. Pressure propagation (distribution) in the fluid pass: 

bubble pressure pushes ink both to the nozzle and to 

the reservoir. 

5. Surface tension at the nozzle: 

surface tension resists ink movement and drop 

formation. 

In the above classification, the 4th term, pressure 

propagation (distribution), depends on the fluid pass design. 

IR drop and thermal transfer are of course important 

subjects in printhead design, but they will be 

argued on another occasion. Herein, we discuss the improvement 

of pressure propagation by modification of 

fluid pass design. 

Transducer effectiveness as a relation of ejected drop 

volume and transducer displacement was investigated 

and the effectiveness was compared between Piezo and 

TIJ printheads. 1 

First, we define energy efficiency (EF) in thermal ink 

jet printhead as a ratio of drop energy E d to consuming 

energy consumed by the heater E h . 2 

Ed 

EF = (1) 

E 

Energy consumed by the heater E h is estimated as 

h 

2 

Eh = Id ⋅Rh⋅tp 

where I d , R h and t p are electric current, heater resistance 

and pulse width, respectively . Defining this energy 

as Eq. 2 can exclude the effect of IR drop in the 

electrode and driver in this discussion. Drop energy is 

the sum of drop kinetic energy E k and surface energy E s 

given by 3 1 2 

Ek = ⋅md ⋅vd 

(3) 

2 

E 

s 

2 

d 

(2) 

= 4⋅π⋅r 

⋅σ (4) 

where m d , v d , r d are the mass of ejected ink drop, initial 

velocity, and drop radius respectively and σ is an ink 

surface tension. Drop radius r d is calculated as the radius 

of a complete sphere based on the measured mass, 

including satellite drops. 

Figure 2. Fuji Xerox conventional TIJ printhead (Slit Bypass 

[SB] design). Printhead has channels fabricated by ODE, 

heater pit and slit bypass characteristically. Nozzle shape is 

an isosceles triangle with 54.7° base angle. (Roman numerals 

indicate divided pass for calculation of inertance.) 

Comparison of Energy Efficiency and Inertance 

Ratio in Various TIJ Printheads 

Considering the ink motion by bubble growth in the fluid 

pass, we examined the relationship of ink mobility 

(namely, the reverse of pressure loss) with fluid pass 

structure. Pressure loss ∆p is described as 4 

∆p = L⋅ dq + Rq ⋅ (5) 

dt 

where L and R are inertance and resistance respectively, 

and q is the flow rate of ink. As we can see from this equation, 

in a rapid motion like a bubble growth (≤10 µs), the 

inertance is dominant in ink mobility. 

We considered that the ratio of heater rear inertance 

L r to heater front inertance L f relates to the efficiency of 

bubble pressure propagation toward the nozzle. We defined 

the inertance ratio K as follows, 

Lr 

K = 

L + L 

Suffixes f and r mean the front and rear pass (refer to 

Fig. 1). We calculated the inertance of each pass as 

f 

r 

(6) 

li 

L = ρ ⋅∑ 

s 

(7) 

where ρ is ink density, l and s are fluid pass length and 

cross-sectional area. 

Figure 2 shows the schematic diagram of our conventional 

side shooter thermal ink jet printhead called as 

Slit Bypass (SB) design. 5 Channel (fluid pass) is formed 

by ODE (Orientation Dependent Etching) on a silicon 

i 

New Thermal Ink Jet Printhead with Improved Energy Efficiency ...Etching Vol. 43, No. 4, July/Aug. 1999 333

channel wafer (C/W), hence the cross sectional shape of 

the channel is an isosceles triangle with 54.7 ° base 

angle, and it is difficult to change the width in the middle 

of channel. Reservoir and inlet are also formed by ODE. 

A polyimide pattern on the silicon heater wafer (H/W) 

forms the heater pit and slit bypass. The heater pit prevents 

air ingestion from the nozzle 6 and the slit bypass 

introduces ink from the reservoir to the channel. The 

heater is located on the pit bottom. Poly-silicon with 

reduced resistivity by doping is used for the heater to 

heat ink. High doped polysilicon exists between the 

heater and Aluminum electrode. Tantalum covers over 

the heater polysilicon to prevent mechanical damages 

due to bubble cavitations. (not shown in Fig. 2). 

We analyzed our conventional and competitive TIJ 

printheads (available in the market) having various designs 

and different nozzle pitches (resolutions), and we 

calculated their inertance ratio K according to Eqs. 6 

and 7. In the calculation of inertance for our SB design, 

we divided fluid pass into six sections symbolized by 

roman numerals in Fig. 2, and calculated L f and L r by 

adding each sections’ inertance. In the case of cross sectional 

area changes in a section, e.g., section V, average 

area is used for Eq. 7. As for the roof shooter design, it 

is difficult to divide the fluid pass into the front or rear 

part. We defined that the area above the heater is the 

front part and the area from the heater to the reservoir 

is the rear part. 

We also evaluated drop volume and drop velocity performances 

with our dye-based ink and calculated the 

energy efficiency under standard drive conditions (voltage 

and pulse width). 

Figure 3 shows the relationship of inertance ratio K 

with energy efficiency between Fuji Xerox and competitive 

TIJ printheads. When we compare them in terms 

of the energy efficiency, it is necessary to note that the 

energy loss in the thermal transfer process depends on 

heater layer structure. We neglected it here. 

The physical properties of dye-based ink used in evaluations 

are also shown in Fig. 3. 

Inertance ratio K has a good correlation with energy 

efficiency among various designs of printheads. In the 

experiments, Roof Shooter B showed high efficiency because 

of high inertance ratio. As usual, the roof shooter 

is obliged to have a 2D alignment of heaters and nozzles, 

and the space from heater to nozzle can become large. 

Therefore the roof shooter can have a high inertance 

ratio. Thus, the printhead size becomes larger in a roof 

shooter. 

Latency in Ink Jet Printers 

High drop in kinetic energy is necessary to keep high 

reliability in ink jet printers for the following reason. 

When drop ejection is halted, ink viscosity near the 

nozzle becomes higher because of evaporation of ink 

components with low boiling point. 7 Therefore, the first 

ejected drop after idling may be misdirected or decelerated 

by viscous or solidified ink. 

Figure 4 shows how the transit time depends on the 

idle time. Transit time is the time required for an ejected 

drop to fly from the nozzle to a 1.5 mm distant position, 

which is measured by an optical drop sensor. 8 In the worst 

case (the idle time is too long), no drop is ejected. 

We evaluated the image quality insofar as it is affected 

by the idle time, and defined latency as the idle time 

generating no image defect. No image defect in our experiment 

infers that dot displacement from an ideal position 

is under 30 µm on paper at a 1.5 mm distance 

from the nozzle. 

Energy Efficiency [EF] (× 10 -4 ) 

Fuji Xerox conventional side shooter [400/600/800dpi] 

Competitor A (side shooter) [360dpi] 

Competitor B (roof shooter) [300dpi] 

Figure 3. Inertance ratio versus efficiency. Inertance ratio has 

a high correlation with energy efficiency. (Small triangle symbol 

designates Trench printhead data, explained later in this 

paper.) 

1400 

1200 

1000 

800 

600 

400 

200 

0 

26°C 

65%RH 

Inertance Ration [K] 

Carbon Ink 

1 10 

100 

Idle Time (s) 

Dye Ink 

Figure 4. Transit time depends on idle time and ink. Carbon 

black ink is worse in latency than dye-based ink. 

Figure 5 shows photographs of printed dots on paper. 

In Photo (a), the first dots’ displacement is under 30 µm 

and the image quality is judged as fair; the displacement 

in Photo (b) is just over 30 µm and defines this 

idle time as latency. 

If we can get a long latency, it is possible to extend 

the maintenance interval, namely by decreasing the 

amount of ink consumed by dummy jetting and 

vacuuming to exhaust viscous ink, thereby enhancing 

productivity. 

334 Journal of Imaging Science and Technology Fujii et al.

TABLE I. Physical Properties of Typical Materials for Channel 

Substrate 

Material Thermal Conductivity Coefficient of Thermal 

(W • m –1 • K –1 ) Expansion (10 –5 • K –1 ) 

Silicon 168 0.415 

Polysulfone 0.15 5.5 

Polyethersulfone 0.26 5.5 

25 

20 

DJ850C 

Black Ink 

Figure 5. Image defects and latency criteria in terms of dot 

displacement. First dots in Photo (b) are 30 µm from an indeal 

position, and the idle time in this case is defined as latency. 

According to our experiments, latency also depends on 

ink components (formulations). Text quality with car - 

bon black ink is superior to that with dye-based ink. 

Our experiments, however, showed that carbon black 

ink is worse in latency than dye based ink. We also measured 

latency and performance with carbon black ink 

(HP Desk Jet 850C black ink). 

Figure 6 shows the relationship between measured 

latency and drop kinetic energy with 850C black ink 

(rectangular symbols with solid line). In this experiment, 

we obtained various kinetic energies by changing the 

drive conditions (voltage, pulse width) or using differ - 

ent designed printheads. W e can see from Fig. 6 that 

when the drop kinetic energy becomes higher , latency, 

one of printer reliability, becomes longer. In most cases, 

drop volume is fixed by image quality (dot size), so high 

kinetic energy means high velocity. High drop velocity 

is necessary to obtain a long latency. 

New TIJ Printhead with Channels Formed by Silicon 

Reactive Ion Etching (RIE) 

In our conventional design shown in Fig. 2, desired drop 

volume almost fixes the nozzle width and even the channel 

width, because the channel is shaped by ODE. If we 

want to increase the inertance ratio to improve the energy 

efficiency based on Fig. 3, the length of the rear 

channel will be long. But in this case, the resistance of 

the rear channel will be also increased, and it deteriorates 

the efficiency of the ink refill, which occurs over a 

relatively long time (100 to 200 µs). To obtain higher 

drop velocity, the nozzle width is reduced further with 

larger heater size, and in this case, to keep a high 

inertance ratio, the rear resistance will be larger and 

the energy consumed will be increased further because 

of large heater size. 

If we can narrow only the nozzle width that dominates 

the drop volume and velocity, and expand pass width, 

we will be able to achieve a high inertance ratio with a 

low resistance. To realize this design concept, it is important 

to enlarge the difference between nozzle and 

channel width. 

One of the methods to narrow the nozzle is plastic injection 

molding compiled with laser ablation. By this method, 

however, it is difficult to make a large difference in width 

due to fabrication problems. Another problem is that the 

15 

10 

5 

26°C 

65%RH 

0 

0 1 2 3 4 5 6 

Drop Kinetic Energy (nJ) 

Figure 6. Latency dependence on drop kinetic energy. High kinetic 

energy can extend Latency.(Triangle symbols with dotted 

line will be explained later in this paper.) 

difference in the thermal expansion coefficients is large 

between plastic and silicon materials comprising the 

heater substrate. Thermal conductivity is also low, which 

affects the thermal accumulation of the printhead. 

Table I shows the physical properties (the coefficient of 

thermal expansion and thermal conductivity) of silicon 

and typical materials used in this plastic fabrication 

method. This method is unsuitable to increase the nozzle 

number with a long printhead due to the gap or stress 

being large between the channel and the heater substrate. 

Considering the above problems, namely , the difference 

between the nozzle and other pass width, thermal 

expansion, and thermal conductivity, we focused on silicon 

reactive ion etching (RIE) 9 as a channel fabrication 

method. We tried to fabricate a new printhead using this 

method to achieve better energy efficiency than our conventional 

printhead. 

Next, we explain the channel fabrication process in 

this new printhead. Inlet and reservoir are formed by 

ODE first, in the same manner as our conventional 

printhead. ODE has a high etching rate in comparison 

with RIE for silicon, hence it is useful to form a deep 

hole like a reservoir . Next, channels (fluid pass) are 

formed by RIE and a rectangular shaped nozzle is 

formed by dicing an aligned and bonded channel and 

heater wafer. 10 

Figure 7 shows the schematic diagram of a new 

printhead with channels fabricated by silicon RIE. 


Figure 8. SEM photograph of channels formed by RIE (without 

channel pit). Channels are aligned in 800 dpi. 

50 

45 

SB Printhead 

Figure 7. Fuji Xerox new Thermal Ink Jet Printhead (Trench 

Design). Channels are fabricated by RIE. Channel pit can be 

obtained by additional ODE process. (Roman numerals in top 

view means divided pass for calculation of inertance. 

40 

35 

Trench Printhead 

Channel height is fixed by etching time and rate, and 

the etching rate depends on ion acceleration energy . 

Etching direction in RIE is also anisotropic because of 

ion rectilinearity. We can obtain an accurate rectangular 

shape and size of channel over the printhead by controlling 

the etching time and energy. 

We squeezed the channel around the nozzle and at the 

entrance to the channel from the reservoir. We call this type 

of printhead the T rench design. In this design, the front 

squeezed length is important. If the length becomes longer, 

the front inertance will be larger. However, if it is too short, 

the meniscus after jetting will become extended and the 

capillary force will not act sufficiently in the refill process. 

If we add one more ODE process, we can obtain a channel 

pit as shown in Fig. 7. In this design, the channel 

size is extended, so the resistance of channel will be decreased 

further. 11 Also in the calculation of inertance for 

the Trench design, we divided fluid pass into twelve parts 

as shown in Fig. 7. L f is calculated by addition of each 

inertance from the part I to V. L r is from VII to XII. 

Figure 8 shows on SEM photograph of the channels 

formed by RIE from one of the new printhead designs. 

Nozzle pitch is about 32 µm, which corresponds to 800 

dpi. From this photo, it can be realized that channels are 

formed accurately even at a high resolution of 800 dpi. 

We believe this method can be applied to over 1600 dpi. 

We designed some printheads with nozzle pitches corresponding 

to 400 dpi and 800 dpi (with and without a 

channel pit), and we evaluated their performances using 

our dye-based ink and DJ850C black ink. 

Performances of a Newly Designed Printhead 

The performance of a new T rench design printhead is 

given in Table II. The performance of our conventional 

design (Slit Bypass) is also given in the same table for 

comparision. In both 400 dpi and 800 dpi/printheads, 

30 

25 

50% Coverage Image 

Drive Frequency : 5.4kHz 

20 

0 1 2 3 4 5 

Time (minute) 

Figure 9. Printhead temperature increase due to printing high 

coverage images. Both printhead have the same heat sink size. 

the energy efficiency of the new design (T rench) was 

more than 2 times greater, compared with the conventional 

design. 

The relationship between the intertance ratio and energy 

efficiency in the new T rench printhead also 

comforms to the trend in Fig. 3. (Small triangle symbols 

in Fig. 3 mean trench printheads’ data.) One of the 

trench printheads is a match for roof shooter. 

In the 400 dpi printhead design, we intended to decrease 

the consuming energy especially, so the drop energy 

was increased only 1.4 times than the conventional 

design, whereas the consuming energy was decreased 

to 67%. In the 800 dpi design, we aimed to achieve high 

drop velocity because latency problem becomes more serious 

at high resolution. As shown in Table II, the kinetic 

energy with 850C ink increased 2.8 to 3.4 times 

and latency was extended 5 to 6 times. 

High energy efficiency enables low consumption energy 

or high drop energy depending on the balance of 

nozzle and heater size in the printhead design. 

Figure 9 shows the increase of printhead temperature 

due to printing of high coverage images. The conventional 


TABLE II. Comparison of Performances between New Trench and Conventional SB Design 

Slit Bypass Trench 

(Conventional) (New) 

Channel Pit - - A A B 

Nozzle Pitch (dpi) 400 800 400 800 800 

Inertance Ratio [K] 0.36 0.28 0.55 0.50 0.57 

Heater Energy [E h ] (µJ) 11.2 5.4 7.5 4.8 4.5 

Drop Volume [m d ] (ng) 37.8 10.6 43.4 14.0 12.3 

Drop Velocity [v d ] (m/s) 8.9 8.4 9.8 13.0 16.0 

Drop Kinetic Energy [E d ] (nJ) 1.50 0.37 2.08 1.18 1.57 

Surface Energy [E s ] (nJ) 0.19 0.08 0.21 0.10 0.09 

Energy Efficiency [EF] (×10 -4 ) 1.51 0.84 3.05 2.68 3.70 

Drop Volume [m d ] (ng) 44.2 10.3 50.5 19.1 14.3 

Drop Velocity [v d ] (m/s) 10.8 11.5 11.0 14.2 18.0 

Drop Kinetic Energy [E d ] (nJ) 2.58 0.68 3.05 1.92 2.32 

Latency (s) 10 2 20 10 12 

Channel Pit A: No Channel Pit 

B: Channel Pit Exists 

50 

45 

40 

Trench Printhead 

Peak 

Peak 

tube. Temperature increase due to printing generates 

bubbles from ink and enlarges their size. Enlarged 

bubbles prevent ink flow, so vacuuming is necessary periodically. 

Mobility of a bubble under vacuuming depends 

on its size and ink flow velocity, namely flow rate. 

According to Eq. 8, under the constant vacuum pressure 

P V , steady flow rate Q becomes larger as the total 

resistance of ink pass R T becomes smaller. 

35 

SB Printhead 

Q 

P V 

= 

R 

(8) 

T 

30 

25 

0 2 4 68 10 8 10 12 14 12 14 16 

Drive Frequency (kHz) 

Figure 10. Drop volume dependence on drive frequency. Peak of 

Trench is 3kHz higher than that of SB. 

and new printheads have heat sinks of the same size. 

Heat accumulation was improved by the T rench 

printhead. 

Latency data of new designed printheads are shown 

in Fig. 6 again. (Small triangle symbols with dotted line). 

It appears that a different trend from the conventional 

exists. We believe that the reason why the Latency of 

Trench printhead is better than the conventional trend 

is the effect of the squeezed part near the nozzle for 

evaporation. 

Figure 10 shows the change of drop volume as a function 

of drive frequency in 400 dpi printheads. Peak of 

curve corresponds almost to the inverse of the refill time. 

Peak by the Trench design is about 9kHz—3kHz higher 

than that by the conventional printhead because of low 

flow resistance. It enables higher printing frequency in 

printer. The oscillation of the trench volume curve is 

larger than that of the SB for low resistance as well. 

Low flow resistance is good not only for refill speed 

but also bubble management in the reservoir and ink 

We can reduce R T by adopting the T rench printhead 

with small channel resistance R ch because R T is described 

as 

R 

T 

Rch 

⋅ RD 

= 

N ⋅ R + N ⋅R 

ch D D ch 

+ Rr 

+ Rpipe 

(9) 

where R ch , R d , R r and R pipe are the resistance of channel, 

dummy channel not being used for printing, reservoir 

and pipe from the ink tank to the printhead. N ch and N d 

are the number of channels and dummy channels. 

Figure 11 shows the distribution of calculated flow 

velocity in printheads for SB and T rench design with 

400 dpi nozzle pitch. In this figure, the flow velocity is 

slower as color gets darker . It is clear that the dead 

water area (low velocity area) in the trench printhead 

is smaller than the SB printhead. W e expect that the 

interval of vacuuming will be longer due to an increase 

in time for bubble growth to close channels. 

Conclusion 

We found that improvement of inertance ratio of the 

rear to the front is effective to increase the energy efficiency. 

Based on this point and other fabrication problems, 

we proposed a new thermal ink jet printhead with 

channels fabricated by silicon reactive ion etching. The 

new printhead showed high energy efficiency as we expected. 

It has been demonstrated that this high efficiency 

enables low energy consumption or high drop 

energy. The new printhead also showed other good 

characteristics (temperature accumulation, ink refill 


Figure 11. Calculated ink flow velocity distribution in reservoir and channels. Dark tones indicate slow velocity area. Dead 

water area in Trench is smaller than that in SB. Velocity is high on both sides for dummy channels with reduced resistance. 

time and bubble management). The type of printhead 

that we proposed herein has advantages for high quality 

and high speed printing which satisfies the mar - 

ket demands. 

Acknowledgment. We would like to thank M. Murata 

and R. Nayve for suggestions on printhead design from 

the standpoint of RIE process and channel fabrication. 

We are also thankful to A. Tohma for assistance with 

performance evaluations. 

References 

1. S. F. Pond, Drop-On-Demand Ink Jet Transducer Effectiveness, IS&T’s 

Tenth International Congress on Advances in Non-Impact Printing 

Technologies, IS&T, Springfield, VA, 1994, p. 414. 

2. B. Hockwind, Design of Micromechanical Bubble-Jet Devices, IS&T’s 

9th International Congress on Advances in Non-Impact Printing Technologies, 

1993, IS&T, Springfield, VA, p. 237. 

3. S. Hirata, IEICE TRANS. ELECTRON E80-C, 214 (1997). 

4. N. Deshapande, J. Imaging Sci. Technol. 40, 396, (1996). 

5. M. Fujii, Japan Patent H03-348525 (1991). 

6. P. A. Torpey, Prevention of Air Ingestion in a Thermal Ink Jet Device, 

IS&T’s 4th International Congress on Advances in Non- 

Impact Printing Technologies, 1988, IS&T, Springfield, VA, p. 275 . 

7. P. A. Torpey, Evaporation of A Two-Component Ink from The Nozzles 

of A Thermal Ink Jet Printhead, IS&T’s 6th International Congress on 

Advances in Non-Impact Printing Technologies, 1990, IS&T, Springfield, 

VA, p. 453. 

8. M. Fujii, Optical Drop Sensor of Continuos Ink Jet Printer, Proc. of 

the Nineteenth Joint Conference on Image Technology, 1988, Tokyo, 

Japan, p. 83 (In Japanese). 

9. J. K. Bhaerdwaj, SPIE 2639, 224 (1995). 

10. R. Nayve and M. Fujii, Japan Patent H09-341658 (1997). 

11. M. Murata and M. Fujii, Japan Patent H09-341659 (1997). 



Thermal Dye Transfer Printing with Chelate Compounds 

Takao Abe, Shigeru Mano, Yorihiro Yamaya, and Atsushi Tomotake 

Konica Corporation, Central Research Laboratory, Tokyo, Japan 

With its excellent color and tone reproduction, thermal dye transfer printing produces continuous-tone color images that rival silver 

halide photography. However, conventional thermal dye transfer images fade easily when subjected to light or heat. T o solve this 

problem, we have studied a chelate compound system and have found that certain sets of azo dyes and transition metal cationproviding 

compounds produce dye-metal complexes, or “chelate compounds”, that provide exceptionally high image stability. 


Original manuscript received October 15, 1998 


Introduction 

For many years, the only practical method of producing 

high-quality continuous-tone color images was silver halide 

photography. But today, several new technologies 

offer images so beautiful that they are often mistaken 

for color photographs. Thermal dye transfer printing, 

with its excellent color and tone reproduction, is one 

such technology. 

Unfortunately, thermal dye transfer prints typically 

suffer from poor image stability when exposed to visible 

or ultraviolet light or if subjected to heat. Many 

approaches have been taken to solve this serious problem, 

including the addition of a protective layer over 

the dye receiver sheet, 1 addition of UV-light-absorbing 

agents and antioxidizing agents to the dye receiving 

layer, 2–4 addition of dye adsorbents to the dye receiving 

layer, 5,6 hardening of the dye receiving layer after thermal 

printing, 7 and employment of chemical reactions between 

reactive dyes and chemical agents in the dye 

receiving layer. 8–12 

Each of these approaches has had some success, but 

the latter approach has been most promising. In exploring 

the utility of chemical reactions between reactive 

dyes and chemical agents in the dye receiving layer, four 

likely avenues suggest themselves: the control of mor - 

dants by ionic bonding force, the production of relatively 

high molecular weight dyes within the dye receiving 

layer, the reaction of special agents such as UV-absorbing 

and/or antioxidant agents with dyes, and the chelate 

reaction of dyes. 

Examples of mordants controlled by an ionic bond 

include a dye with a phenolic OH group and a mordant 

with a base, as reported by Fuji Photo Film researchers, 

12 and a mixture of cationic dyes andalkylammoniummodified 

montmorillonite clays that provide protection 

from organic solvents and from hot water , as reported 

by Sony researchers. 13 

An example of a high molecular weight dye produced 

in the dye receiving layer is an arylidene dye produced 

by the reaction between a coupling agent and an electrophilic 

compound, as seen in an Eastman Kodak 

patent. 8 

While the reaction with dyes of such special agents 

as UV-absorbing and/or antioxidant agents holds promise, 

no published reports of research in this area are 

currently available. 

However, perhaps the most successful avenue has 

been to exploit the chelate reaction of dyes. 14,15 In this 

study, we investigated newly synthesized dyes and transition 

metal cation-providing compounds. W e utilized 

the chelate reaction of azo dyes with transition metal 

cations to form stable dye-metal complexes, that we refer 

to as chelate compounds, and observed dramatically 

enhanced image stability under exposure to light and 

heat. 

Experimental 

The basic structure of the samples studied are shown in 

Fig. 1. For the dye donor sheet, a PET film substrate was 

used, with a thin backing layer to prevent sticking against 

the thermal heads. In addition to lubricants such as silicone 

compounds, the backing layer was occasionally composed 

of a resin hardened by chemical reaction with such 

compounds as isocyanate in order to make the backing 

layer heat resistant. On the obverse side of the dye donor 

sheet, a subbing layer was coated. Following that, 

dyes dissolved in an organic solvent with polymers were 

coated to create a dye donating layer . The relative dye 

concentration was about 40% in weight. These four layers 

constituted the basic structure of the dye donor sheet. 

For the dye receiver sheet, either resin-coated or synthetic 

paper could have been used as the substrate because 

the whiteness and touch of each are similar to 

photographic paper. We chose to use synthetic paper be- 

339

Figure 1. Structure of samples studied. 

cause of its higher thermal transfer sensitivity allowed 

easier observation of the systems under study. The reverse 

side consisted of a polyethylene layer and then a 

backing layer. The obverse side consisted of a TiO 2 white 

layer, then an adhesion layer, and, finally, a dye receiving 

layer. The receiving layer contained vinyl chloride– 

vinyl acetate copolymer as a binder and a metal 

cation-providing compound to produce dye-metal complexes. 

The relative concentration of the metal cationproviding 

compound was about 40% in weight. The 

whiteness of the receiver sheet was similar to conventional 

silver halide photographic paper and the values 

of (L, a*, b*) were (93–95, 0.5, –2.0). 

All of the metallizable dyes and metal cation-providing 

compounds were synthesized in our laboratory. The 

matters concerning the synthesis are described in another 

paper. 16 

Thermal dye transfer printing was performed by an 

off-the-shelf CHC-S845-5C (Shinko Electric Co.) printer. 

No modification of hardware was made to accommodate 

the thermal dye transfer material samples fabricated 

for study, and color management was performed using 

computer software, not computer hardware. 

The absorption spectra of dyes and chelate compounds 

were measured with an Hitachi U-3300 spectrophotometer, 

and we examined the effects of light and heat upon 

the stability of printed images. The lightfastness of 

printed images was evaluated by measuring optical density 

after irradiation with a xenon lamp. To determine 

color fading, printed image samples were placed in an 

incubator at controlled temperatures for prescribed periods, 

and the optical density of the printed images were 

then measured. In addition, the degradation of imageedge 

sharpness was evaluated by measuring the optical 

density around image-edges with a microdensitometer. 

Results and Discussion 

The system utilizing chelate compounds consisted of 

metallizable dyes and transition metal cation-providing 

compounds and Fig. 2 shows the fundamental structure 

of the metallizable dyes. From the report on metal 

complexes of o-hydroxyazobenzenes, 17 the chelate sites 

are expected to be located as shown in Fig. 2. 

These metallizable dyes had to meet a long list of requirements. 

They had to have sufficient reactivity with 

transition metal cation-providing compounds to produce 

the dye-metal complexes that we refer to as chelate compounds. 

The dyes had to be highly soluble in organic 

solvents in order to provide high manufacturing productivity 

of the dye donor sheets. They had to transfer 

efficiently from the dye donor sheet to the dye receiver 

sheet under the heating conditions of a conventional 

Figure 2. Metallizable dyes. Azo dyes with three metal chelating 

sites performed best. 

thermal dye transfer printing system. Also, they had to 

serve product development demands for long shelf life, 

faithful color reproduction, product safety, and environmental 

protection. To all of these demands, the best performance 

was found in azo dyes with three metal 

chelating sites for a transition metal cation. 

The transition metal cation-providing compounds 

that function as metal cation sources consist of a transition 

metal cation, ligands, and counter anions (if the 

ligand has no charge), as shown in Fig. 3. The transition 

metal cation strongly affects the hue, light stability, 

and heat stability of the printed images, as well as 

reactivity with the metallizable dyes; we examined cobalt, 

copper, zinc, and nickel. The metal chelating ligands 

influence reactivity with metallizable dyes, as well as 

shelf life, whiteness, and the solubility of the transition 

metal-cation-providing compound in organic solvents; we 

examined ethylene diamine, α-amino acid amide, and 

β-diketone ligands. The counter anions, when present, 

also influence solubility in organic solvents. 

As reported previously, 18 high performance, in terms 

of the requirements listed above, was best obtained with 

chelate compounds that resulted from azo dyes in reaction 

with a nickel metal cation and β-diketone ligands. 

The image stability described below is the image stability 

of this chelate compound. 

Generally, chelate reactions result in a marked shift of 

the light absorption spectra of a chemical compound, and 

observation of this spectrum shift can often be used to 

determine if a chelate reaction has occurred. We observed 

340 Journal of Imaging Science and Technology Abe et al.

Figure 3. Transition metal cation-providing compounds. M = 

transition metal cation, Lig = ligand, X = counter anions. 

Figure 5. Chelating system. 

Figure 4. Absorption spectra of Dye 1, Fig. 2. 1 = Dye 1 before 

chelate reaction, 1' = Dye 1 after chelate reaction. 

just such shifts of absorption spectra in this study, as 

seen in Fig. 4, strongly suggesting that chelate reactions 

were occurring in the dye receiving layers. 

Figure 5 shows the chelate reaction as we applied it. 

When metallizable azo dyes move from the dye donor 

sheet to the dye receiver sheet, the dye molecules take 

the place of the ligands of the transition metal cationproviding 

compounds waiting in the dye receiving layer, 

resulting in chelate compounds. We will refer to a thermal 

dye transfer printing system that employs this process 

as a chelating system. 

An important point to note when comparing the 

chelating system under study with a conventional thermal 

dye transfer system is that achieving higher optical 

density does not necessarily depend on higher 

Figure 6. Higher optical density versus higher thermal transfer 

sensitivity. X = hypothetical substance acting as dye molecule 

sink, A = chelating system, B = conventional system. 

thermal transfer sensitivity. As seen in Fig. 6, if a hypothetical 

substance in the dye receiving layer acts as 

a sink for the dye molecules, the diffusion of the dyes 

through the dye receiving layer can be expected to accelerate, 

and this higher thermal transfer sensitivity 

would, of course, result in higher optical density. However, 

note that dye transfer from the dye donating layer 

into the dye receiving layer with an actual chelating 

system begins at the same thermal energy level as a 

Thermal Dye Transfer Printing with Chelate Compounds Vol. 43, No. 4, July/Aug. 1999 341

Figure 7. Color fading of printed images exposed to a 70000 lx Xenon lamp. 

conventional thermal dye transfer system, with the 

threshold of the characteristic curves almost the same 

for both. This suggests that the transition metal cations 

do not act as a sink for the dye molecules. Yet the 

characteristic curve of the chelating system rises more 

steeply because the chelate compounds here have larger 

coefficients of light absorption than the conventional 

dyes, indicating higher optical density . At any point 

along the two characteristic curves, the chelating system 

exhibits approximately twice the absorbance at 

λmax, which may be explained by the chelate compound 

having a light absorption coefficient of 32300 at 456 

nm in acetone as compared to the conventional dye’ s 

13500 at 392 nm in acetone. 

The chelating system dramatically improves the light 

stability of printed images, bringing light stability almost 

to the level of silver halide photographic paper . 

Figure 7 shows the degree of color fading when the 

printed images have been exposed to a 70000 lx xenon 

lamp. For comparison here, if the illuminance of a typical 

room is assumed to be 500 lx, ten hours per day, our 

experimental condition of 70000 lx, 24 hours per day , 

for 20 days would be equivalent to about 18.4 years of 

typical room illuminance. Because the same kind of polymer 

binders were used in both the chelating and conventional 

systems here, the increased light stability that 

is evident can be attributed to the greater stability of 

the chelate compound over conventional dyes. 

As seen in Fig. 8, the chelating system also strongly 

inhibits color fading when printed images are subjected 

to high temperatures, even to temperatures above the 

glass transition temperature of the dye receiving layer, 

and it is important to note here that two color fading 

mechanisms appear to be active. At temperatures below 

the dye receiving layer’s glass transition temperature 

of approximately 70°C, fading depends chiefly on 

the stabilities of the colorants. In the case of the chelating 

system, note carefully that the colorant consists not 

of the dyes, but of the chelate compounds of which the 

dyes are a part. In the conventional systems, however, 

the colorant is constituted by the dyes themselves. The 

lower intrinsic stability of the dyes in the conventional 

system explains the compensation provided by adding 

a protective layer, which acts as a barrier against air. 

At temperatures above the dye receiving layer’s glass 

transition temperature, a second mechanism of fading 

takes additional effect. Above the glass transition temperature, 

the colorants suddenly have much greater freedom 

of movement, resulting in lateral diffusion of the 

colorants, which not only physically disperses the 

colorants but also results in greater exposure to such 

reactive agents as oxidizing and reducing agents. The 

result is a decrease in optical density. As seen here, both 

the chelating and the conventional systems are subject 

to this mechanism, but the chelating system is less 

strongly affected because the chelate compounds, composed 

of two dye molecules and a transition metal cation, 

are relatively large and heavy and are thus more 

inhibited in their movement. A complex composed of dye/ 

metal/ligand = 1/1/1 may exist together with the [dye/ 

metal = 2/1] complex. However, the results of spectroscopic 

and elementary-analytical study have indicated 


Figure 8. Color fading of printed images at high temperatures. 

that the main part of the complexes is composed of dye/ 

metal = 2/1. We report the results concerning the composition 

in Ref. 16. 

Directly related to this inhibited movement is the 

chelate system’s resistance to the degradation of image 

edges, as seen in Fig. 9. In conventional systems, a degradation 

of image edges is often observed when printed 

images are subjected to high temperatures. Like the accelerated 

color fading that occurs at temperatures above 

the glass transition temperature of the dye receiving 

layer, this degradation of image edges results from the 

lateral diffusion of dyes. However, this degradation is 

not observed in the chelating system. If the dye-metal 

complexes are insoluble in the polymer matrix of the 

dye receiving layer, the complexes are not expected to 

move easily. However, we have observed the complexes 

show relatively high solubility there. Accordingly it is 

valid to consider again the size and weight of the chelate 

compounds inhibit their movement in the dye receiving 

layer. 

Beyond the superior light stability, resistance to image 

fading at high temperatures, and minimized degradation 

of image edges reported above, the chelating 

system also showed performance better than or equal to 

conventional systems by such measures as image transfer 

to PVC plastic sheets, color fading caused by finger 

prints, and image fading in the presence of ethanol. 

Conclusion 

A chelating system for thermal dye transfer printing 

that produces chelate compounds in the dye receiving 

layer consisting of a set of azo dyes, a nickel cation, and 

a β-diketone ligand dramatically increased light stability, 

reduced image fading, and minimized the degradation 

of image edges. 

Acknowledgements. The authors express great appreciation 

to Mr. Hiroshi Watanabe, Ms. Kaori Fukumuro, 

and Mr. Tomomi Yoshizawa for their invaluable discussion 

and constant encouragement. 

References 

1. S. Honda and Y. Fujiwara, Japanese Patent 1771210 (1993). 

2. R. Takiguchi, Y. Nakamura and N. Egashira, Japanese Patent Publication 

Heisei 04-211995 (1992). 

Thermal Dye Transfer Printing with Chelate Compounds Vol. 43, No. 4, July/Aug. 1999 343

Figure 9. Degradation of image edges. 

3. K. Kushi, T. Iseki, M. Fujiwara, K. Hisafuku, and A. Ueda, Japanese 

Patent Publication Heisei 05-301466 (1993). 

4. S. Yoneyama and T. Shimazaki, Japanese Patent Publication Heisei 

05-318953 (1993). 

5. A. Imai, H. Matsuda, K. Yubagami, and N. Taguchi, Japanese Patent 

2126053 (1997). 

6. K. Renda and N. Yokota, Japanese Patent Publication Heisei 04- 

267196 (1992). 

7. H. Moriguchi, Japanese Patent Publication Heisei 02-70488 (1990). 

8. L. Shuttleworth and M. J. McManus, U. S. Patent 5011811 (1991). 

9. Y. Yamamoto, Japanese Patent 1720122 (1992). 

10. T. Niwa, Y. Murata and S. Maeda, Japanese Patent 1798935 (1993). 

11. M. Tanaka, T. Kamozaki and T. Tateishi, Japanese Patent Publication 

Heisei 06- 64343 (1994). 

12. S. Fujita, Japanese Patent 1808718 (1993). 

13. K. Ito, N. Zhou, K. Fukunishi, and Y. Fujiwara, J. Imag. Sci. Technol. 

38, 575 (1994). 

14. T. Abe, Poly. Mat. Sci. Eng. (ACS) 72, 62 (1995). 

15. T. Abe, S. Mano, Y. Yamaya, and K. Fukumuro, Proc. IS&T’s PICS 

Conference, 1998, p. 110. 

16. A. Tomotake, S. Kida, H. Watanabe, S. Mano, and T. Abe, J. Soc. 

Photogr. Sci. Technol. Japan 62, 228 (1999). 

17. J. Griffiths, A. N. Manning and D. Rhodes, J. Soc. Dyers Colourists 

88, 400 (1972). 

18. N. Miura, T. Komamura and T. Abe, IS&T’s 9th International Congress 

on Advances in Non-Impact Printing Technologies/Japan Hardcopy 

‘93, 1993, p. 314. 



Dot Allocations in Dither Matrix with Wide Color Gamut 

Ryoichi Saito and Hiroaki Kotera 

Faculty of Engineering, Chiba University, Chiba, Japan 

The color gamut in bi-level digital printers depends on the allocation of the CMY primary ink dots placed in dithering matrices. 

The typical color mixture model is based on Neugebauer theory, where CMY dots are placed at random, but recent digital printers 

don’t obey that theory. The simplest method used in digital printers is “coaxial” allocation, where the CMY ink dots are 

placed in the same positions in each color dither matrix. The coaxial model produces sharp edges, but may generate too many 

secondary colors with unsaturated chromaticities. A mixture of C and M inks may produce a more brilliant bluish color when the 

C and M dots are placed side-by-side to avoid overlapping. In this article, “min-med”, “min-max” and “min” models with side-byside 

dot allocation are discussed. These are designed to suppress the occurrence of secondary colors. The corresponding color 

gamuts are analyzed and compared. 


Introduction 

Today, low cost, high quality color printers are being 

widely used. Beautiful color images are reproduced by 

digital halftoning and color rendition technologies. 

The color gamut in bi-level printers depends on the 

allocation of the CMY dots placed in the dithering matrices. 

The Neugebauer model has been applied for conventional 

printing, where CMY dots are placed at 

random, as given by Demichel. 1 The unit area is composed 

of at most, eight colored areas; white (W), three 

primary colors (C, M, Y), the secondary colors (R, G, B), 

and the 3rd-order color (K), caused by random mixing 

of the C, M, Y colorants. These eight basic colors form 

the 12 outer edges of a color solid, regardless of color 

mixing methods. The surfaces of the color solid within 

these 12 edges are determined by the allocation of the 

primary color dots. We previously reported 2 the highly 

saturated colors that come from mixture of two primary 

colors placed on white paper. 

In this article, we reconsider the colors produced by 

bi-level printers, and discuss dot allocation problems to 

provide wider color gamuts. 

Color Gamut of Dot Allocations 

Color Dot Allocation Models. Classically, the theoretical 

model of color mixture in a bi-level printer is 

described by the well-known Neugebauer equation 1,2 

that is applied for conventional printing using halftone 

screens. Figure 1a shows the random mixture model of 

3 primary color inks given by Demichel. However , the 

color dot allocations in recent digital printers differ from 

Demichel’s. For example, Fig. 1b illustrates a typical 

model, that we call “coaxial” (Balasubramanian 3 intro- 

Original manuscript received June 24, 1998 

Supplemental materials—Figure 4 (in color) and T able III can be found 

on the IS&T website (www.imaging.org) for a period of no less than 2 years 

from the date of publication, and on the JIST CD-ROM 

©1999, IS&T—The Society for Imaging Science and Technology 

duced it as “dot-on-dot”), where the CMY primary ink 

dots are placed in the same dot position in each color 

matrix and the unit area is composed of at most, 4 colored 

areas; one primary, one secondary, black (K), and 

white (W). The coaxial model can be realized because of 

the precise control of dot positioning that is possible in 

digital technology. It produces sharp edges, but may give 

a narrow color gamut due to the frequent occurrence of 

secondary colors with unsaturated chromaticities. 

Figure 1c, 1d and 1e show three different models, “minmed”, 

“min-max” and “min,” to suppress the occurrence 

of secondary colors. Here, the primary color inks P , Q 

and S are placed in the unit area with dot area ratios p, 

q and s. In the min-med model, the dots of P and Q are 

placed on opposite sides to minimize overlapping, while 

S is placed perpendicular to P and Q, which results in 

medium overlapping. The min-max model differs from 

the min-med model only in that S is placed in the same 

position as P or Q. In the min model, the starting points 

of P, Q and S are equally separated by one-third of the 

unit area to minimize the average overlap. 

Surfaces of Color Solid. Figure 2 illustrates that the 

outer surface of the color solid is composed of the following 

6 faces. 

1. M and Y inks on W : W-M-Y-(R) 

2. C and Y inks on W : W-C-Y-(G) 

3. C and M inks on W : W-C-M-(B) 

4. M and Y inks on C : C-(B)-(G)-(K) 

5. C and Y inks on M : M-(B)-(R)-(K) 

6. C and M inks on Y : Y-(G)-(B)-(K) 

The bracket ( ) denotes second- and third-order colors. 

Each face is not flat, but is formed by a tetrahedral surface 

depending on the allocation of the primary ink dots. 

Area Ratio Equations and Tables 

The tristimulus vector T of the unit area is given by the 

additive mixture of tristimulus vector T i for each colored 

area i as follows. 

345

W 

P 

P 

W 

Q S 

p 

P 

W 

q 

Q 

p 

s q p q 

S P W Q P Q S 

s 

Q S 

s S 

1 

1 1 1 1/3 1/3 1/3 

(a) Neugebauer (b) coaxial (c) min-med (d) min-max (c) min 

Figure 1. Basic models of color allocations in bi-level printer. 

3) C C& & M inks on W W: : 

W-C-M-(B) 

C 

W 

M 

G 

1) M M& & Y inks on W W: : 

W-M-Y-(R) 

Y 

2) C & Y inks on W W: : 

W-C-Y-(G) 

5) C & Y inks on M ink: 

: 

M-(B)-(R)-(K) 

R 

B 

4) M & Y inks on C ink : : 

C-(B)-(G)-(K) 

K 

6) C & M inks on Y ink: 

: 

Y-(G)-(R)-(K) 

Figure 2. Outer surface is composed of 6 planes. 

Neugebauer Model. As well known, eight colored areas 

appear as a result of random mixture of C, M and Y. 

8 

T = ∑ aT; 

i i 

i= 

1 

i = W, C, M, Y, R, G, B, K (1) 

Coaxial Model. At most, four colored areas appear; six 

different cases occur for the selections of P and Q from 

CMY. 

4 

T = ∑ aT i i ; 

i= 

1 

i = W, P, PQ, 

K 

P = max( C, M, Y) 

PQ = max( C, M, Y) ∩mid( C, M, Y) 

P and PQ denote one of the primary and secondary colors. 

Min-Med Model. Six different cases occur; three selections 

for S from CMY and two conditions for p + q ≤ 1 or 

p + q > 1. Each case includes six colored areas, 

6 ⎧W, C, M, Y, PS, QS ; for p + q ≤1 

T = ∑ aT i i ; i= 

⎨ 

i= 

1 ⎩ PQRGBK , , , , , ; for p+ q> 

1 

Min-Max Model. Six different cases occur, as for the 

min-med model. Each case includes at most four colored 

areas, 

4 

T = ∑ aT i i 

i= 

1 

(2) 

(3) 

(4) 

Min Model. This model is very complicated. In total, 

sixty different cases appear , each including i = 4 ~ 6 

colored areas, according to the combinations of the 

ranges for, 

1 1 2 2 

0 ≤ pqs , , < , ≤ pqs , , < , ≤ pqs , , ≤1 (5) 

3 3 3 3 

Tables I, II, and III ( Supplemental materials—Table 

III can be found on the IS&T website (www .imaging.org) 

for a period of no less than 2 years from the date of publication, 

and on the JIST CD-ROM) show examples of equations 

for colored dot area ratios. T able I shows the 

min-med model compared with the Neugebauer and coaxial 

models. Here, C and M are placed side by side and 

Y is perpendicular to them. Table II gives the area ratios 

for the min-max model. Here, C and M are again 

placed side by side, but Y is placed in the same position 

as C. Table III shows the area ratios for the min model. 

Results 

Calculation Condition and Dither Matrix . Table 

IV shows the tristimulus values of the eight basic colors 

printed by an inkjet printer (EPSON PM700C). The 

color chips were printed without color correction and 

their tristimulus values were measured by spectrocolorimeter 

(GRETAG Spectrolino). These values are 

used for simulation. 

Figure 3 illustrates an example of the ordered dither 

matrices to simulate the dot allocation models. Figure 

346 Journal of Imaging Science and Technology Saito and Kotera

TABLE I. Colored Dot Area Ratios in Min–Med Model 

Neugebauer coaxial model min–med model (C||M⊥Y) 

color i area ratio a i 

color i area ratio a i 

color i area ratio a I 

(c + m < 1) area ratio a I 

(c + m > 1) 

W (1 – c)(1 – m)(1 – y) W 1 – Max(c,m,y) W (1 – c – m)(1 – y) 0 

C c(1 – m)(1 – y) P Max(c,m,y) – Mid(c,m,y) C c(1 – y) (1 – m)(1 – y) 

M (1 – c)m(1 – y) PQ Mid(c,m,y) – Min(c,m,y) M m(1 – y) (1 – c)(1 – y) 

Y (1 – c)(1 – m)y K Min(c,m,y) Y y(1 – c – m) 0 

R (1 – c)my B 0 (c + m – 1)(1 – y) 

G c(1 – m)y G cy (1 – m)y 

B cm(1 – y) R my (1 – c)y 

K cmy K 0 (c + m – 1) 

TABLE II. Colored Dot Area Ratios in Min–Max Model 

min – max model W C M Y B G R K 

c + m < 1, c < y 1 – c + m c – y m 0 0 y 0 0 

m + y < 1, y > c 1 – m – y 0 m y – c 0 c 0 0 

c + y > 1, m + y < 1 0 1 – m – y 1 – c 0 c + m – 1 y 0 0 

m + y > 1, c + m < 1 0 0 1 – y 1 – c – m 0 c m + y – 1 0 

m + y > 1, c > y 0 0 1 – c 0 c – y 1 – m 0 m + y – 1 

c + m > 1, c < y 0 0 1 – y 0 0 1 – m y – c c + m – 1 

0 

8 

2 

10 

15 7 13 5 0 

8 

2 

10 

12 4 14 

6 

3 

11 

1 

9 

12 4 14 

6 

3 

11 

1 

9 

12 4 14 

6 

3 

11 

1 

9 

15 7 13 5 0 

8 

2 

10 

15 

7 

13 

5 

cyan magenta yellow 

(a) min-max model 

0 

3 

8 

2 

12 4 14 

11 

1 

10 

6 

9 

11 

15 7 13 5 10 2 8 0 

7 

14 

3 

15 

6 

13 

9 

12 

5 

1 

4 

6 

2 

9 

5 

14 

1 

8 

3 

0 

10 4 12 

cyan magenta yellow 

(b) min model 

Figure 3. Examples of ordered dither matrix in side-by-side 

dot allocation model. 

13 

7 

15 

11 

Blue 

Green 

Red 

(a) Coaxial(Max) 

Blue 

Green 

Red 

(b) Min(Side by Side) 

Figure 4. Color chips of RGB tone in equal mixing of two primary 

colors (Screen-dot dither). ( Supplemental materials—Figure 

4, in color, can be found on the IS&T website (www.imaging. 

org) for a period of no less than 2 years from the date of publications, 

and on the JIST CD-ROM) 

3a shows the min-max model. Here, for instance, the 

threshold values of C are arranged in forward order but 

those of M are reversed to minimize overlapping, and Y 

is set the same as C. Figure 3b shows the min model, where 

threshold values are placed rotationally shifted by onethird 

from each other to minimize average overl apping. 

This example uses the well known 4 × 4 Bayer’s matrix. 

The other matrices are designed in the same manner. 

Analysis of Secondary Color . Figure 4 shows most 

typical color differences between color tones printed by 

two different models. Here, RGB gradation patterns are 

generated by half and half mixtures of two primaries, 

C+M, C+Y and M+Y. Figure 4a is the coaxial model and 

Fig. 4b is the side by side model. In the coaxial model, 

for example, the perfectly overlapped C and M produces 

unsaturated blue tones, while side by side location of C 

and M produces different bluish colors. The red and 

green tones also differ between the models (Supplemental 

materials—Figure 4, in color can be found on the IS&T 

website (www.imaging.org) for a period of no less than 2 years 

from the date of publication, and on the JIST CD-ROM). 

Figure 5 illustrates how the RGB color tones differ 

between the models. For example, the red tones trace 

Dot Allocations in Dither Matrix with Wide Color Gamut Vol. 43, No. 4, July/Aug. 1999 347

Journal of Imaging Science and Technology Vol. 43, No. 4, July/Aug. 1999 345s 

TABLE III. Colored Dot Area Ratios in Min Model 

W C M Y B G R K 

1 c

Figure 5. Chromatic locus in equal mixing of two primary colors. 

Figure 6. Outer surface of color gamut in each model (ink-jet printer). 

different loci when M and Y are mixed in equal percentages. 

In the coaxial model, the locus of red tone is on 

the straight line from W to R, whereas in the side by 

side model, its locus is broken into two just at the point 

of the 50% dot area ratio, and goes into very different 

hue angle directions, as shown in the bending broken 

line. This is because the M and Y inks are placed side 

by side without overlapping at below 50%, but at above 

50%, M and Y begin to overlap, causing the secondary 

color R. The measured color plots are reasonably 

matched to the theoretical calculations in CIELAB 

space. 

Outer Surface and Color Distribution. The outer 

surface of the color solid is constructed from six faces, 

each comprising the tetrahedral color points W-M-Y-(R), 

W-C-Y-(G), W-C-M-(B), C-(B)-(G)-(K), M-(B)-(R)-(K), Y- 

(G)-(B)-(K). The 3D outer surface of the color solid is 

synthesized from the six tetrahedral faces. Figure 6 

shows a calculated result for an inkjet printer. The color 

gamuts differ in each model. For example, W, C, M and 

B are not in the same plane, but make a specified tetrahedron 

in each dot allocation model. 

The coaxial model appears the smallest in volume. 

The min-med and min-max models are calculated for 


Figure 7. Comparison of color gamut in each model (ink-jet printer). 

the case that C and M are placed side by side. The 

gamut of the min model has a ragged surface, but it 

appears to give a larger volume than the min-med and 

min-max models. 

Details of the color gamuts were inspected inside the 

color solid. Figure 7 shows a comparison of 3D plots inside 

the color solids when the (c, m, y) area ratios of the 

primary color inks are changed from 0 to 1 in steps of 

0.1, generating 11 3 = 1331 colors. In the coaxial model, 

the population is very irregular and includes empty 

space. The Neugebauer model results in better-balanced 

populations than the coaxial model. The min-med and 

min-max models show similar distributions and give fine 

densities. Additionally, the min model seems to give 

balanced mixtures of CMY, like Neugebauer’s model. 

Volume of Color Solid. The problem of gamut description 

has no definitive solution yet. Tanaka, Berns, and 

Fairchild reported a means of calculating gamut using 

tetrahedron. 4 Kappele reported 5 a means of calculating 

gamut using Green’s theorem. 6 Mahy introduced the idea 

that it is possible to determine gamut analytically in 

the case of the localized Neugebauer equations. 7 

Green’s theorem provides a means of calculating 

gamut. It states that the area size A inside a simple 

closed curve S can be calculated as follows: 

1 

A = ∫ S ( xdy −ydx) (6) 

2 

where S is the perimeter of the gamut plot in the simple 

closed curve or polygon. The integral A can be approximated 

as a sum. First we calculate the mean value between 

two neighboring coordinates, such as a* i and a* i+1 , 

or b* i and b* i+1 , that is, half of the coordinates’ sum. Next, 

we compute the differential distances between these two 

neighboring coordinates. Finally, we substitute these 

values for Eq. 6 and get Eq. 7. 

1 ⎧a* i+ 

1 + a* i 

b i+ 

+ b i ⎫ 

A = ∑ S ⎨ ( 

* * * 1 * 

bi+ 

1 −bi 

) − 

( 

* * 

ai+ 

1 − ai 

) ⎬ (7) 

2 ⎩ 2 2 

⎭ 

Therefore A can be estimated by calculating all of the 

mean values and differential distances between two 

neighboring coordinates for a* and b* in a counterclockwise 

direction, combining and summing as given in Eq. 7. 

The details of color gamuts are inspected by slicing 

the 3D color solid into 2D planes. Figure 8 shows the 

comparison of the a* - b* plane sliced in 41 < L* < 45 for 

the outer surface of the color solids when the (c, m, y) 

area ratios of primary color inks are changed from 0 to 

1 in steps of 0.04, generating 26 2 × 6 = 4056 colors. 

Using Eq. 7, we calculated the gamut area in each 

model sliced by L* value. Figure 9 shows the calculated 

area per L* (every four slice levels) for the Neugebauer, 

coaxial and min-max models. The coaxial model has a 

large area in the low lightness region. In Fig. 8, the coaxial 

model is supposed to have a slightly larger area in 

the Y region. As the Y ink itself is a highly saturated 

bright color, it produces still saturated colors in the 

lower lightness region in spite of occurrence of unsaturated 

secondary color. This effect widens the color gamut 

on the dark side of the Y region. The min-max model 

shows a wider gamut in the middle to high lightness 

regions, because of side by side dot allocation, that, in 

turn, produce brilliant colors by suppressing the secondary 

colors. In particular, when C and M are placed 

side by side and overlapping by more than 50%, the resultant 

bluish colors give the wider color gamut to the 

bright side. The min-med and min models were similar 

to the min-max model, but slightly narrower. 

Consideration of n-Value. To predict the tones of halftone 

reproduction on the paper, the optical dot-gain is 

often considered. Yule and Nielsen considered the effect 

of the penetration of light into the paper. 8 Their model 


TABLE IV. Tristimulus Values of Eight Basic Colors 

color i X Y Z L* a* b* 

W 82.97 84.46 78.95 93.65 2.98 –8.11 

C 10.33 14.61 43.25 45.1 –25.85 –55.99 

M 33.8 16.98 14.29 48.23 75.7 –0.78 

Y 66.54 62.74 4.27 83.31 13.84 96.65 

CM(B) 5.22 4.19 15.33 24.29 15.5 –44.71 

CY(G) 5.44 10.49 4.59 38.71 –44.03 17.94 

MY(R) 32.22 17.48 4.24 48.86 67.43 37.44 

CMY(K) 1.87 1.92 1.66 15.06 0.46 –0.87 

(a) Neugebauer (b) coaxial (c)min-med 

b* 

a* 

(d) min-max 

(e) min 

Figure 8. Outer surface in a* – b* plane for 41 < L* < 45 and calculation points. 

Areas 

Neugebauer 

coaxial 

min-max 

Figure 9. Areas per L* in each model (ink jet printer). 

L* 


TABLE V. Area Values of Each Model 

Neugebauer coaxial min – max min – med min 

0 < L* < 50 30187.62 32342.82 30506.68 30187.80 30032.20 

n = 1 50 < L* < 100 28443.46 28835.67 31521.70 29404.90 28217.92 

Total 58631.08 61178.49 62028.37 59592.70 58250.11 

0 < L* < 50 28295.42 30142.09 27457.18 27223.64 27500.78 

n = 2 50 < L* < 100 36651.40 38465.88 39327.71 36537.35 35892.68 

Total 64946.81 68607.97 66784.89 63760.99 63393.45 

n=1 

n=2 

L* 

where n is the Yule-Nielsen parameter. The n-value depends 

upon several factors; the dot size, dot overlapping 

and type of paper are perhaps the most important three. 

We calculated the Neugebauer model for typical case 

of n = 2 using Eq. 8. Figure 10 shows L* – a* plots of 

outer points of color solid. Large light points show the 

result of calculated for n = 1, and small dark points show 

that for n = 2. As a whole, the lightness in the case of n 

= 2 is lower than the case of n = 1. In the high lightness 

region, as opposed to the middle one, the case of n = 2 

has the wider chromaticity than that of n = 1. Figure 11 

shows calculated gamut area per L* using Eq. 7 on the 

Neugebauer model. The gamut area of n = 2 is smaller 

than that of n = 1 in low lightness region, but shows the 

wider gamut from middle to high lightness regions. 

The other four models also show similar results. Table 

V shows calculated total areas of each models. It is noa* 

Figure 10. Outer surface in L* – a* plane at the Neugebauer model. 

was for a single-color halftone tint. T aking the Yule- 

Nielsen effect into consideration, the Neugebauer model 

is given by, 

8 

1 

T = ∑ ( aT ) 

i= 

1 

i i 

n n 

(8) 

ticed that the gamut of coaxial model is widen by the 

Yule-Nielsen effect for the larger n-value than unity. In 

each model, the n-value may be different according to 

dot’s allocations. The more detailed calculations of 

gamut volumes need to use the actual n-values measured 

by halftone dot analyzer and will be discussed in 

future works. 

Discussion and Conclusion 

The additive mixture of CMY inks can produce a wider 

color gamut than that of a subtractive mixture in bilevel 

printers. Here the 3D color gamuts in three side 

by side dot allocation models are analyzed and compared 

with that of the typical coaxial model. 

The coaxial model shows very irregular populations 

including partially unpopulated areas in the colors produced. 

On the other hand, the side by side models produce 

well-balanced populations and give fine densities. 

The volume of the color solid can be calculated by summing 

the areas of (a*–b*) planes sliced by an L* value. 

Comparing these color solid volumes, the coaxial model 

shows the larger gamut on the low lightness side, while 

the side by side models show the larger gamut on the 

middle to high lightness side. 


Areas 

Figure 11. Areas per L* in the Neugebauer model (using n-value). 

Yule-Nielsen parameter n-value affects the gamut 

volume of each model. The accurate computations of 

gamut volume need to measure the actual n-value of 

each model. On the other hand, V iggiano reported the 

spectral Neugebauer model. 9 In each model, spectral 

tristimulus n-value may be also considered. 

The extension of the fundamental ideas to dot placement 

in the error diffusion method will be continued in 

further studies. 

L* 

n=1 

n=2 

Acknowledgement. The authors wish to thank 

Tateishi Science and Technology Foundation, Kyoto for 

their financial support of part of this work. 

References 

1. H. E. J. Neugebauer, Die Theoretischen Grundlagen des 

Mehrfarbendruckes, Z. Wiss. Photo. 36(4), 73 (1937). 

2. K. Kanamori and H. Kotera, Analysis of Color Gamut for Hardcopy 

based on Neugebauer Theory, Neugebauer Memorial Seminar on 

Color Reproduction, SPIE Japan Chapter, Tokyo, pp.36–42 (1989). 

3. R. Balasublamanian, Color Hard Copy and Graphic Arts IV, Proc. 

SPIE 2413, 356 (1995) 

4. T. Tanaka, R. Berns and M. Fairchild, Predicting the Image Quality 

of Color Overhead Transparencies Using a Color-Appearance 

Model, J. Electron. Imag. 6(2), 154 (1997) 

5. W. D. Kappele, Quantifying Color Gamut, IS&T’s NIP13: International 

Conference on Digital Printing Technologies, IS&T, Springfield, 

VA, 1997, pp. 470–474. 

6. Thomas and Finney, Calculus and Analytic Geometry, 5th ed., 

Addison-Wesley, 1980, p.711. 

7. M. Mahy, Gamut Calculation of Color Reproduction Devices, Fourth 

Color Imaging Conf.: Color Science, Systems and Applications, 

IS&T, Springfield, VA, 1996, pp. 145–150. 

8. J. A. C. Yule and W. J. Nielsen, The Penetration of Light into Paper 

and Its Effect on Halftone Reproduction, Proc. TAGA, 65–76 

(1951). 

9. J. A. S. Viggiano, Modeling the Color of Multi-Colored Halftones, 

Proc. TAGA, 44–62 (1990). 



Symmetry Properties of Halftone Images I: 

Scattering Symmetry and Pattern Symmetry 

Jonathan S. Arney ▲ 

Center for Imaging Science, Rochester Institute of Technology, Rochester, New York 

and Shinya Yamaguchi 

Nippon Paper Industries, Imaging Technology Center, Saitama, Japan 

Previous work has shown that the mechanism of color and tone reproduction in halftone imaging systems can be described 

quantitatively by modeling functions for mean level probability, P ij , for light scattering from region i to region j, where regions i 

and j may be, for example, regions of the printed paper covered by different inks in the halftone process. The value of P ij has been 

shown to be a function of the area fractions of the regions, f i and f j . In the past, the P ij functions were written empirically to fit 

observed data or determined by convolution calculations involving the paper point spread function, PSF, and the transmittance 

geometry of the halftone pattern, T(x,y). In the current work it is shown that characteristics of the P ij functions can be deduced 

from symmetry properties of light scattering in paper and symmetry properties of the halftone pattern. This allows some P ij 

functions to be derived directly without the need to carry out a convolution with the point spread function of the paper . Models of 

these symmetry properties and methods for experimental analysis are presented. 


Probability Model 

Tone and color reproduction by the halftone process is 

based on the Murray–Davies equation, where R is the 

reflectance of the image as we see it, Ri and Rp are the 

reflectance of the ink and the paper, and F and (1 – F) 

are the area fractions of ink and paper. 1 

R = F⋅ Ri 

+ ( 1 −F) 

⋅Rp 

(1) 

The Neugebauer equation is an expanded form of this 

expression for color halftones, with f i the area fractions 

of each R i color making up the image. 2 Equation 2 is an 

example for a cmy halftone system where the dots are 

assumed to overlap randomly. 

8 

R = ∑ fi 

⋅Ri 

i= 

1 

Equations 1 and 2 appear to be liner functions in terms 

of dot area fraction, F, or f i . R. However, it is commonly 

observed that the printed image reflectance, R, of a halftone 

image are not linear functions of the dot area fractions, 

F, or f i . 1 This is not due to a failure of Eqs. 1 and 

2. Indeed, these equations must be correct because they 

are a form of the law of conservation of energy. The rea- 


▲ IS&T member 


(2) 

son R is not linear in F is that R i and R p are not constants, 

as often assumed, but are themselves functions of the 

area fractions, F and f i . 1 Therefore, in order to model 

tone and color reproduction, we must model the R i and 

R p as functions of area fractions. 3 

As shown earlier, the relationship between area fractions, 

F, and the reflectance values of R i and R p can be 

modeled with probability functions, P ij , for the scattering 

of light from region i of area fraction f i to region j of 

area fraction f j . 5,6 This is illustrated in Fig. 1 as a schematic 

drawing of a halftone image with two regions (regions 

0 and 1) on a substrate of reflectance R g , 

illuminated with light at irradiance I a (units of photons/ 

sec/area). The regions are ink dots with Beer–Lambert 

transmittance values of T 0 and T 1 . For T 0 = 1 and T 1 < 1 

we have a single ink system, and the “ink” in region 0 is 

air. The amount of light that encounters region 0 is I a. F 0 . 

Similarly, I a. F 1 hits region 1. These are attenuated by 

the transmittance of the ink layer, so I a. F 0. T 0 and I a. F 1. T 1 

photons enter the paper in regions 0 and 1 respectively. 

The light is further attenuated by the absorption of the 

paper, leaving so I a. F 0. T 0. Rg and I a. F 1. T 1. Rg photons to 

return to the surface of the paper substrate. However , 

scattering in the paper means some of the light from 

region 0 returns to region 0, and some to region 1. 

The probability of returning to region 0 from region 0 

is P 00 , and similarly for P 11 , P 10 , and P 01 . Thus, the total 

amount of light returning to the surface of region 0 is 

the sum ( I a. F 0. T 0. Rg . P 00 ) + ( I a. F 1. T 1. Rg . P 10 ). Similarly, 

(I a. F 1. T 1. Rg . P 11 ) + (I a. F 0. T 0. Rg . P 01 ) returns to the surface 

of region 1. Finally, the light is attenuated a second time 

by the inks in regions 0 and 1, so the total light reflected 

353

multiplication of probabilities that lead to Eqs. 3 and 4. 

This also lets us sum the light so that we can write the 

following. 

P01 = 1− P00 

(5) 

P10 = 1− P11 

(6) 

If we consider the special case of Fig. 1 in which R g = T 0 

= T 1 = 1 (no light is absorbed), then we know that R p = 

R i = 1. In this special case, we can equate the right hand 

sides of Eqs. 3 and 4 and combine with Eqs. 5 and 6 to 

derive the following two expressions. 

P 10. F 1 = P 01. F 0 (7) 

P 11 =1 – (1 – P 00 ) . (F 0 /F 1 ) (8) 

Figure 1. A unit area of a halftone image of two regions. 

from regions 0 and 1 are [( I a. F 0. T 0. T 1. Rg . P 00 ) + 

(I a. F 1. T 1 

2. 

Rg . P 10 )] and [(I a. F 1. T 1. T 0. Rg . P 11 ) + (I a. F 0. T 0 

2. 

Rg . P 01 )]. 

Dividing by the amounts incident at each region, I a. F 0 

and I a. F 1 , gives the reflectance values one would measure 

experimentally for regions 0 and 1. Calling these 

reflectance values R p and R i gives us the following. 

F 

Rp = Rg ⋅ T ⋅ ⎛ 

T ⋅ P +⎛ ⎞ 

⎜ 

T P 

⎝ ⎜ F 

⎟ 

⎝ 

⎠ 

⋅ ⋅ 

⎞ 

1 

1 0 00 

⎟ 

⎠ 

⎛ F 

Ri = Rg⋅T ⋅ T ⋅ P + ⎛ T 

⎝ ⎜ 0 

⎞ 

0 ⎜ 1 11 ⎟ 

⎝ F ⎠ 

⋅ 

1 

0 

1 10 (3) 

⋅ 

⎞ 

P ⎟ 

⎠ 

0 01 (4) 

These expressions give us a way to model the reflectance 

of the halftone inks, R i , and the paper between 

the halftone dots, R p , for a single ink system. Note that 

F1 = F and F0 = 1–F in Eq. 1. Thus, Eqs. 1, 3, and 4 

model halftone reflectance, R versus F provided the 

probability functions can be modeled. 

The Symmetry of Scattering 

In previous reports, the probability functions, P ij , were 

shown to be useful both for tone and color modeling. 4,6 

The functions that were employed were derived empirically 

to fit observed experimental data. Rogers has 

shown these functions can be derived from convolution 

calculations with the more fundamental probability 

function, PSF, that describes the point spread function 

for lateral scattering in paper. 5 On an even more fundamental 

level, one might attempt to derive the PSF 

from, for example, a random walk model of scattering, 

as was done by Gustavson and Kruse. 7 In this article, 

we will remain at an empirical level to describe the P ij 

functions. However, by exploring some basic symmetry 

characteristics of light scatter and of halftone patterns, 

we can deduce some useful properties of the P ij 

functions without resorting to more complex scatter - 

ing models. 

The simplifying assumption on which the current 

analysis of P ij rests is that scattering and absorption 

are independent probabilities. That is, the P ij and the 

absorption probability Rg are assumed to be independent. 

For the two region case of Fig. 1, this allows the 

Equations 7 and 8 are based on the assumption of the 

symmetry of light scattering. Light scatters to the right 

and to the left equally. If we also assume scattering and 

absorption are independent, then Eqs. 7 and 8, which 

contain no terms for absorption, must be true for any 

values of R g , T 0 , and T 1 . In other words, Eq. 8 must apply 

for all systems regardless of the reflectance of the 

paper or the absorption of the inks. The practical significance 

of these equations is that they relate all four 

probabilities, P 00 , P 01 , P 10 , and P 11 , together. It is necessary, 

therefore, to model only one probability function, 

P 00 for example, in order to model tone reproduction, R 

versus F. We can apply Eq. 8 to Eqs. 3 and 4 and obtain 

the following. 

( ) 

Rp = Rg⋅T0⋅ P00⋅( T0 − T1) + T1 

(9) 

( ) 

Ri = Rg ⋅ T1 ⋅ P11 ⋅ ( T1 − T0) + T0 

(10) 

Measuring and Modeling Tone Reproduction 

An example of the use of these functions to model tone 

reproduction is illustrated with a halftone gray scale 

printed by offset lithography. Figure 2 shows the microdensitometry 

data with reflectance values and the 

dot area fractions, F, measured by histogram analysis 

as described previously. The P 00 function can be modeled 

empirically, as described previously , 6 for an AM 

halftone with the following function. 

( ) 

w w 

P00 = 1−F⋅ 2−F −( 1−F) (11) 

With this expression for P 00 , we apply Eqs. 8, 9, 10 and 

then Eq. 1 in sequence to model the data. The value of 

Rg was measured as the average image R at F = 0. The 

value of T 0 is 1.0 for air (no ink), and T 1 was calculated 

by assuming Beer–Lambert ink (zero scattering) and 

measuring R min at F = 1 (the solid ink region). Then, T 1 

= (R min /Rg) 1/2 . The value of the power constant, w in 

Eq. 11, was adjusted to give the least RMS deviation 

between the R p data and the line. The result was w = 

0.37. By fitting the model only to the R p data, the model 

also resulted in a good fit to the R i and R data, indicating 

the model is a reasonable description of P 00 and 

tone reproduction with this halftone system. The physical 

meaning of the power factor, w, has been described 

previously. 4 

354 Journal of Imaging Science and Technology Arney and Yamaguchi

1Reflectance 

1 

P 00 P 11 

R 

R p 

Probability 

R i 

0 

0 F 

1 

Figure 2. Microdensitometry data for a 65 LPI, AM halftone 

gray scale printed by offset lithography. 

0 

0 F 

1 

Figure 3. P 00 and P 11 versus dot area fraction, F, calculated 

from the data in Fig. 2. 

Measuring and Modeling P 00 

and P 11 

The experimental data on R p and R i can also be used to 

generate experimental estimates of P 00 and P 11 as follows. 

First, Eqs. 9 and 10 are solved for P 00 and P 11 . 

(A) 

P 

00 

P 

11 

Rp 

−Rg⋅T1⋅T0 

= 

Rg⋅T ⋅( T −T 

) 

0 0 1 

Ri 


= 

Rg⋅T ⋅( T −T 

) 

1 1 0 

(12) 

(13) 

F= 0.1 F= 0.8 

(B) 

With experimental estimates of Rg, T 1 , and T 0 = 1, Eqs. 

12 and 13 convert experimental data on R p and R i versus 

F into data on P 00 and P 11 versus F, as illustrated in 

Fig. 3. In this analysis, the values of P 00 and P 11 were 

calculated from data on R p and R i respectively. The line 

through the P 00 data is Eq. 12, and the line through the 

P 11 data is Eq. 13 converted to P 11 with Eq. 8. 

The Symmetry of the Halftone Pattern 

The results shown in Fig. 3 are quite symmetrical. However, 

this is not a result of the scattering symmetry that 

lead to Eq. 7, rather , this is a property of the halftone 

pattern produced by the printing process. Indeed, Rogers 5 

carried out a rigorous analysis of the convolution of a 

paper point spread function with a symmetrical halftone 

pattern and predicted exactly the functional shape for 

the probability functions observed in the data in Fig. 3. 

It is not uncommon for halftones to show a pattern symmetry 

where the halftone dots of ink fraction 0 < F 1 < 0.5 

are the same shape as the paper “dots” of paper fraction 

0 < F 0 < 0.5. In other words, if for F > 0.5 the paper became 

the ink and the ink became the paper (negative 

image), it would be identical to the ink gray scale for F < 

0.5. Figure 4 illustrates two halftone patterns; one with 

pattern symmetry and one without. 

If a halftone image has pattern symmetry, then it is 

necessary only to know the P 00 function from F = 0 to F = 

Figure 4. Example of halftone patterns with and without pattern 

symmetry. 

0.5 in order to model the entire halftone system. For example, 

at any value of F = x (where x is some value 0 < x 

< 0.5), the value of P 00 at F = x produces the corresponding 

value of P 11 at F = x by the application of Eq. 8. Moreover, 

pattern symmetry requires that the value of P 00 at 

F = (1 – x) equals the value of P 11 at F = x, and that the 

value of P 11 at F = (1 – x) equals the value of P 00 at F = x. 

This is illustrated schematically in Fig. 5 where point 

(A) on the line representing P 00 leads to point (B) for P 11 

at the same value of F. This is a result of scattering symmetry 

and Eq. 8. Then points (C) and (D) for P 00 and P 11 

respectively are known as a result of pattern symmetry. 

In the example shown in Fig. 5, the values of P 00 from 

F = 0 to F = 1 were chosen in such a way that the corresponding 

value of P 11 over this range is zero by Eq. 8. 

This in turn produced the mirror image function for P 11 . 

Consideration of Eq. 8 leads to the following equation 

for this example of P 00 . 

1 2 F 

P00 

= − ⋅ 

for F < = 0.5, and P 

1− 

F 

00 = 0 for F > 0.5 (14) 

Symmetry Properties of Halftone Images I: Scattering Symmetry and Pattern Symmetry Vol. 43, No. 4, July/Aug. 1999 355

1 

Incident Light 

Probability 

A 

P 00 P 11 

C 

Region 1Region 0Region 0 Region 1Region 0 

N Pa 

0 B 

D 

0 F 

1 

F = x 

F = 1 - x 

Figure 5. Modeling by assuming both scattering and pattern 

symmetry. 

Because probabilities must be greater than or equal 

to zero, this represents a limiting boundary for possible 

values of P 00 and P 11 in a system that has both scattering 

symmetry and pattern symmetry . Values must be 

equal to or greater than the values indicated by the 

curves in Fig. 4. 

It should be noted that Eq. 14 marks limits for the P 00 

function when both scattering symmetry and pattern 

symmetry apply. Scattering symmetry is a fundamental 

property and must apply. However, pattern symmetry, 

as we will see subsequently, does not have to apply. 

In the case of the AM system shown in Fig. 2, Eq. 1 1 

was chosen to model P 00 because it provides this property 

of pattern symmetry. 

Components of the P 00 

Function 

Additional insights into the nature of the P 00 function 

can be obtained by considering the paths of light in the 

substrate in more detail. Recall that P 00 is a fraction of 

light which emerges from region 0 after entering region 

0. However, as illustrated in Fig. 6, there are many regions 

0. The particular region 0 to which the light travels 

may or may not be the same region 0 it came from 

originally. To describe this, we can divide P 00 into two 

parts, as illustrated in Fig. 6. An amount of light, N, 

enters a particular region 0. A fraction of this light, P a , 

returns to the surface after scattering and exits the same 

region 0. Another fraction (1 – P a ) scatters and leaves 

this region 0. Thus, N•(1 – P a ) is the amount of light 

that leaves this region 0. Of the light that leaves the 

original region 0, some will emerge under a region 1, 

but some will emerge at a different region 0. Define P b 

as the fraction of the amount of light N•(1 – P a ) that 

emerges under a different region 0. The total amount of 

light which emerges under any of the regions 0 is N•P a 

+ N•(1 – P a )•P b . Thus, the P 00 function can be written as 

follows. 

P 00 = P a + P b. (1 – P a ) (15) 

By decomposing P 00 into the smaller functions P a and 

P b , it is easier to model the nature of the P 00 function. 

Figure 6. Components of the P 00 function. For a single ink 

system, region 0 is paper and region 1 is ink. 

For example, consider the P a function for a digital, FM 

halftone where the size of the individual regions 0 and 

1 are fixed. This means the value of P a is a constant at 

all values of P a . The value of this constant could easily 

be calculated by a convolution of a single region with 

the PSF of the paper. 

The P b part of the function carries information about 

the digital halftone. For example, if all the halftone regions 

are randomly distributed on the paper, the probability 

that the light N•(1 – P a ) will emerge under a given 

region will be proportional to its area fraction. This, for 

a completely random FM halftone, we can immediately 

write Eq. 16 for P b . 

P b = (1 – F) (16) 

Note that we identify region 0 as paper between ink dots 

and region 1 as ink dots of area fraction F. Note also 

that two or more of the same type of region may occur 

side by side in a random system. 

Experimental Analysis of Pattern Symmetry 

We can apply the P a , P b model to describe an FM halftone 

system, as shown in Fig. 7. The halftone gray scale 

was printed by offset lithography on plain paper using 

black ink. The halftone pattern used in this system was 

generated digitally by a proprietary algorithm. The lines 

in Fig. 7 were modeled as follows. First, Eq. 16 was used 

to model P b . Then P 00 was modeled by Eq. 15 with P a as 

an arbitrary constant between 0 and 1. P 11 was calculated 

with Eq. 8, then Eqs. 9, 10, and 1 were applied to 

calculate the lines in Fig. 7. The value of Rg was measured 

independently, and T i was calculated as before 

from (R min /Rg) 1/2 , assuming Beer–Lambert. The value of 

P a was the only arbitrary constant in the model, and 

the lines shown in Fig. 7 were drawn with P a = 0.34. 

Figure 8 shows the data used with Eqs. 12 and 13 to 

measure P 00 and P 11 experimentally. Because measured 

values of R i are small, there is significant experimental 

error in using R i and Eq. 13 to estimate experimental 

values of P 11 . Nevertheless, the symmetry of the halftone 

pattern is evident in Fig. 8. 

Figure 9 illustrates another FM halftone printed by 

offset lithography. This system was identical to the system 

in Fig. 7 except that it was printed on a coated 

paper, and the halftone pattern was generated by a proprietary, 

error diffusion algorithm. This system was 


1Reflectance 

1Reflectance 

R p 

R p 

R 

R 

0 

R i 

0 F 

1 

Figure 7. Microdensitometry data for an error diffusion, FM 

halftone printed on plain paper with black ink by offset lithography. 

The error diffusion process was proprietary and produced 

square halftone regions 0.13 mm on a side. Output was 

to film and then to plate. 

0 

R i 

0 F 

1 

Figure 9. Microdensitometry data for an error diffusion, FM 

halftone printed on coated paper. The system is the same as in 

Fig. 7, but a different error diffusion algorithm was used to 

generate the halftone pattern. 

1 

1 

Probability 

P 00 P 11 

Probability 

P 00 

P 11 

0 

0 F 

1 



0 

0 F 

1 



modeled similarly to the system in Fig. 7 except that 

an arbitrary power factor, m, was added to the model 

for P b . 

P b = (1 – F) m (17) 

By selecting P a = 0.72 and m = 2.7, the model lines shown 

in Fig. 9 resulted. Applying Eqs. 12 and 13 produced 

Fig. 10. From this analysis of the halftone data, it is 

evident that pattern symmetry is not a property of this 

halftone system. 

Conclusion 

By noting the symmetry properties intrinsic to the behavior 

of light scattering and the symmetry of the halftone 

pattern, it is possible to deduce properties of tone 

reproduction in a halftone system. In the case of a completely 

random halftone system with both scattering 

and pattern symmetry, the exact function for the scattering 

probability, P 00 , can be derived without resorting 

to a convolution calculation involving the PSF of 

the paper, as was illustrated in Fig. 8. Perhaps, of more 

practical utility, however, is the result represented by 

Symmetry Properties of Halftone Images I: Scattering Symmetry and Pattern Symmetry Vol. 43, No. 4, July/Aug. 1999 357

Pb 

1 

0 

m = 1 

m = 2.7 

0 F 

1 

Figure 11. P b versus F for m = 2.7 in Eq. 17. 

Eqs. 12 and 13. These expressions are based on the 

symmetry of light scatter but do not require pattern 

symmetry. The only other assumptions on which these 

two equations depend are that the ink dots are on top 

of the substrate (good hold-out) and obey Beer–Lambert. 

Then these equations can be applied to experimental 

data on R i and R p to provide a direct analysis 

of P 00 and P 11 . This, in turn, can indicate otherwise hidden 

properties of a halftone system, such as the presence 

or absence of pattern symmetry. In the example 

shown in Fig. 9 the absence of pattern asymmetry was 

not evident to the authors on visual inspection, but the 

data in Fig. 9 provides a basis for a quantitative evaluation 

of the degree of asymmetry. 

The algorithm that produced the FM halftones used 

in this project were proprietary and not available to the 

authors. However, the power factor m = 2.7 suggests an 

interesting characteristic of the error diffusion algorithm 

of Fig. 8. A value of m = 1 makes sense for a totally 

random halftone pattern, but a value of m > 1 

indicates a rapid decline versus F at low values of F as 

illustrated in Fig. 11. This means that as light scatters 

out of its original region 0, it has a lower probability , 

P b , of encountering another region 0 compared to the 

expectation based on totally random chance. This can 

be rationalized if the halftone pattern is designed in such 

a way as to maximize the distance between like regions. 

Indeed, the visual noise associated with traditional random 

granularity can be decreased in many error diffusion 

algorithms by applying a “blue noise filter” which 

shifts the granularity to higher spatial frequencies. Such 

a shift might be expected to result in a shift toward more 

space between dots and less clustering, that in turn 

might indeed result in m > 1. Thus, the techniques of 

microdensitometry analysis of P 00 and P 11 suggested in 

this study appear to be of practical utility. 

Acknowledgment. Special thanks to our lab colleagues, 

Akio Tsujita and Katsuya Ito for stimulating 

discussions and challenging arguments. Thanks also to 

Geoffrey Rogers for stimulating thoughts, and for pointing 

the way. 

References 

1. An excellent introduction to the topic by Peter G. Engeldrum, The Color 

Between the Dots, J. Imag. Sci. Technol. 38, 545 (1994). 

2. J. A. S. Viggiano, TAGA Proc. 37, 647 (1985). 

3. J. S. Arney, P. G. Engeldrum and H. Zeng, An expanded Murray- 

Davies Model of Tone Reproduction in Halftone Imaging, J. Imag. 

Sci. Technol. 39, 502 (1995). 

4. J. S. Arney and M. Katsube, A Probability Description of the Yule- 

Nielsen Effect, J. Imag. Sci. Technol. 41, 633 and 637 (1997). 

5. G. L. Rogers, Optical Dot Gain: Lateral Scattering Probabilities, J. 

Imag. Sci. Technol. 42, 341 (1998). 

6. J. S. Arney, T. Wu and C. Blehm, Modeling the Yule-Nielsen effect 

on Color Halftones, J. Imag. Sci. Technol. 42, 335 (1998). 

7. S. Gustavson, Modeling of light scattering effects in Print, Thesis 

LIU-ISBN:91-7871-623-3, and J. Imag. Sci. Technol. 41, 283 

(1997). 



Symmetry Properties of Halftone Images II: 

Accounting for Ink Opacity and Dot Sharpness 

Jonathan S. Arney ▲ 


and Akio Tsujita 

Hitachi Koki Co., Ltd., Katsuta Research Laboratory, Japan 

Previous work has shown that tone reproduction characteristics of halftone images can be modeled with knowledge of the probability 

function P 00 , for light to reflect from the paper between the halftone dots after having entered the paper between the 

halftone dots. In the current report, experimental measurements of the micro-reflectance, R p , of the paper between the dots is 

measured as a function of dot area fraction, F, and used with the model to calculate experimental values for P 00 versus F. It is 

then shown that the model can be modified to account for inks that have significant scattering. The model is shown to fit data on 

halftones printed with electrophotography toner which is highly opaque. In addition, the model is further modified to account orf 

the effects of the non-sharpness of the edges of halftone dots. Using both of these effects, the model is shown to fit well wit h 

measured data from a variety of AM and FM halftones printed at different resolutions with different colorants. In addition, the 

model is shown to fit experimental data on the tone reproduction characteristics of a continuous tone, electrophotographic, off ice 

copy machine. 


Introduction 

The overall reflectance, R, of a halftone image is described 

by the Murray–Davies Eq. 1 in which R i and R p 

are the reflectance values of the ink and paper in the 

halftone for an ink fractional area coverage of F. 

R = F⋅ Ri 

+ ( 1 −F) 

⋅Rp 

(1) 

This equation accurately describes the relationship between 

the dot area fraction and the reflectance of a halftone 

image provided the values of R i and R p are 

expressed as functions of F. 1 In the accompanying report, 

2 probability functions P ij were employed to model 

the R i and R p versus F functions. The P ij functions describes 

the lateral scattering of light in the paper substrate. 

Light which enters a region i of the paper has a 

probability, P ij , of scattering to another region, j, and 

exiting as reflected light. For example, in a one ink halftone 

we define regions 0 and 1 as the regions between 

the halftone dots and the region of the substrate under 

the halftone dots, respectively. The previous report describes 

the halftone model based on these probability 

functions. 2 The current report describes how this model 

can be modified to account for artifacts commonly encountered 

in halftone systems. These artifacts are (1) 




opaque inks that scatter as well as absorb light, and (2) 

inks that form halftone dots with diffuse, poorly defined 

edges. 

The model begins with the P 00 function which describes 

the probability that the light that enters the paper between 

the halftone dots will also exit as reflected light 

between dots. Another fraction of the light, P 01 = 1 – P 00 , 

enters the paper in the region between the dots and 

emerges under a dot. P 10 and P 11 are similarly defined, 

and as described previously the symmetry of scattering 

leads to the following relationship between P 00 and P 11 , 

with F 1 = F defined as the area fraction of the halftone 

dot and F 0 = 1 – F the area fraction between the dots. 2 

P 11 = 1 – (1 – P 00 ) . (F 0 /F 1 ) (2) 

The reflectance factors for the two regions of the halftone 

were shown to be related to the probability functions 

as follows. 2 

( ) 

Rp = Rg⋅T0⋅ P00⋅( T0 − T1) + T1 

(3) 

( ) 

Ri = Rg⋅T1⋅ P11⋅( T1− T0) + T0 

(4) 

In these expressions, Rg is the reflectance of the unprinted 

paper, T 1 is the Beer–Lambert T ransmittance 

of the ink, and T 0 is the transmittance of the “ink” over 

region 0. T 0 = 1 when region 0 is bare paper. By applying 

these equations for R p and R i to Eq. 1, we can calculate 

the overall reflectance of the halftone image, R. 

359

1Reflectance 

1 

P 00 P 11 

R 

R p 

Probability 

R i 

0 

0 F 

1 


gray scale printed by offset lithography with magenta ink. 

0 

0 F 

1 

Figure 2. P 00 versus F measured from R p using Eq. 5 and fit to 

a polynomial (solid line). P 11 (dashed line) from Eq. 1 using the 

regression line for P 00 . 

Thus, in order to model halftones, R versus F, we need 

to know the P 00 function. 

Modeling the P 00 Function 

In other reports it has been shown that the P 00 function 

may be modeled starting from the point spread function 

of the substrate, 3 starting from empirical functions 

for P 00 found to fit many common halftones, 

4 

or from 

symmetry properties of light scattering. 2 In the current 

work we will model P 00 empirically from indirect, experimental 

measurements of P 00 . This can be done by 

measuring the reflectance of the paper between the halftone 

dots, R p , using microdensitometric techniques described 

previously. 1,5 Equation 3 is then solved for P 00 , 

as shown in Eq. 5, and the measured values of R p are 

used to calculate the corresponding values of P 00 . 

Rp 


P00 

= 

Rg⋅T0⋅( T0 −T1) 

Thus, experimental values of R p versus F provide experimental 

estimates of P 00 versus F. In the work described 

below, the P 00 versus F data was fit to a 

seventh-order polynomial by a regression analysis. Then 

tone reproduction was modeled by applying the polynomial 

function for P 00 to Eqs. 2, 3, 4, and 1. 

Well Behaved System 

Figure 1 shows microdensitometry data for a traditional 

AM halftone printed at 65 LPI by offset lithography. Reflectance 

values were measured for the overall image, 

R, the halftone dots, R i , and the paper between the dots, 

R p , as described previously. 1,5 P 00 values were calculated 

from the measured R p by Eq. 5, with Rg measured as 

the image reflectance, R, at F = 0. The value of T 0 is 1.0 

for air (no ink), and T 1 was calculated by assuming Beer– 

Lambert ink (zero scattering) and measuring R min at F 

= 1 (the solid ink region). Then, T 1 = (R min /Rg) 1/2 . The 

resulting values of P 00 are shown in Fig. 2. 

(5) 

A polynomial regression was performed to fit the data 

in Fig. 2 (solid line). Then the corresponding model for 

P 11 was calculated from Eq. 2 (dashed line). Finally, R p , 

R i , and R versus F were modeled. The results are shown 

as the solid lines in Fig. 1. The model must, of course, 

fit the data for R p , but the agreement between the model 

and the R i and R data shows the halftone to be quite 

well described by the probability model. 

Scattering in the Halftone Dot 

Thus far we have assumed the ink in the halftone dot 

obeys Beer–Lambert optics so that T 1 = (R min /Rg) 1/2 . That 

is, only absorption occurs, and light scatter is confined 

to the paper substrate. However, scattering within the 

ink might be expected to contribute significantly to the 

reflectance, R i , of some halftone systems. Also, as shown 

earlier, 6 penetration of ink into the substrate behaves 

as if the scattering coefficient of the ink itself increases. 

Another system in which light scatter in the ink is 

expected to play a significant role is electrophotography. 

Toner particles are highly opaque, and most of the 

light reflected from a halftone dot made of toner par - 

ticles can be expected to come from the toner bulk and 

the surface of the toner. For example, the data in Fig. 

3 was measured for a 36 LPI AM halftone printed by a 

laser printer using a proprietary algorithm for generating 

traditional, clustered halftone dots. The lines 

through the data were modeled exactly as described 

above for the 65 LPI system of Fig. 1. Clearly the model, 

based on Beer–Lambert optics, does not fit the observed 

behavior of the electrophotographic halftone. The 

model was modified to account for the opacity of the 

colorant. 

A layer of ink of thickness x at F = 1 (solid coverage) 

on top of a scattering substrate of reflectance Rg can be 

modeled with the Kubelka–Munk absorption and scattering 

coefficients, K and S, both in units of mm –1 . The 

equations for the system are as follows. 

(A) The reflectance, R min , of the solid ink region of the 

halftone: 

360 Journal of Imaging Science and Technology Arney and T sujita

1Reflectance 

1Reflectance 

R 

R p 

R 

R p 

R i 

R i 

0 

0 

0 F 

1 


gray scale printed by electrophotography with a proprietary 

laser printer using a clustered dot halftone algorithm. Modeled 

with Beer–Lambert optics. 

0 F 

1 


gray scale printed by electrophotography with a proprietary 

laser printer using a clustered dot halftone algorithm. Modeled 

with Kubelka–Munk optics and k = 0.99. 

1 Rg [ a b coth( b S x)] 

Rmin 

= − ⋅ − ⋅ ⋅ ⋅ 

a− Rg+ b⋅coth( b⋅S⋅x)] 

where a = (S/K + 1), and b = (a 2 – 1) 1/2 . 

(6) 

convert experimental values of R p versus F into P 00 versus 

F. Then we perform the polynomial regression to 

model P 00 , and Eq. 2 models P 11 . Equation 3 then models 

R p versus F as before. We approximate a model for 

R i versus F by adding R o to Eq. 4. 

(B) The fraction of light, T KM , that penetrates all the 

way through the ink to the paper: 

b 

T KM = a ⋅ b ⋅ S ⋅ x + b ⋅ b ⋅ S ⋅ (7) 

Sinh( 

) Cosh( 

x ) 

(C) The reflectance, R 0 , the ink would have with a black 

background: 

R 

0 

1 

= (8) 

a − b ⋅coth( b ⋅ S ⋅ x ) 

R 0 is the light which reflects from the colorant without 

penetrating all the way to the paper. R min is the reflectance 

we measure experimentally for the solid ink 

region of the halftone at F = 1. We define an index of 

opacity, k, as the ratio (R 0 / R min ). For a completely opaque 

colorant k = 1, and for a Beer–Lambert colorant with no 

scattering, k = 0. 

R0 = k ⋅ Rmin (9) 

We will treat k as an arbitrary variable in the P 00 model. 

By measuring R min and selecting a value for k, we obtain 

R 0 . Then by inverting Eqs. 6 and 8 (using numerical techniques) 

we can solve for the values of Kx = K•x and Sx = 

S•x. Then Eq. 7 is used to calculate T KM . 

The value of T KM from Eq. 7 is used as an estimate of 

the amount of light which enters the paper substrate 

under the halftone dot. W e use T KM for T 1 in Eq. 5 to 

( ) + 

Ri = Rg⋅T1⋅ P11⋅( T1− T0) + T0 R0 

(10) 

Finally, R versus F is modeled with Eq. 1. 

The model contains a single arbitrary constant, k. 

With k = 0, the model reduces exactly to the model of 

Figs. 1 and 2. However, by adjusting k = 0.99 to achieve 

a minimum RMS difference between the model and the 

data for R i , the model shown in Fig. 4 results. This is 

clearly an improvement over the results shown in Fig. 

3. Moreover, the resulting model of R versus F also 

agrees well with the observed data. 

Sharpness of Halftone Dots 

The most common approximation implied in most halftone 

models is that halftones have discrete, definable 

edges, as illustrated on the right side of Fig. 5. However, 

real halftones suffer from effects such as feathering 

of the ink; edge raggedness, or misplaced ink 

particles (satellite drops, loose toner, etc.) as illustrated 

on the left of Fig. 5. It is important to distinguish between 

such dot edge effects and physical dot gain. Dot 

gain is the difference between the size of the dot commanded 

by the printing process (halftone screen or digital 

signal) and the actual size of the dot that ends up on 

the paper. The edge effect, on the other hand, has to do 

with the sharpness of the edge, as illustrated in Fig. 6. 

All of the effects illustrated in Fig. 5 can lead to an effective 

edge softness as shown in Fig. 6. In the experimental 

work described in this article, dot gain is not a 

factor because the actual dot size is measured experimentally 

from the printed samples, but the sharpness 

of the edge can influence tone reproduction. 

Symmetry Properties of Halftone Images II: Accounting for Ink Opacity and Dot Sharpnes s Vol. 43, No. 4, July/Aug. 1999 361

Figure 5. Illustration of soft edges on halftone dots. 

Figure 7. Experimental histogram of a typical halftone, as 

seen by microdensitometry, where H(R) is the relative frequency 

of occurrence of each gray level, R, measured by the 

microdensitometer. 

Figure 6. Illustration of physical dot gain and the edge effect. 

(A) are dots commanded by the printer . (B) are dots actually 

printed. 

When dot edges are poorly defined, the meaning of 

“dot edge” becomes a matter of arbitrary definition. It 

is common to resort to an experimental “threshold” reflectance, 

R t , to define the edge of dots, as illustrated in 

Fig. 7. Then the two state approximation of Eq. 1 can 

be applied with area fractions and reflectance values 

defined as metrics from the histogram. In the current 

work, the values of R i , R p , and F were defined in terms 

of the peak and valley points illustrated in Fig. 7. 

As a result of this method of defining dot edges, the 

apparent reflectance values of R i and R p vary with F 

not only because of the Yule–Nielsen effect of light scatter, 

but also because of overlap of colorant when dots 

get close together. For example, when dot edges get close 

together, the space between the dots will fill in with some 

amount of colorant, as illustrated in Fig. 5. The impact 

of this effect on T 0 and T 1 may be approximated by the 

following empirical functions, as suggested in earlier 

work. 1 v 

T = 1−( 1−T ) ⋅( 1−F 

) (11) 

0 KM 0 

v 

1 KM 1 

T = 1−( 1−T ) ⋅F 

(12) 

Figure 8. Data for the 35 LPI, AM halftone gray scale of Fig. 

6 printed by electrophotography and modeled with a dot opacity 

k = 0.99 and dot sharpness v = 0.05. 

In these expressions, T KM is the transmittance of the 

solid colorant layer described in Eq. 7, and the power 

factor, v, is an empirical index of dot sharpness. Note 

that at v = 0, Eqs. 11 and 12 revert to T 0 = 1 and T 1 = 

T KM for perfectly sharp dots. 

The addition of Eqs. 11 and 12 to the model provides 

a model containing two arbitrary parameters, k and v. 

By adjusting both k and v, the RMS deviation between 

the model and the data for R i was minimized to produce 

the solid lines shown in Fig. 8. This is clearly a much 

improved fit. 

Modeling Different Halftone Systems 

The model modified to include ink opacity , k, and the 

dot edge effect, v, was applied to a variety of halftone 


1Reflectance 

TABLE I. Opacity and Edge Indices Required to Fit Halftone 

Gray Scales 

System k v 

AM 65 LPI Offset 0.00 0.00 

AM 150 LPI Offset 0.00 0.12 

AM 35 LPI EP 0.98 0.04 

Con-tone EP 1.00 0.12 

FM 191 DPI Offset 0.00 0.00 

FM 1200 DPI Offset 0.70 0.07 

FM 300 DPI Ink Jet 0.94 0.00 

Offset = offset lithography 

EP = laser electrophotography 

Con-tone EP = electrophotographic office copy machine 

Ink Jet = thermal ink jet on plain paper 

Contact = halftones on silver halide film pressed in close contact with the paper. 

LPI = lines per inch for an AM clustered dot halftone 

DPI = inverse of dot size in inches for an AM halftone 

R i 

R 

R p 

H(R) 

0 

0 

R mean = 0.124, F=0.85 

R mean = 0.296, F=0.39 

Figure 9. Histograms from two different gray levels printed 

by the continuous tone, electrophotographic copy machine. 

systems. In every case the agreement between data and 

the model was as good as that shown in Fig. 8. T able I 

summarizes the observations. 

One system in T able I is not typically considered a 

halftone. That was a gray scale image generated by placing 

samples of different reflectance on a Xerox model 

5365 office copy machine. Such a copy machine is generally 

considered to be a continuous tone imaging system. 

However, microdensitmetric examination of the mid 

tones produced by such a copy machine shows toner 

particles distributed randomly in much the same way 

as printed dots in a stochastic halftone. The histograms 

from microdensitometric analysis of these gray levels 

often show the same bi-modal distribution typical of 

printed halftones. Figure 9 illustrates two histograms 

for two copied gray levels produced by the 5365 machine. 

The exposure that produced the mean reflectance of 

0.296 in Fig. 9 is clearly bi-modal, though the two gray 

populations are much overlapped. Visual inspection of 

the image with a loupe had the appearance of a random 

distribution of toner “dots”, and the eye could clearly 

distinguish these dots. 

Bi-modal behavior is also suggested by the skewed 

shape of the histogram of mean reflectance R mean = 0.124. 

R 

1 

0 

0 F 

1 

Figure 10. Microdensitometry data for the continuous tone, 

electrophotographic copy machine. Experimental data, (O), and 

model (solid lines) with k = 1 and v = 0.12. 

Here also visual inspection clearly distinguishes the 

toner from the paper. The toner “dot” area fractions, F, 

for a set of copier images were determined by fitting a 

bi-modal histogram model to the experimental histograms, 

as described previously. 5 From the area fraction, 

the transition reflectance, R t , and then the mean reflectance 

values on each side of the transition reflectance, 

R i and R p were determined. The results are shown in 

Fig. 10. The R p versus F data in Fig. 10 was fit by a 

polynomial regression, and the rest of the tone reproduction 

model was carried out as described above. With 

k = 1.00 (completely opaque toner) and v = 0.12 (a very 

soft “dot”), the results displayed as lines in Figs. 10 and 

11 resulted. 

Discussion 

The probability model, modified to include colorant opacity, 

k, and non-sharpness of the edges of the halftone 

dots, v, fit the observed experimental model for all the 

halftones in this study quite well. Moreover, the values 

of k and v in Table I, make physical sense. For example, 

high values of k were observed for all of the toner systems, 

as one would expect. Values of k = 0 fit the data 

for the offset lithographic prints, and indeed transparency 

is a common assumption used in most models reported 

in the literature for lithographic halftones. The 

ink jet system utilized a water based dye known to be 

transparent. However, the ink jet system fit best with k 

= 0.94. As shown previously, this can be a result of the 

colorant penetrating the surface so that the ink behaves 

as if it has the opacity and scattering power of the substrate. 

Only the system labeled “FM 1200 DPI Offset” 

seems out of line in Table I. In this case, however, one 

might speculate that the transparent dots, being quite 

small (1/1200 inch in diameter) may interact with the 

paper substrate (calendered plain paper in this case) to 

induce behavior similar to a scattering ink. Clearly , 

additional investigation would be required to resolve 

this observation. 

Symmetry Properties of Halftone Images II: Accounting for Ink Opacity and Dot Sharpnes s Vol. 43, No. 4, July/Aug. 1999 363

1 

Probability 

0 

P 00 

P 11 

0 F 

1 

Figure 11. Measured P 00 versus F for data in Fig. 10 and fit to 

a polynomial (solid line). P 11 (dashed line) from Eq. 1 using the 

regression line for P 00 . 

The edge sharpness parameter, v, also seems reasonable 

for the samples examined. For the low frequency 

samples, edge sharpness is of less significance, so v = 0.0 

for the 65 LPI AM system and the 191 DPI FM system. 

The ink jet image produced small drops, but they were 

heated on contact with the paper (HP1600C printer) and 

formed very well defined dots. The result was a halftone 

system with v = 0.0. 

A particularly interesting case is the contone gray 

scale from the Xerox 5365. In this case the value of k = 

1.00 makes sense for an opaque toner system. However, 

toner particles intrinsically have very sharp, well defined 

edges. Indeed, examination of the toner image 

through a microscope clearly revealed toner particles 

that were well defined, sharp edged particles. Never - 

theless a value of v = 0.12 was required to fit the data. 

The authors would like to suggest that for very small 

halftone dots (toner particles 10 µm and smaller) the 

diffraction of light around the dots may cause an apparent 

edge softness and require v > 0. If this indeed is 

the origin of v > 0 in the analysis of the copy machine 

image, then the edge effect has both a physical and an 

optical component, much as does dot gain. 

The magnitude of a refraction effect at the edges of 

toner particles is a function of the numerical aperture 

of the densitometer used to measure the image. Thus 

if refraction does play a significant role in toner systems, 

one would expect the numerical aperture of the 

densitometer to influence the measured tone and color 

reproduction of halftone images. To the author’s knowledge, 

such an effect has not been reported or explored. 

One additional feature of the model applied to the 

continuous tone image should be noted. The experimental 

shape of the P 00 curve in Fig. 11 is not symmetrical 

with respect to the corresponding P 11 curve (dotted 

line). This indicates the open spaces between toner near 

F = 1 are not the negative image of the toner on the 

paper near F = 0. This non-symmetry is not surprising, 

but the apparent minimum in P 00 near F = 0.6 and 

the limiting value of P 00 as F approaches 1.00 are difficult 

to rationalize. The easy explanation is to suggest 

these apparent observations are just experimental artifacts 

which result from the uncertainty in the analysis 

of the histograms. Nevertheless, it is also tempting 

to believe there may be significance to these curves and 

that this type of analysis might lead to useful insights 

about image formation in electrophotographic and 

other systems. The authors hope to explore these effects 

in more detail. Perhaps eventually a unified tone 

reproduction model might evolve that describes everything 

from macroscopic halftones to molecular level 

“dots” of colorant. 

Acknowledgment. Special thanks to our lab colleague 

Katsuya Ito for stimulating discussions and challenging 

arguments. Thanks also to Geoffrey Rogers for 

stimulating thoughts, and for pointing the way. 

References 

1. J. S. Arney, P. G. Engeldrum and H. Zeng, An expanded Murray- 

Davies Model of Tone Reproduction in Halftone Imaging, J. Imag. 

Sci. Technol. 39, 502 (1995). 

2. J. S. Arney and S. Yamaguchi, Symmetry Properties of Halftone Images 

I: Scattering Symmetry and Pattern Symmetry, J. Imag. Sci. 

Technol. 43, 353 (1999). 



4. S. Gustavson, Modeling of light scattering effects in Print, Thesis 

LIU-ISBN:91-7871-623-3, and J. Imag. Sci. Technol.41, 283 (1997). 

5. J. S. Arney and Y. Wong, Histogram analysis of the microstructure 

of halftone images, Proc. IS&T’s PICS Conference, IS&T, Springfield, 

VA, 1998, p. 206. 

6. J. S. Arney and M. Alber, Optical Effects of Ink Spread and Penetration 

on Halftones Printed by Thermal Ink Jet, J. Imag. Sci. Technol. 

42, 331 (1998). 



Kubelka–Munk Theory and the Yule–Nielsen Effect on Halftones 

Jonathan S. Arney ▲ and Eric Pray 


and Katsuya Ito 

Toyobo Co. Ltd., Film Research Laboratory, Otsu-city Shiga, Japan 

This report experimentally relates the Yule–Nielsen n parameter for optical dot gain to the scattering and absorption parameters, 

S and K, of Kubelka–Munk theory. The relationship between the parameters is made through another metric of light 

scatter, k p , defined as the inverse of the frequency, ω in cy/mm, at which the MTF of the paper equals 1/2. The value of n is related 

exponentially to k p , as shown in earlier work, and the current work indicates that k p = c/S, where c is a constant equal approximately 

to 10. However, contrary to some intuition and to previous theoretical projections, the absorption coefficient of the paper, 

K, has no significant influence on k p or the MTF of paper. 


Introduction 

The overall reflectance, R, of a halftone image is described 

by the Murray–Davies Eq. 1 in which R i and 

R p are the reflectance values of the ink and the paper 

when the halftone is at an ink area fraction, F, between 

0 and 1. 1 R = F • R i + (1 – F) • R p (1) 

Equation 1 appears to indicate a linear relationship 

between R and F, but the reflectance values, R i and R p , 

are also functions of F. 2,3 This occurs because light scatters 

laterally inside the paper substrate, increasing the 

probability it will encounter ink and be absorbed. However, 

it is common practice to assume R i = R b and R p = 

R g , where R b and R g are the reflectance values of the 

ink at F = 1 (black) and the reflectance of the paper at F 

= 0 (ground). When these approximations are used in 

Eq. 1, the calculated values of R are generally higher 

than the actual measured values. In order to compensate, 

an empirical n parameter can be used. 1,2,3 

[ ] 

1/ b n 1/ 

g n n 

R = F⋅ R + ( 1 −F) ⋅R 

(2) 

Equation 2, the Yule–Nielsen equation, has been applied 

successfully to model tone and color reproduction in 

many halftone systems. If light does not scatter later - 

ally in the paper to any significant extent, then n = 1, 

Original manuscript received October 13, 1998 



R i = R b , R p = R g , and Eq. 2 reduces to Eq. 1. If light 

scatters thoroughly in the paper and becomes completely 

scrambled over distances much larger than the dot size, 

then n = 2. 2–4 Thus, the n factor can be used as an index 

of the effect of light scattering on the halftone image. 

The purpose of this article is to examine how n is related 

to other indices of light scatter in printing substrates 

such as paper. 

Which Dot Fraction? The effect of lateral light scatter 

on halftone images is called the Yule–Nielsen effect, but 

the term “optical dot gain” has also been used to characterize 

the phenomenon. If we assume n = 1 but increases 

the values of F in Eq. 2 to a larger value, called F’, then 

the value of R we calculate can be made to fit the experimental 

value of R. In other words, it is assumed the ink 

dots behave as if they were larger than they really are, 

and an index called “optical dot gain” is defined as G o = 

F’ – F. Plots of G o versus F are commonly reported in the 

literature. The G o metric was developed by analogy with 

the “physical dot gain” metric, G p = F – F c , where F c is 

the dot area fraction commanded by the printing process 

(screen, digital signal, etc.) The G p metric actually measures 

the difference between the intended dot size and 

the size of the dot that is actually formed on the paper . 

By using F c in Eq. 2, the empirical n parameter can still 

model tone and color reproduction in many halftone systems, 

but n values greater than 2 are often observed. The 

focus of the current work is on Yule–Nielsen effect of light 

scatter, and F values reported below are those measured 

by microdensitometry analysis of the printed images, as 

described perviously. 1,5 

Relating n to Other Scattering Metrics. Two theories 

commonly applied to describe the optical behavior 

of paper and other printing substrates are Kubelka– 

Munk theory 6 and Linear Systems theory . The former 

365

describes reflectance and transmittance properties of 

scattering materials in terms of a scattering coefficient, 

S, and an absorption coefficient, K. Linear Systems 

theory uses a point spread function, PSF( r), that describes 

the probability of light emerging from a paper 

at distance r from the point at which it entered the paper. 

7,8 The PSF is often described in the Fourier domain 

as the Modulation Transfer Function, MTF(ω), where ω 

is spatial frequency in units of 1/ r. Intuition suggests 

that the Yule–Nielsen parameter, n, must be related both 

to the MTF of the substrate and also the S and K parameters 

of Kubelka–Munk theory. 

The MTF is often modeled empirically as follows. 

1 

MTF = 

1 + ( ⋅ 

m 

k p ω) 

In this function, ω is spatial frequency in cy/mm and 

k p is a constant proportional to the mean distance light 

scatters in paper between entering and exiting as reflected 

light. The m parameter is an empirical parameter 

used to adjust the shape of the function to fit 

experimental data. The value of k p is equal to 1/ω o , where 

ω o is the value of ω where MTF = 1/2. Thus, regardless 

of the value of m, k p is a definable, experimental metric 

for lateral scattering in the paper. 

The k p metric and the n metric are clearly related, 

but attempts to derive n quantitatively from application 

of linear systems theory leads only to approximations 

because n is really an empirical parameter used 

to fit an empirical model to experimental data. However, 

within typical limits of experimental error, it has 

been shown experimentally that n can be related to k p 

through the following expression. 10 

{ } 

(3) 

n ≅ 2 −exp −( A⋅k p ⋅υ ) 

(4) 

The value of the constant A is dependent on the particular 

geometric pattern of the halftone. 10 For an AM 

clustered dot halftone, ν is the frequency of occurrence 

of halftone dots. For an FM halftone, ν is the inverse of 

the distance, L, between the centers of adjacent dots in 

the halftone. Note that ν is in mm –1 for both AM and FM 

systems, and k p is in mm. 

Equation 5 has been derived by Engeldrum and 

Pridham 11 from Kubelka–Munk theory to relate the MTF 

of a material to the S and K constants. 

⎡ 

/ 

j 

R πω 

MTF( ω) 

= ⋅ ⋅ + ⎛ − 

⎡ 

− ln( − R ) j j ⎝ ⎜ ⎞ ⎤ ⎤ 

∞ 2 2 

3 2 

1 ⎢ ∞ 2 

⎢ ⎟ ⎥ ⎥ 

∑ 1 

2 

1 ⎢ ⎢ jbS⎠ 

⎥ ⎥ 

∞ = 1 2 

⎣⎢ 

⎣ ⎦ ⎦⎥ 

In this function a = 1 + K/S, b = (a 2 – 1) 1/2 , and R ∞ = a – b. 

If Eq. 5 is correct, then one need only measure K and S 

of the printed substrate to calculate MTF versus ω. Then 

the value of ω = ω o at which MTF = 1/2 should provide 

the value k p = 1/ω o . The value of k p can then be applied 

to Eq. 4 to calculate the Yule–Nielsen n factor. 

Equation 5 indicates that the absorption coefficient K 

should have a significant impact on k p , and in turn, on 

the Yule–Nielsen n factor. In addition, because K is 

strongly dependent on the wavelength of light, λ, then 

Eq. 5 also predicts a strong influence of k p and n on λ. 

However, as will be shown, the impact of K on k p is not 

significant, and n is not strongly dependent on λ. 

(5) 

CCD camera 

Illumination 

Microscope 

black video tape 

Crisper TM 

Figure 1. Microdensitometer. 

4.0 mm 

Scan 

Monitor 

Cover 

glass 

Measuring MTF 

A sample of a commercial plastic substrate called 

Crisper (Toyobo Co., Ltd.) was placed under a reflection 

microscope with a CCD video camera as shown in 

Fig. 1. The camera was attached to a frame grabber , 

and digital pixel values in this system were linearly 

related to sample luminance. This system was used as 

a reflection microdensitometer, and the MTF of the instrument 

was measured as 0.5 at 40 cy/mm. A piece of 

black video tape, 20 µm thick, was placed on top of the 

Crisper sample with the edge of the tape positioned 

to run through the center of the field of view of the microdensitometer. 

The tape was clamped in place with a 

microscope cover glass, and the tape edge was illuminated 

with two fiber optic bundles 45 degrees from the 

vertical on each side, and in directions collinear with 

the tape edge. The image of the edge was captured, as 

illustrated in Fig. 1, and software was used to scan a 

section of the edge. With the edge in the vertical direction 

as shown, the scan was done in the horizontal direction 

across 4 mm of the sample. The scan was 

achieved by averaging pixel values in a vertical column 

of 100 pixels (0.8 mm) to produce an average pixel value 

at each horizontal pixel position in the scan. The scanned 

edge of the plastic substrate is shown in Fig. 2 as pixel 

value, P, versus position, x, in millimeters. 

The MTF was calculated from the edge scan by Fourier 

analysis. The P versus x data from Fig. 2 was differences 

point-to-point, dP = (P i+1 - P i ) , to calculate the 

derivative of the edge as shown in Fig. 3. The pixels 

under the tape edge could not be measured experimentally 

and were assumed to have the same distribution 

as the pixel values on the measured side of the edge. 

Thus, the derivative at x < 0 (under the edge) was assumed 

to be the same as x > 0 where the data was taken. 

A Fourier transform algorithm was applied to the data, 

and the MTF of the reference material was calculated 

as the modulus of the Fourier transform, normalized to 

1.00 at zero frequency, as shown by the data points in 

Fig. 4. The data was fit by Eq. 3 with m = 1.2 and k p = 

0.14 millimeters. 

Measuring the Yule–Nielsen Effect 

The k p of other printing substrates might be found 

through a similar line scan analysis. However , many 

printing substrates have rough surfaces and are not 

easily measured by this technique. The rough surface 

366 Journal of Imaging Science and Technology Arney et al.

150 

P 

1 

MTF 

k p = (1/7.1) mm 

k p = 0.14 mm 

80 

0 X Millimeters 

0.3 

X (mm) 

Figure 2. Edge scan of Crisper TM as pixel value, P, versus position 

in millimeters. X = 0 at the edge. 

0 

0 (7.1) 10 

20 

ω, cy/mm 

Figure 4. Crisper TM standard. The dots (O) were calculated 

from the edge scan, and the line is Eq. 3 with k p = 0.14 mm 

and m = 1.2 

1 

dP 

R p /Rg 

0 

-0.2 

0 0.2 

X (mm) 

0 

(R p /R g ) = 0.59 at F = 1 

0 F 

1 

Figure 3. Derivative of edge scan in Fig. 2. 

Figure 5. Crisper TM R p versus F. 

adds significant noise to the edge scan, and many scans 

must be averaged to estimate the average k p of the 

sample. An alternative approach is to place a halftone 

image on the paper and measure the average Yule– 

Nielsen effect of the substrate and relate the effect to 

the value of k p . In the current work, the Yule–Nielsen 

effect was measured by placing a graphic arts “lith” film 

with a stochastic halftone wedge ( F = 0 to F = 1) in 

vacuum contact with the substrate, emulsion to paper. 

The stochastic halftone was generated by a proprietary 

error diffusion process and printed on a commercial 

image-setter. The halftone dot pattern was generated 

as a grid of square dots and spaces of L = 0.042 mm on 

each side. Figure 5 shows R p versus F measured from a 

histogram analysis of this halftone using microdensitometric 

analysis techniques described perviously. 1,5 

The R p versus F function for a stochastic halftone has 

been shown to be well modeled with Eq. 6 when R i is 

zero, 10 and the value of R i was zero within experimental 

error in the current work. 

[ ] 

B 

Rp 

/ Rg 

= 1−w⋅ 1−( 1 −F) 

(6) 

A power factor of B = 1.2 was found to fit measurements 

made with the halftone film in contact with all 

paper and synthetic printing substrates used in this 

study. The value of w is the value of (1 – R p /R g ) extrapolated 

to F = 1. 

The value of w has been shown experimentally to be 

related to k p by Eq. 7. 10,12 

or 

⎧−Ak 

⋅ p ⎫ 

w = 1−exp ⎨ ⎬ 

(7a) 

⎩ L ⎭ 

Kubelka–Munk Theory and the Yule–Nielsen Effect on Halftones Vol. 43, No. 4, July/Aug. 1999 367

1 

100 

K.100 

R 

50 

mm –1 

S 

0 

500 600 

Figure 6. Reflection spectrum of yellow plain paper at infinite 

thickness, R∞ (O), and over black, R b (X). Paper is 0.072 

mm thick. 

L w 

kp = − ⋅ln( 1 − ) 

(7b) 

A 

The value of L = 0.042 mm for this stochastic halftone, 

k p = 0.14 mm and w = 0.59 for the Crisper TM reference 

material. Thus, the value of A = 0.267 can be calculated. 

The physical justification for Eq. 7 is based on the 

probability model of halftone optics discussed previously. 

8,13 For R i = 0, P a = (1 – w) where P a is defined as 

the fraction of light which emerges from a single square 

area of the paper of dimension L after entering that same 

area and scattering within the paper . The value of P a 

must be unity for a paper of zero scattering length, k p = 

0, with w = 0. But as the scattering length, k p , increases, 

P a decreases and w increases. As k p approaches infinity, 

w must approach unity and P a must approach zero asymptotically. 

Equation 7 has the required limit of w = 0 

at k p = 0 and w = 1 as k p ∞ and thus is a reasonable 

empirical model for w versus k p . 

The values of L = 0.042 mm and A = 0.267 were used 

with this halftone film to measure R p versus F for all 

substrates in this project. Equation 7 was applied to calculate 

the corresponding value of the MTF constant k p . 

By using 20 nm band pass filters, k p values versus λ 

were measured. 

K and S for Yellow Plain Paper. K and S values for 

several papers and synthetic substrates were deter - 

mined by measuring the reflectance, R ∞ , of a thick stack 

of the substrate and then measuring R b , the reflectance 

of a single sheet of the substrate with a black background. 

The thickness of the substrate was also measured, 

and the values of K and S were calculated by a 

numerical solution of the Kubelka–Munk equations for 

R∞ and R b . 6 As a check of the experimental method, an 

integrating sphere spectrophotometer was used to measure 

the total transmitted light through the samples, 

T, and values of K and S were calculated from the 

Kubelia–Munk equations for R ∞ and T. The two methods 

gave the same K and S values within experimental 

error. T data lead to lower experimental error for highly 

absorbing samples. 

λ 

0 

500 600 

Figure 7. Values of S in mm –1 and 100 . K in mm –1 from data in 

Fig. 6. 

Figure 6 shows R ∞ and R b for a commercially manufactured 

sample of yellow plain paper. The corresponding 

values calculated for of K and S are shown in Fig. 7. 

Note the value of S does not change significantly , but 

the value of K does. Equation 5 was applied to each pair 

of K and S values to calculate the MTF versus ω function. 

The value of ω = ω o at which MTF = 0.5 was noted. 

Table I summarizes the values of K, S, k p , and 1/ ω o . If 

Eq. 5 is correct, then 1/ ω o should be a good correlate of 

k p . However, as shown in Fig. 8, the change in K over 

the range of this experiment does not result in the 

change in k p predicted by 1/ ω o from Eq. 5. 

K and S for Coated Paper and Crisper TM . An experimental 

correlation between S and k p has previously 

been shown. 14 In the current work five substrates, 

shown in Table II, were examined at two wavelengths, 

500 nm and 580 nm, using 20 nm band pass filters. 

Values of S, K, and k p were measured as described 

above, and the results are summarized in T able II. 

These samples show only small differences in K but 

significant differences in S. Figure 9 shows the relationship 

between k p and 1/S. For a negligible absorption 

coefficient, then, this data indicates Eq. 8 is an 

adequate model of k p versus S within experimental error, 

with a unitless constant of c = 10. 

k p = c/S (8) 

In order to determine the impact of higher values of K 

on k p , samples of the Crisper TM standard were dyed by 

boiling in a proprietary cyan dye solution. The dye was 

meant for use with this type of sample and produced 

darker cyan color as a function of boiling time. Samples 

λ 

TABLE I. Spectral Data on Yellow Plain Paper 

k p 

, in mm, measured 1/ω o 

, in mm, 

λ, nm S in mm –1 K in mm –1 from R p 

versus F from Eq. 5 

480 43 2.66 0.23 0.22 

500 45 0.89 0.24 0.32 

540 45 0.38 0.23 0.44 

568 45 0.23 0.28 0.53 

580 45 0.20 0.24 0.56 

600 44 0.17 0.26 0.60 

640 43 0.26 0.29 0.61 


k p and (1/ω o ), in mm 

0.5 

0 

1/ω o 

k p 

500 600 

Discussion 

Figure 11 does not indicate any significant impact of 

the Kubelka–Munk absorption coefficient K on the Yule– 

Nielsen effect, represented by the k p metric. Intuition 

might suggest that a high value of K would decrease 

the average distance that light scatters before emergλ, 

nm 

Figure 8. k p and 1/ω ο versus wavelength. 

TABLE II. Scattering Properties of Different Substrates 

Material λ, nm S, mm –1 K, mm –1 kp, mm 

coated paper 500 39.8 0.51 0.21 

coated paper 580 36.5 0.70 0.27 

Crisper TM 500 85.7 0.26 0.13 

Crisper TM 580 77.8 0.17 0.19 

HS plastic 500 143.0 0.23 0.10 

HS plastic 580 130.0 0.20 0.12 

LS plastic 500 23.6 0.05 0.37 

LS plastic 580 22.8 0.05 0.41 

plain paper 500 45 0.89 0.24 

plain paper 580 45 0.20 0.24 

1 

0.04 

1/S, mm 

0.02 

0 

0 0.2 0.4 

k p , mm 

Figure 9. 1/S versus k p from Table II. 

R × 

Figure 10. Spectra of coated paper at three dye levels. 

16 

0 

450 λ, nm 650 

of the coated paper were also dyed by soaking in an aqueous 

solution of a proprietary cyan ink jet dye. Again, 

dying time governed the darkness of the color . Figure 

10 illustrates the reflection spectra for the coated paper 

samples. 

Both the dyed and not dyed samples of both substrates 

were analyzed for K and S values as before. S was found 

not to change, but K increased with the dying time, as 

expected. Measurements of k p were made at 500 nm 

where R ∞ and K changed only slightly, and at 580 nm 

where a significant changes in R ∞ and K were observed. 

The results are summarized in T able III. Figure 1 1 

shows the K as a function of k p . 

K, mm -1 

0 

500 nm 

580 nm 

0 0.3 

k p , mm 

Figure 11. Dye concentration series, K versus k p for: Coated 

paper at 500 nm (O); Coated paper at 580 nm (●); and Crisper TM 

at both at 500 and 580 nm, (X). 

Kubelka–Munk Theory and the Yule–Nielsen Effect on Halftones Vol. 43, No. 4, July/Aug. 1999 369

TABLE III. The Effect of Cyan Dye on the Properties of Substrates 

Paper/dye K in mm at 500 nm k p in mm at 500 nm R ∞ at 500 nm K in mm at 580 nm k p in mm at 580 nm R∞ at 580 nm 

P.Paper_0 0.51 0.21 0.830 0.70 0.27 0.823 

P.Paper_1 0.56 0.20 0.853 1.41 0.27 0.744 

P.Paper_2 0.65 0.19 0.842 3.80 0.25 0.574 

P.Paper_3 0.16 0.20 0.736 15.10 0.21 0.278 

Crisper_0 0.26 0.13 0.925 0.17 0.19 0.935 

Crisper_1 0.95 0.14 0.854 3.25 0.18 0.704 

Crisper_2 1.39 0.16 0.834 6.93 0.19 0.600 

1.5 

1 

K -1 , mm 

R × 

0 0 0.3 

k p , mm 

Figure 12. Coated Paper at 580 nm. 

0 

1 2 

Figure 13. Coated paper and Crisper TM at both at 580 nm. 

Calculated from the data shown in Fig. 11 with A = 0.267 and 

a dot size of 80 µm. 

n 

ing from the paper substrate. Thus, one might expect a 

decrease in k p as K increases. The only data that might 

suggest such behavior is the dyed coated paper at 580 nm 

in Fig. 11. This data was re-plotted as K –1 versus k p as 

shown in Fig. 12, and there is no convincing evidence for 

the kind of linear trend observed between k p and S –1 . 

It is not possible to reach the conclusion that K has 

no impact on the Yule–Nielsen effect. However, it is possible 

to reach practical conclusions. Figure 13 shows the 

values of R ∞ versus n for the dyed samples at 580 nm, 

where n is calculated from the k p values in Table III by 

using Eq. 4. Over this range of R ∞ there is no evidence 

of a correlation of any kind between K and k p or n. Therefore, 

if K has an effect on k p it is not of sufficient magnitude 

to be of any practical significance. Thus, Eq. 7 

rather than Eq. 5, coupled with Eq. 4, provides a useful 

connection between Kubelka –Munk theory and the 

Yule–Nielsen effect. 

A final caution about experimental accuracy in this 

work is in order. The measured values of k p are internally 

consistent and are based on the same experimental 

technique. The experimental precision is indicated 

by the scatter in the data. However , the experimental 

accuracy is based on a single Fourier analysis of an edge 

scan of a reference material. Thus, while the trends and 

functional relationships are well represented, the calibration 

constants A and c may or may not be accurate. 

Moreover, the particular value of A may depend on the 

particular geometry of the halftone one uses. While it is 

easy to compare relative values of k p , absolute values 

are much more difficult to measure with confidence. 

Acknowledgment. Special thanks to our lab colleagues, 

A. Tsujita and S. Yamaguchi for stimulating 

discussions and challenging arguments. 

References 

1. J. S. Arney, P. G. Engeldrum and H. Zeng, An expanded Murray-Davies 

Model of Tone Reproduction in Halftone Imaging, J. Imag. Sci. Technol. 

39, 502 (1995). 

2. P. G. Engeldrum, The color between the dots, J. Imag. Sci. Technol. 

38, 545 (1994). 

3. P. G. Engeldrum, The color of halftone printing with and without the 

paper spread function, J. Imag. Sci. Technol. 40, 240 (1996). 

4. S. Gustavson, Modeling of light scattering effects in Print, Thesis LIU- 

ISBN:91-7871-623-3, and J. Imag. Sci. Technol. 41, 283 (1997). 

5. J. S. Arney and Y. Wong, Histogram analysis of the microstructure of 

halftone images, Proc. IS&T PICS Conf. IS&T, Springfield, VA, 1998, 

p. 206. 

6. D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry, 

J. Wiley & Sons, NY, pp. 420–438 (1975). 

7. G. L. Rogers, Optical dot gain in a halftone print, J. Imag. Sci. Technol. 

41, 643 (1997). 



9. J. C. Dainty and R. Shaw, Image Science, Academic Press, NY, 1974, 

p. 258. 

10. J. S. Arney and M. Katsube, A probability description of the Yule- 

Nielsen Effect II: The impact of halftone geometry, J. Imag. Sci. 

Technol. 41, 637 (1997). 

11. P. Engeldrum and B. Pridham, Application of turbid medium theory to 

paper spread function measurements, Proc. TAGA, 339 (1995). 

12. J. S. Arney, C. D. Arney and P. G. Engeldrum, Modeling the Yule- 

Nielsen halftone effect, J. Imag. Sci. Technol. 40, 233 (1996). 

13. J. S. Arney and S. Yamaguchi, Symmetry Properties of Halftone Images 

I: Scattering symmetry and pattern symmetry, submitted to J. 


14. J. S. Arney, C. D. Arney, M. Katsube, and P. G. Engeldrum, An MTF 

Analysis of Papers, J. Imag. Sci. Technol. 40, 19 (1996). 



The Free Radicals and Iron of Photographic Gelatin Doped with Na 2 

S 2 

O 3 

* 

Yi-Heng Zhang,* Ji Tan , Jie Li, Tian-Tang Yan, Shu-qin Yu † 

* Department of Applied Chemistry, University of Science and Technology of China, Hefei, Anhui Province, Peoples Republic of China 

† 

Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui Province, Peoples Republic of China 

Si-Yong Zhuang 

Research Institute of Fine Chemicals, East China University of Science and Technology, Shanghai, Peoples Republic of China 

Bi-Xian Peng 

Institute of Photographic Chemistry, Academia Sinica, Beijing, Peoples Republic of China 

Five kinds of gelatins were investigated, and varying amount of sodium thiosulfate was added to study the effect of Na 2 S 2 O 3 on 

photographic gelatin. The ubiquinone and RS• radicals were detected and the change of their concentrations in photographic 

gelatins were studied by electron spin resonance (ESR). The concentration of ubiquinone, which was dependent on the equilibrium 

among the hydroubiquinone, ubiquinone radical and ubiquinone compounds, increased to a maximum value and then 

decreased with the increasing amount of sodium thiosulfate. The study of the chemical state of iron in gelatin with varying 

amounts of sodium thiosulfate by x-ray photoelectron spectroscopy (XPS) showed that the state of iron in gelatin was not affect ed 

by adding sodium thiosulfate. 


Introduction 

Although many people have tried to substitute synthetic 

materials for photographic gelatin, gelatin is still a basic 

material in preparing photographic emulsions. Gelatin 

affects almost every step of the photographic process. 

Sodium thiosulfate is one of the most commonly used 

sensitizer. 1 The sensitization mechanism owing to the 

interaction between sodium thiosulfate and silver halide 

grains has been widely reported. The main function 

of sodium thiosulfate in the sensitization is that it 

reacts with silver halide, forming sensitization centers 

on the surface of silver halide grains. 2,3,4 However, few 

studies of the interaction between sodium thiosulfate 

and gelatin have been disclosed so far. It is well known 

that during the production of gelatin in industry , foreign 

iron may be unaviodably introduced into gelatin 

by the raw materials, accessory materials and equipment. 

The foreign iron, which complexes with gelatin, 

has strong desensitization effect on the photographic 

emulsion. 5 During the sulfur sensitization, the change 

Original manuscript received July 7, 1998 

* This project was financially supported by National Nature Science 

Foundation of China (29876038) 

† To whom correspondence should be addressed 


of the chemical state of foreign iron, which acts as a 

deep electron trap, is a subject that interests many photographic 

scientists. In this paper , the composition of 

active free radicals and their changes in gelatin before 

and after the addition of sodium thiosulfate were studied 

by electron spin resonance (ESR) technique and the 

effect of the amount of sodium thiosulfate on foreign 

iron in gelatin was studied by x-ray photoelectron spectrometry 

(XPS). The study of the interaction between 

thiosulfate and photographic gelatin undoubtedly will 

give new experimental evidences to the mechanism of 

the sulfur sensitization. 

Experimental 

The Preparation of Samples for ESR and XPS Measurement. 

Five kinds of photographic gelatins, A: 

Baotou gelatin 600 # (Baotou, China), B: Kaiping gelatin 

(Kaiping, China), C: Rousselot gelatin N51811 (France), 

D: Japanese gelatin NCH 1-3, and E: Japanese gelatin 

2104 were used. Samples A, B, C and D are limed processing 

gelatin, and E is from IAG. The gelatins of each 

kind were soaked in water at room temperature for 30 

min., then heated to 50 ° C and dissolved. After varying 

amounts of an aqueous solution of sodium thiosulfate 

was added (see Table I), the gelatin solutions were coated 

onto film bases. After drying at room temperature, thin 

film samples were obtained which were used directly 

for XPS measurement. For ESR measurement the gelatin 

films were separated from the film bases and ground 

to powder. 

371

TABLE I. Series Numbers and Amounts of Added Sodium 

Thiosulfate 

The amount of Na 2 S 2 O 3 Five kinds of gelatins 

mg/ g gelatin A B C D E 

0 A-a B-a C-a D-a E-a 

2.44 A-b B-b C-b D-b E-b 

14.80 A-c B-c C-c D-c E-c 

27.10 A-d B-d C-d D-d E-d 

39.50 A-e B-e C-e D-e E-e 

49.30 A-f B-f C- f D-f E-f 

ESR Measurement. The ESR measurement of the 

sample powder was carried out in an electron spin resonance 

spectrometer, Varian E115 (Varian Co. U. S. A.) 

at room temperature. The ESR spectrometer worked at 

X band and the magnetic modulation was 100 kHz. The 

first order derivative ESR spectra were recorded at room 

temperature. DPPH (diphenyl-picryl-hydrazyl, g = 

2.0036) and the distance between the third peak and 

the fourth peak of the ESR spectrum of ZnS • Mn 2+ (6.81 

mT) were used as the standards to determine the parameters 

of ESR spectra of the samples. The Landé g- 

factor is determined by the equation: 

Figure 1. The ESR spectra of gelatin A with varying amount 

of Na 2 S 2 O 3. a: to f: the amounts of Na 2 S 2 O 3 are 0, 2.44, 14.8, 

27.1, 39.5, 49.3 mg/g gelatin, respectively. 

⎡ HR 

− HS 

⎤ 

gS 

= gR⎢1 

+ ⎥ 

⎣ HS 

⎦ 

where: 

S — the samples measured, 

R — the standard samples, 

H — the intensities of the resonance magnetic 

field of the corresponding samples. 

The spin signals of gelatins A and D were quantitatively 

analyzed by weighing samples and integrating the 

areas under the ESR spectral curves. DPPH 9.7 × 10 15 

spin/g was taken as the standard to determine the spin 

concentrations of the corresponding free radicals. 

XPS Measurement. ESCA analysis was carried out 

with a multi-function X-ray photoelectron spectrometer, 

Model ESCALAB MK II (VG Co. England). The pressure 

in the ultrahigh vacuum chamber of the spectrometer 

was lower than 5 × 10 –7 Pa. Mg Ka radiation with 

photon energy hν = 1253.6 eV was used as a radiation 

source. The power of the X-ray target was 320 W and 

the pass energy was 30 eV . Carbon deposited on the 

sample surface which exhibits the sharp peak of C1s at 

284.6 ± 0.1 eV was used as the standard of binding energy. 

The characteristic peak of Fe(2p 3/2 ) was used in 

the analysis. Because the iron content was very low in 

the gelatins, the XPS signal of iron was accumulated 

several times. 

Results and Discussion 

The Effect of Na 2 S 2 O 3 on the Photographic Gelatin. 

The ESR spectra of all five series of gelatin samples 

are shown in Figs. 1 through 5. The figures show that 

the five gelatin samples in which no Na 2 S 2 O 3 was added 

can exhibit free radical signals at g = 2.004 and, except 

D, all other four series of gelatins in which varying amount 

of Na 2 S 2 O 3 was added show the same signals. Zweier and 

co-workers and Zhao and co-workers 6,7,8,9 thought that 

in the biological system the free radicals that could exist 

at room temperature and could give ESR signals at 

Figure 2. The ESR spectra of gelatin B with varying amount 



g = 2.004 were ubiquinone or ubiquinone-like free radicals, 

whose structure can be expressed below: 

R 

R 

O. 

OH 

CH 3 

CH 3 

- 

n =5 – 10 

- 

CH 2 CH C CH 2 H 

- 

-n 

This class of free radicals acts mainly as electron or 

hydrogen carriers in redox reaction in the biological 

system. 7,8 Gelatin is a mixture made up from various 

biological materials, so that the signal at g = 2.004 obtained 

in this study must be contributed by ubiquinone 

or ubiquinone-like radicals. 

372 Journal of Imaging Science and Technology Zhang et al.

TABLE II. Effect of the Amount of Na 2 S 2 O 3 on the Spin 

Concentration of a Radical with g = 2.004 in Gelatin 

The spin concentration (× 10 16 spin/g) 

The gelatin series A B C D E 

0 0.7 0.2 0.4 0.4 0.5 

The amount of 2.4 2.9 1.9 1.5 / 0.8 

Na 2 S 2 O 3 14.8 2.6 1.6 2.1 / 0.8 

(mg/g gelatin) 27.1 2.3 1.6 2.4 / 1.6 

39.5 1.3 1.1 2.1 / 1.8 

49.3 1.1 0.5 0.8 / 1.5 

TABLE III. Effect of the Amount of Na 2 S 2 O 3 on the Binding 

Energy of Iron in Gelatin 

The amount of Na 2 S 2 O 3 The binding energy 

Gelatin (mg/g gelatin) of Fe (2p 3/2 , eV) 

0 707.3 

A 27.1 707.6 

49.3 707.4 

0 706.8 

D 27.1 707.5 

49.3 707.6 

Figure 3. The ESR spectra of gelatin C with varying amount 



Figure 5. The ESR spectra of gelatin E with varying amount 



Figure 4. The ESR spectra of gelatin D with varying amount 



In addition, samples A-a, B-a and E-a give ESR signals 

at g 1 = 2.246 and g 2 = 1.934, that gradually disappear 

with increase of the amount of Na 2 S 2 O 3 . Sample 

C-a did not exhibit ESR signals at g 1 = 2.246 and g 2 = 

1.934, but these signals appear and their intensities 

increase with increase of the amount of Na 2 S 2 O 3 . It was 

reported that the signals at g 1 = 2.246 and g 2 = 1.934 

corresponded to g // and g ⊥ of RS • radicals, respectively. 10,11 

We presume the RS • radicals come from the low level of 

cysteine/cystine present in gelatins. 

The ESR spectra of gelatin D are quite different from 

the others. Among six samples of gelatin D only the 

sample without addition of Na 2 S 2 O 3 (D-a) exhibits an ESR 

signal at g = 2.004 This result indicates that there are 

relatively few active groups in Roussalot gelatin that may 

be considered as an inert gelatin with high purity. 

It is well known that a free radical has high reactivity, 

so the free radicals in gelatin can certainly be expected 

to influence the photographic properties of an 

emulsion, in which gelatin is a principal component. 

Figures 1 through 5 show that the kinds and contents 

of radicals are obviously different in five gelatins. This 

is possible because the raw materials and the technologies 

of the production of gelatin are different for different 

gelatins. 

Because the ESR spectra of almost all gelatin 

samples exhibit the signal of the ubiquinone radical, 

the spin concentrations of five series of gelatin samples 

were quantitatively determined by using DPPH 9.7 × 

10 15 spin/g as the standard. The results are listed in 

Table II. 

Table II indicates that for gelatins A, B, C and E, 

the spin concentrations of the ubiquinone radical (g = 

2.004) change when Na 2 S 2 O 3 is added. The spin concentration 

of the ubiquinone radical increases first to 

a maximum value and then decreases with the increasing 

amount of Na 2 S 2 O 3 . The amounts of Na 2 S 2 O 3 that 

The Free Radicals and Iron of Photographic Gelatin Doped with Na 2 S 2 O 3 * Vol. 43, No. 4, July/Aug. 1999 373

correspond to the maximum spin concentration are different 

for different gelatins. The effect of the amount 

of Na 2 S 2 O 3 on the spin concentration may be interpreted 

by the following. 

In the gelatin system there are two reversible successive 

reactions, shown in Eqs. 1 and 2: 

R 

R 

R 

R 

R 

R 

R 

R 

O 

O 

OH 

OH 

O. 

OH 

O. 

OH 

CH 3 

CH 3 

- 

- 


- 

-n 

CH 3 

CH 3 

- 

- 


- 

-n 

+ H + + e 

(1) 

CH 3 

CH 3 

- 

- 


- 

-n 

(2) 

CH 3 

CH 3 

- 

- 


- 

-n 

+ H + + e 

Because Na 2 S 2 O 3 is a reducing agent, it can provide 

electrons. When Na 2 S 2 O 3 is added the equilibria of both, 

reactions 1 and 2 shift to the left. The change of the 

concentration of the ubiquinone radical has two contributions: 

it is formed by the reverse of reaction 2, but is 

depleted by the reverse of reaction 1. Therefore, as 

Na 2 S 2 O 3 is constantly added the concentration of the 

ubiquinone radical rises first, and then drops. The 

change of the concentration of the RS • free radical and 

the equilibrium relationship have yet to be studied. 

The Effect of Na 2 S 2 O 3 on the Chemical State of Iron. 

To study the effect of Na 2 S 2 O 3 on the chemical state of 

iron, the XPS spectra of gelatins A and D with varying 

amount of Na 2 S 2 O 3 were measured. The binding energy 

values of iron are shown in Table III. 

The iron binding energy values for both gelatins without 

adding Na 2 S 2 O 3 are 707.3 eV and 706.8 eV, respectively. 

In comparison with the binding energy of typical 

ferric ions, e.g. 711.4 eV for FeCl 3 

12 

, notable chemical 

shifts to lower value occur. The shift values are 4.1 eV 

to 4.6 eV, indicating that in both gelatins the concentration 

of outmost shell electron cloud of iron is higher 

than that of FeCl 3 and the iron in the gelatin is not in 

the trivalent state, but in a complex state with lower 

valence, bivalence, univalence or zero valence. 9 Table 

III also indicates that the addition of Na 2 S 2 O 3 has no 

effect on the iron state in gelatin. 

Conclusion 

Five kinds of gelatins with varying amount of Na 2 S 2 O 3 

were studied by ESR technique. The ubiquinone radical 

and RS • radical were detected in these gelatins. The 

kinds and concentrations of the free radicals are closely 

related to both Na 2 S 2 O 3 amount and the kind of the gelatin. 

The concentration of ubiquinone is dependent on 

the equilibrium among the hydroubiquinone, ubiquinone 

and ubiquinone compound. The addition of Na 2 S 2 O 3 has 

no effect on the state of iron in gelatin. 

References 

1. T. H. James, The Theory of Photographic Process, 4th ed., New York, 

Macmillan Publishing Co., 1977. 

2. J. W. Mitchell, Photogr. Sci. Eng. 22, 49 (1972). 

3. J. W. Mitchell, Photogr. Sci. Eng. 29, 1 (1979). 

4. E. Moisar, J. Photogr. Sci. 16, 102 (1968). 

5. R. Wang and B. Peng, Photogr. Sci. Photochem. (Chinese) 7, 35 

(1988). 

6. J. L. Zweier, P. Kuppusamy and R. Williams, J. Biological Chem. 

264(32), 18890 (1989). 

7. B. Zhao, W. Xi and Y. Chen, J. Biological Phys. (Chinese) 10(1), 170 

(1994). 

8. J. Xu, G. Liu and R. Zhen, J. Spectroscopy (Chinese) 12(6), 635 

(1995). 

9. Y.-H. Zhang, J. Li, T-T. Yan, S.-Q. Yu, S.-Y. Zhuang, and B.-X. Peng, 

Imaging Sci. J. 46(4), 25 (1998). 

10. L. D. Kisprt and L. A. Files, J. Chem. Phys. 78, 4858 (1983). 

11. T. P. Nguyen, M. Giffard and P. Molinie, J. Chem. Phys. 100(11), 8340 

(1994). 

12. C. D. Wagner, Handbook of X-ray Photoelectron Spectroscopy, Minnesota, 

Perkin-Elmer Co., 1979. 

374 Journal of Imaging Science and Technology Zhang et al.


Calculated Properties of Sulfur Centers on AgCl Cubic Surfaces 

Roger C. Baetzold 

Imaging Research and Advanced Development, Eastman Kodak Company, Rochester, New York 

Calculations of various sulfur-containing centers adsorbed to sites on the AgCl surface are presented. A density functional method 

followed by a classical lattice ion relaxation is employed in this work. Several different centers such as Ag 4 S 2 have energy levels 

positioned to trap holes, while Ag 3 S + and Ag 5 S 2 

+ 

have levels positioned to trap electrons. It is found that a sulfide ion at a kink site 

that is compensated by interstitial silver ion undergoes relaxation in the presence of an electron leading to a trap depth of 

several tenths of an electronvolt. It appears that this may be an important step in chemical sensitization. These results are 

consistent with stepwise addition of electrons and silver ions resulting in latent image formation. 


Introduction 

While the importance of S sensitization of silver halide 

emulsion grains is well established, 1 the microscopic description 

of the structure, composition and function of 

the active centers is still being elaborated. In Hamilton’ s 

analysis 2 of latent image formation, the improved efficiency 

of the photographic response is attributed to an 

increase in efficiency of the nucleation step whereby a 

stable two-electron center is formed. In this model it is 

thought that small sensitizing aggregates of Ag 2 S provide 

electron trapping levels adjacent to surface-positive 

kink sites, that enhance the probability of electron 

trapping leading to latent image. A further analysis 3 of 

electron coupling to the silver halide surface sites led 

to a concept whereby electron trapping at a silver atom 

is promoted by the chemical sensitization center . This 

is due to an electron-trapping level roughly 0.2–0.3 eV 

below the conduction band that is associated with the 

sensitization center. This allows for a more efficient initial 

trapping into a shallow level followed by de-excitation 

into a deeper level at the silver center. 

Different viewpoints about the role and energy levels 

of silver sulfide in sulfur sensitization have been expressed. 

Several experiments have been cited 4 that are 

consistent with an electron trapping role of the sulfide 

centers. For example, thermally stimulated current 

spectra measured 5 on emulsion grains have given an 

electron trap depth of 0.39 eV at sulfur centers. Experimental 

electron lifetime and ionic conductivity data 6 

were analyzed for cubic AgBr emulsions to give a 0.31 

eV electron trap depth for S sensitized grains. The temperature 

dependence of the efficiency of red light sensitivity 

of S sensitized emulsions was measured to be 0.33 



eV 4 , which was interpreted to represent the electron trap 

depth. Later experiments by Zhang and Hailstone, 7 however, 

led to an interpretation that the technique measures 

the activation energy for hole release from the 

excited center rather than electron release. Overall, 

however, there seems to be agreement as to the electron 

trapping role of the S sensitization centers. 

Tani 8 has characterized S sensitization centers on 

AgBr emulsion grains through photoconductivity, sensitometry 

and a variety of physical measurements. The 

results were interpreted in terms of hole trapping at 

monomers of Ag 2 S and electron trapping at (Ag 2 S) 2 centers 

in the AgBr solid solution. The Ag 2 S cluster was 

thought be a fog center if located on the AgBr grain surface. 

Attention was drawn to the role of dimeric chalcogenides 

as hole trapping centers in silver halide in the 

review by Spoonhower and Marchetti. 9 Keevert and 

Gokhale 10 have presented evidence that the sensitizing 

center consists of dimers of Ag 2 S. Kanzaki and 

Tadakuma 11 has also presented physical evidence for two 

S atoms as involved in the sensitization center . An interesting 

physical model is presented that seems to focus 

on attraction of interstitial silver ions to the S 

centers. The interstitial silver ion is known to be a shallow 

electron trap, and it is argued that two S centers 

can attract two Ag + interstitial ions and form a deeper 

electron trap. The deep trapped state is postulated to 

result from the displacement of interstitial silver ions 

near the sensitization center. 

The purpose of this report is to investigate some of 

the concepts discussed above in terms of the electronic 

properties of S centers on and in the silver chloride surface. 

We hope to identify the positions of energy levels 

which could be involved in electron or hole trapping. 

Then it should be possible to construct a geometric model 

for the sensitization center and evaluate whether latent 

image formation is possible at such a site according 

to the nucleation and growth mechanism. 

Additionally, we hope to understand to what degree the 

properties of S centers in, as compared to on, the silver 

375

Figure 1. Sketch of the models used in this calculation. (a) 

Hemispherical point-charge array showing placement of the 

cluster. (b) Ag 5 Cl 4 cluster used for (100) surface. (c) Ag 4 Cl 4 cluster 

used for positive kink. (d) Ag 4 Cl 3 S cluster used for single 

kink. 

halide surface may differ . In Part II we describe the 

methods of calculation used in this work. The results 

for free and adsorbed S centers are given in Part III. 

The results are discussed in Part IV where we evaluate 

the likely geometric structure of the S sensitization center. 

Conclusions are given in Part V. We begin our studies 

on the (100) AgCl surface because of its 

computational ease compared to AgBr. Future work will 

concentrate on the AgBr surfaces. 

Method 

These calculations have been performed quantum mechanically 

with the local density method using the BLYP 

functional, which has worked well for studies of silver 

clusters. 12 The overall model consists of an array of point 

charges to which a cluster unit treated quantum mechanically 

is attached. The point-charge array contains 

roughly 1200 unit charges placed at silver and halide 

sites, has a hemispherical shape. The flat surface of this 

array has the (100) surface. Studies on the (100) sur - 

face are carried out by embedding a planar Ag 5 Cl 4 unit 

into the surface and treating the entire unit quantum 

mechanically. The entire unit has 0 charge in the ground 

state. Sketches of these pieces are shown in Fig. 1. A 

kink site is modeled by adding a partial layer of point 

charges to the flat surface and embedding a Ag 4 Cl 4 unit, 

sketched in Fig. 1(c). Kink sites containing one S ion 

are treated in much the same way as shown in Fig. 1(d). 

We employ a Ag 4 Cl 3 S embedded cluster to represent the 

single positive kink. The sulfur ions must be properly 

compensated in this model. The sulfur ion is compensated 

by adding an interstitial silver ion at the adjacent 

interstitial position. A silver center is treated by 

placing a number of silver atoms on these clusters and 

determining their optimum position. In this calculation 

the long-range Coulomb field of the crystal is provided 

by the point-ion array, while the atoms of the silver center 

interact directly with other quantum mechanical 

ions. Then a second calculation is performed in order to 

account for the lattice polarization energy. This is a classical 

atomistic calculation for surfaces performed with 

the MIDAS/CHAOS code. 13 The ions represented quantum 

mechanically are fixed at their positions determined 

in the first calculation and assigned a charge determined 

Figure 2. Sketches of calculated equilibrium structure for 

Ag 2 S, Ag 3 S + , Ag 4 S ++ , Ag 4 S 2 , and Ag 6S 2 

++ 

. Bond angles and distances 

(Å) are given. 

from the Mulliken procedure. All of the silver and halide 

ions are allowed to displace to an equilibrium position 

in response to the cluster . The energy change for 

this step is added to the quantum mechanical energy 

determined in the first part to give the total system 

energy. Total energies of the appropriate charge states 

are subtracted to give the ionization potential or electron 

affinity of the cluster. 

The CADPAC code 14 is employed for the quantum 

mechanical calculations. A double zeta plus polarization 

full basis is used for S and Cl basis functions. The Ag 

atom is described by a model potential 15 with a double 

zeta plus polarization basis. We have previously shown 12 

the accuracy of this type of calculation by comparison 

of calculated ionization potential values for silver clusters 

with experimental values. The agreement with our 

experiment is within a few tenths of an eV. 

There are several approximations in this first treatment 

of the sulfur sensitization centers adsorbed to 

the silver chloride surface. The use of larger fragments 

representing the defect surface site in the quantum mechanical 

part of the calculation would be desirable. This 

would prevent the possible unphysical penetration of 

wave functions from the quantum mechanical unit into 

the point ions. A second approximation involves the 

computation of the lattice polarization energy by a procedure 

that attempts to achieve self-consistency between 

the quantum mechanical unit and the rest of 

the crystal. This gives a lattice polarization energy of 

the order of a few electronvolts for some of the charged 

silver centers and cannot be neglected. Overall, there 

is no independent means to specify the absolute accuracy 

of these calculations without experimental data, 

thus, we emphasize the relative values for different 

sized silver clusters. 

Results 

Free Ag n S m (n = 1 to 6; m = 1, 2). A good starting place 

for the study of sensitization by silver sulfide centers is 

376 Journal of Imaging Science and Technology Baetzold

TABLE I. Calculated Properties of Silver Sulfide Clusters at 

Optimized Geometry 

A. Reaction Energy (eV)a 

Reaction 

∆E 

1 –0.08 

2 –2.70 

3 1.60 

4 –2.58 

5 –0.76 

B. Ionization Potentials (IP) and Electron Affinity (EA) 

Cluster IP EA 

Ag 2 S 7.40 1.23 

Ag 3 S + 12.11 5.89 

Ag 4 S + 10.33 5.87 

Ag 4 S 2 5.38 2.17 

Ag 5 S 

+ 

2 9.91 5.74 

++ 

Ag 6 S 2 13.96 8.68 

a 

Negative values indicate exothermic reactions. 

Figure 3. The kink model containing sulfide and a compensating 

silver ion is shown in top view. The ions surrounded by 

squares are in the top plane and ions surrounded by circles 

are in the second plane. The starred ions also contain a second 

plane of ions underneath. The hemispherical point ions complete 

this model. 

the free clusters. We determine the optimized geometry 

of several small clusters as well as their ionization potential 

(IP) and electron affinity (EA). The optimized 

geometry is shown in Fig. 2 for several of these clusters. 

Note the nonlinear bond angles in Ag 2 S and Ag 3 S + 

characteristic of directional covalent bonding as contrasted 

to ionic bonding. The Ag 3 S + and Ag 4 S ++ cluster 

geometry deviates from planar by the indicated bond 

angles. We also show some larger Ag 4 S 2 and Ag 6 S 2 

++ 

clusters 

that are slightly favored in a three-dimensional 

versus entirely planar structure. These cyclic structures 

are favored, which can be visualized to result from coupling 

of fragments like Ag 2 S. 

We now turn to the reactions of the small chalcogenide 

clusters with silver ion because the latter species is often 

available for reaction in silver halide grains. The 

reactions considered include: 

Ag 2 S + Ag 2 S → Ag 4 S 2 (1) 

Ag 2 S + Ag + → Ag 3 S + (2) 

Ag 3 S + + Ag + → Ag 4 S ++ (3) 

Ag 4 S 2 + Ag + → Ag 5 S 2 

+ 

(4) 

Ag 5 S 2 

+ 

+ Ag + → Ag 6 S 2 

++ 

(5) 

We have computed the energy change for each of these 

forward reactions from the total quantum mechanical 

energy of each species and give these values in Table I. 

Several comments are noteworthy. Dimerization of Ag 2 S 

units is exothermic. The addition of a silver ion to Ag 2 S 

is very exothermic to form Ag 3 S + , but addition of a second 

silver ion becomes endothermic. In the case of the 

dimerized species Ag 4 S 2 , addition of the first silver ion 

is very exothermic and similarly for a second silver ion. 

Both reaction 3 and reaction 5 involve the addition of a 

silver ion to a positively charged species. Reaction 5 is 

more favorable energetically because the relative weak 

stability of the Ag 5 S 2 

+ 

intermediate species of low symmetry 

while Ag 3 S + is of higher symmetry. Thus, forming 

the product Ag 6 S 2 

++ 

is relatively favored and accounts 

for the exothermicity of reaction 5. These results suggest 

that there will be a monomeric and dimeric charged 

species containing excess silver ions in an emulsion system 

depending upon the availability of silver ion concentration. 

We will consider this possibility when we 

treat these clusters adsorbed to the surface in later parts 

of this report. 

The ability of silver sulfide clusters to trap electrons 

or holes is determined by their electron affinity (EA) or 

ionization potential (IP), respectively. These values are 

strongly perturbed by the number of bound silver ions 

in the cluster as shown by the data in Table I. This effect 

is due to the net charge of the cluster. As more silver 

ions are associated with the cluster , it becomes a 

better electron trap. In this way the ionic equilibria in 

silver halide, which controls the availability of interstitial 

silver ions, is coupled to the electronic factors that 

control electron or hole trapping. Secondly, the dimeric 

fragments generally have smaller IP and larger EA values 

than their monomeric analogues, as can be seen by 

comparing the values for Ag 2 S and Ag 4 S 2 in Table I. Both 

of these trends promote carrier trapping at the dimers 

relative to the monomer. 

Electronic Effect of Sulfide at Kink Sites. Earlier 

work has shown that the positive kink site is a likely 

site for the nucleation and growth of latent image. Thus, 

we have examined whether the initial electron trapping 

of an electron at these sites is affected by a structural 

relaxation as proposed 3 in strong coupling models of this 

process. A positive kink containing sulfide with a compensating 

silver ion is considered, as shown in Fig. 3. 

This surface defect is represented by a Ag 9 Cl 6 S + quantum 

mechanical model embedded in fixed point ions of 

the type discussed before. Five of the quantum ions are 

blocked from view in Fig. 3. Two silver ions and two 

chloride ions are included below the starred ions to complete 

a cube of ions. The fifth ion is an interstitial silver 

ion placed at the center of this cube. In the first stage of 

the calculation, the quantum mechanical ions in the top 

layer and the interstitial silver ion are allowed to relax 

to their equilibrium positions. This corresponds to the 

equilibrium kink site. Then, an electron is added and 

the quantum mechanical ions are allowed to relax to 

Calculated Properties of Sulfur Centers on AgCl Cubic Surfaces Vol. 43, No. 4, July/Aug. 1999 377

TABLE II. Calculated Equilibrium Positions for Ag Clusters at 

Ag 4 Cl 3 S Kink Model 

Cluster X Y Z 

Ag° 0.15 0.25 0.18 

Ag 2 ° –0.16 0.65 1.32 

4.61 0.65 1.36 

Ag 3 ° –0.95 5.31 0.87 

5.61 0.05 1.25 

0.06 0.17 1.05 

Ag 4 ° 0.31 0.41 0.56 

6.86 –0.23 0.08 

–2.75 4.60 –0.30 

6.67 4.73 0.19 

Positions (au) relative to (000) at the kink center. 

TABLE III. Calculated Properties of Ag n Centers Adsorbed to 

Various S Kink Models 

A. Properties at S Kink on AgCl 

Cluster Binding Energy (eV) Average Charge IP (eV) EA (eV) 

Ag 1.77 –0.10 6.48 4.69 

Ag 2 3.16 –0.04 6.13 4.33 

Ag 3 4.12 –0.05 5.43 4.73 

Ag 4 6.79 –0.03 6.75 4.43 

B. Electron Trap Depths (eV) 

Cluster S Kink, AgCl Single Kink, AgCl 

Ag 1.09 1.31 

Ag 2 0.73 0.10 

Ag 3 1.13 1.85 

Ag 4 0.83 1.80 

find new equilibrium positions. We associate the change 

in energy, which occurs in this second relaxation, with 

a deepening of the electron trap caused by the interaction 

of the electron with lattice ions. 

Prior to this step, the trap depth of the electron is determined 

by coulombic effects and, according to effective 

mass considerations, would be expected to amount to a 

few hundredths of an electronvolt. The calculated energy 

change due to relaxation is 0.31eV, which dominates the 

effective mass trap depth. The approximate quantitative 

nature of this calculation is emphasized because of the 

small quantum cluster size. Qualitatively , this result 

provides support for the concepts involved in the strongcoupling 

model of sensitization proposed by Hamilton. 3 

Figure 4. Electron affinity and ionization potential are shown 

for Ag n , n = 1 to 4 clusters adsorbed next to kink model S with 

and without sulfide. 

Latent Image Formation at Kinks Containing S 

Ions. Some proposals 8,11 for the function of S sensitization 

attribute the collection of excess silver ions as leading 

to a sensitizer site. These silver ions might be 

interstitial or on the surface of the grain. W e consider 

these possibilities near a positive kink site, which our 

previous calculations have shown 12,16 to be a favorable 

site for latent image formation in the absence of sulfur. 

A single positive kink was considered, as sketched in 

Fig. 1. In the single kink the double charge of the sulfur 

ion substituted for halide is balanced by an adjacent 

interstitial silver ion. This model is represented through 

Ag 4 Cl 3 S quantum mechanical units embedded in a pointcharge 

array containing the appropriate charges for S, 

Cl, or Ag ions. 

When silver atoms are adsorbed to the S kink model 

their optimized geometry is calculated to be near planar, 

similar to earlier findings at kink sites 12 in the absence 

of S. W e report the calculated equilibrium 

geometries in Table II for the S kink model. The bond 

lengths in the silver clusters are similar to those calculated 

in the gas phase and suggest that the silver cluster 

retains its integrity. For example, we calculate 2.52 

Å for Ag 2 and 2.95 and 2.94 Å for Ag 3 . Turning to other 

properties of the cluster in T able III, we see a significant 

binding energy for these clusters that represents 

the sum of adsorption energy and the intra-atomic bonding 

terms. The silver atom has a significant adsorption 

energy. The average Mulliken charge of these clusters 

is very close to neutral. The ionization potential (IP) 

and electron affinity (EA) of these centers are considerably 

larger than the conduction band edge for AgCl, 

which we calculated 12 at 3.6 eV as a reference level. 

Thus, electron capture at the silver centers is energetically 

possible at all sizes and permits latent image formation 

according to the nucleation and growth mechanism. 

The valence band edge is positioned at 6.8 eV as 

derived from the AgCl band gap and is such that 

photoholes could attack any of these clusters. 

We can compare the electron trap depths with and 

without S ions present. We employ data from our ear - 

lier calculations 12 in Table III for this comparison. On 

AgCl the electron affinity of the Ag° is slightly decreased 

in the presence of S by 0.22 eV at the kink. At Ag 2 , the 

situation is reversed and electron trapping at this stage 

may be important for latent image growth. In the absence 

of S the trap depth is only 0.1 eV for Ag 2 but increases 

to 0.73 eV at the S kink model. The electron trap 

depth at cluster sizes greater than these are quite large 

and should not provide a barrier to latent image growth. 

Thus, these results suggest that an important role of S 

in AgCl is to assist electron trapping at Ag 2 , which has 

the smallest electron trap depth of a size series of silver 

clusters. These energy levels are plotted in Fig. 4 to facilitate 

this comparison. 

An interstitial silver ion can add to the latent image 

center after an electron is trapped. This process is assisted 

by Coulomb attraction as in the nucleation and 

growth model. In this mechanism, it is worth emphasizing 

the electron capture ability of the silver atom 

state. Its electron affinity is 4.69 eV, as shown in 

Table III, which makes it a deep electron trap. This re- 


Figure 5. Sketch of the equilibrium structure calculated for Ag 3 S + , Ag 2 S, and Ag 4 S 2 on the (100) AgCl surface in top view. 

sult may be surprising in view of the approximately 1eV 

electron affinity of the free atom. The difference occurs 

because of the partial charge of the kink site and the 

lattice polarization of silver halide. Thus, there are no 

thermodynamic barriers to the formation of latent image 

by stepwise addition of electrons and silver ions to 

the silver atom center. 

Ag n S m Clusters (n = 1 to 5; m = 1, 2) on AgCl Flat 

Surfaces. We consider the energy levels of various silver 

sulfide clusters adsorbed to the (100) AgCl surface. 

The models are sketched in Fig. 1 where the Ag n S m clusters 

are placed on the Ag 5 Cl 4 fragment embedded in point 

ions. A geometry optimization was performed to determine 

the relaxed cluster structure registry and height 

above the surface. A sketch of the structure of some 

adsorbed clusters is shown in Fig. 5 along with geometric 

information. The Ag 2 S molecule is adsorbed with its 

S atom over the top of a lattice silver ion. The Ag-S-Ag 

bond angle is 100°, which is very close to the free cluster 

value. The Ag 3 S + molecule also is adsorbed with the 

sulfur atom over a lattice silver ion. In the case of Ag 4 S 2 , 

both sulfur atoms are positioned nearly on top of underlying 

silver ions while the silver atoms are positioned 

nearly on top of lattice chloride ions. 

The calculated ionization potential and electron affinity 

of the adsorbed Ag n S m clusters are shown in Fig. 

6 for various sizes. The levels are labeled by the initial 

and final cluster charge when an electron is added to 

the cluster. Thus, electron trapping at Ag 2 S is represented 

by the label 0/–1 which can be seen to lie above 

the conduction band of AgCl. Therefore, Ag 2 S on the 

(100) AgCl surface is not able to trap an electron. The 

same is true for the neutral Ag 4 S 2 molecule although its 

electron accepting level is within 0.2 eV of the conduction 

band edge and this difference is less than our estimated 

possible error of this calculation. When one or 

two silver ions are added to Ag 2 S or Ag 4 S 2 , there are 

electron accepting levels within the band gap. In order 

to trap a photohole the level must lie in the band gap. 

Interestingly, Ag 2 S does not have such a level in the band 

Figure 6. The calculated ionization energies are shown for various 

silver sulfide clusters adsorbed to the (100) AgCl surface. 

The notation gives the cluster charge before/after ionization. 

gap. The other clusters that have the best chance of trapping 

a hole must have a zero or negative charge, in order 

to avoid Coulombic repulsion. The clusters filling 

this criterion are Ag 3 S°, Ag 4 S°, Ag 4 S 2 °, and Ag 5 S 2 °. The 

positively charged clusters such as Ag 3 S + , Ag 4 S + , and 

Ag 5 S 2 

+ 

would capture electrons. This finding again points 

to the importance of the ionic equilibria in a grain that 

determines the concentration of interstitial silver ions 

that in turn controls the majority species such as Ag 2 S 

or Ag 3 S + on the surface. 

Ag n Clusters on Flat AgCl Surfaces Containing Sulfide. 

We now consider (100) AgCl surfaces where oneor 

two-chloride ions are replaced by sulfide. The quantum 

mechanical surface fragment that is then embedded 

in point ions is shown in Fig. 7 for the two cases. 

The Ag atoms are first placed on the surface near the 

hollow site between two cations and two anions and then 


Figure 7. Cluster units containing one or two sulfide ions that 

were used to treat adsorption next to sulfide. 

its lateral and vertical position is optimized. The total 

energy is then calculated for several charge states in 

order to determine the energy levels in Fig. 8. It is clear 

that many neutral Ag n clusters would not be stable near 

the sulfide ion on this (100) surface. These clusters have 

the level +1/0 above the conduction band edge, which 

indicates that they would release an electron to the conduction 

band if they were ever formed on this surface. 

The exceptions to this behavior are Ag 2 at both sites and 

Ag 4 near the two S model. By the same token these neutral 

clusters have the correct charge and energy levels 

to become hole traps. All of the other clusters with energy 

levels in the band gap should not trap holes because 

of their positive charge. Thus, it is clear that a 

silver ion must be associated with the sulfide-silver cluster 

in order to permit electron trapping. Therefore, centers 

such as Ag 2 

++ 

, Ag 3 

++ 

, and Ag 4 

++ 

near one-sulfide ion 

or Ag 2+ , Ag 4+ , or Ag 5 

++ 

near two-sulfide ions would be 

needed to trap electrons at these centers. 

Discussion 

We have examined silver-sulfur clusters on a silver chloride 

crystal surface where the cluster was adsorbed to 

the surface or in which the sulfur ions have replaced 

halide ions in different surface sites. The adsorbed clusters 

show size-dependent properties. On the flat (100) 

AgCl surface Ag 2 S or Ag 4 S 2 have electron accepting levels 

slightly above the conduction band edge. When associated 

with a silver ion, these molecules become 

electron traps. The Ag 4 S 2 molecule has an occupied level 

in the band gap that could trap a hole. When sulfide 

replaces halide ions in the flat (100) AgCl surface, the 

resulting centers are generally not electron traps unless 

they have adsorbed sufficient silver ions to acquire 

+ 

a positive charge. The Ag 2 cluster near one-sulfide ion 

+ 

or Ag 2+ , Ag 4 near two-sulfide ions have electron trapping 

levels just larger than the crystal. It is possible 

that this type of species is responsible for the S center 

trapping levels in the range of 0.3 – 0.4 eV observed 

experimentally 4–6 in AgBr systems. However, these centers 

may not be the ones directly active in latent image 

growth, while they may play an important role in the 

overall process. 

In considering the overall role of S sensitization it is 

well to appeal to some of the classic experiments that 

have helped to define the situation. A variety of workers 

have referred to the role of the sensitization in over - 

coming the inherit negative surface potential in silver 

chloride and bromide that opposes the movement of photoelectrons 

to the surface. In this regard, the classic experiments 

of Saunders, Tyler, and West 17 are worthy of 

attention. They demonstrated in unsensitized AgBr 

sheet single crystal an insensitivity for the formation 

of surface latent image because of the space-charge potential 

opposing the motion of electrons to the surface. 

The same effects were demonstrated 18 in emulsion 

Figure 8. The calculated ionization energies are shown for 

Ag n (n = 1 to 5) for adsorption next to one S or two S ions in the 

(100) AgCl surface. 

grains where the sensitization centers were placed at 

different positions. With sensitization centers placed on 

the surface, latent image only formed on the surface, 

but when the sensitization center was in the grain interior 

no surface latent image formed. The role of the surface 

sensitization centers in overcoming the 

space-charge potential in this manner has also been 

emphasized by Slifkin. 19 

The distribution of development centers in a model 

silver bromide emulsion was studied by Spencer, Brady, 

and Hamilton. 20 The effect of S sensitization on highintensity 

exposures was striking. At high intensities the 

number of development centers increase when S sensitization 

is applied. This effect is not observed at low 

intensities. The effect has been interpreted to indicate 

an increase in nucleation efficiency 21 as caused by S sensitization. 

In the absence of S sensitization the nucleation 

efficiency is very low. 

These experimental results and calculations are consistent 

regarding a role for S sensitization in silver 

halide. There is a temporary trapping of electrons that 

reach the surface in opposition to the space-charge 

potential. At a surface defect site such as a kink containing 

sulfide a relaxation involving small ion displacements 

can take place to stabilize the electron. This 

initial shallow trapping is important in leading to a deexcitation 

of the electron 3 permitting electron trapping 

at the silver atom where the calculated electron affinity 

is 1.1 eV greater than the crystal electron affinity . 

Thus, the net effect is to increase the probability of electron 

trapping at the silver atom in competition with 

recombination. Possibly, there is a second function of 

the sulfur center that increases the electron trap depth 

at Ag 2 . 

The luminescence-modulation spectroscopic measurements 

of Kanzaki and Tadakuma 11 on sulfur sensitization 

centers in AgBr emulsions give evidence for 

deep carrier trapping at S centers. A thermal trap depth 

for electrons of 0.3 eV is associated with the sulfur 

dimer centers on the basis of the concentration dependence 

of peaks in the modulation spectra. These centers 

were thought to consist of two adjacent 

substitutional sulfide ions that attract two interstitial 

silver ions and is supposed to lead to an enhancement 

of the interstitial electron trapping function. In this 

mechanism, the displacement of interstitial silver ions 

leads to the relaxed state with a thermal trap depth of 


0.3 eV. This mechanism has some similarities with the 

kink relaxation mechanism and could be investigated 

in more detail. 

These first calculations have dealt with the AgCl surface 

because of computational ease. In many cases we 

have assumed that the electronic properties of the sensitizer 

centers will be similar on AgCl and AgBr. This 

assumption will have to be tested computationally. 

Conclusions 

We have applied state-of-the-art computations to describe 

the electronic properties of sulfur sensitization on AgCl. 

1. There is a tendency for free Ag 2 S centers to dimerize 

to Ag 4 S 2 clusters and the clusters could add one or 

more silver ions depending upon the availability of 

these ions for reaction. The dimers are better electron 

traps than the corresponding monomers. 

2. Sulfur centers at a kink site can promote electron 

trapping through relaxation of its ions. This trap 

deepening promotes electron de-excitation to deeper 

latent image precursor levels. 

3. The properties of sulfur-silver centers adsorbed to flat 

surfaces are different than if the sulfur is incorporated 

into the surface to form a sulfide. 

4. On the (100) AgCl surface, electron trapping centers 

include Ag 3 S + , Ag 4 S + , and Ag 5 S 2+ . 

5. When sulfide is introduced into the (100) AgCl surface 

silver ions are required to compensate its charge. 

Electron trapping can occur at (Ag 2 S) but not (AgS) 

centers. At dimeric S centers, electron trapping is 

more favorable. 

References 

1. J. M. Harbison and H. E. Spencer, The Theory of the Photographic 

Process, T. H. James, Ed., 4th ed., Macmillan Publishing 

Co., New York, 1977. 

2. J. F. Hamilton, Adv. Phys. 37, 359 (1988). 

3. J. F. Hamilton, J. Imaging Sci. 34, 1 (1990). 

4. J. F. Hamilton, J. M. Harbison and D. L. Jeanmaire, J. Imaging 

Sci. 32, 17 (1988). 

5. L. Kellogg and J. Hodes, IS&T’s 46th Annual Conference, IS&T, 

Springfield, VA, 1987, p. 179. 

6. T. Kaneda, J. Imaging. Sci. 33, 115 (1989). 

7. D. Zhang and R. Hailstone, J. Imaging Sci. 37, 61 (1993). 

8. T. Tani, J. Imaging Sci. 39, 386 (1995). 

9. J. P. Spoonhower and A. P. Marchetti, J. Phys. Chem. Solids 51, 

793 (1990). 

10. J. E. Keevert and V. V. Gokhale, J. Imaging. Sci. 31, 243 (1987). 

11. H. Kanzaki and Y. Tadakuma, J. Phys. Chem. Solids 55, 631 

(1994); 58, 221 (1997). 

12. R. C. Baetzold, J. Phys. Chem. 101, 8180 (1997). 

13. P. W. Tasker, Philos. Mag. 39, 119 (1979). 

14. CADPAC: The Cambridge Analytical Derivatives Package, Cambridge, 

1996, Version 6, R. D. Amos with contributions from I. L. 

Alberts, J. S. Andrews, S. M. Colwell, N. C. Handy, D. Jayatilaka, 

P. J. Knowles, R. Kobayashi, K. E. Laidig, G. Laming, A. M. Lee, 

P. E. Maslen, C. W. Murray, J. E. Rice, E. D. Simandiras, A. J. 

Stone, M.–D. Su and D. J. Tozer. 

15. Y. Sakai, E. Miyoshi, M. Klobukwski, and S. Huzinaga, J. Comp. 

Chem. 8, 256 (1987). 

16. J. F. Hamilton and R. C. Baetzold, Photogr. Sci. Eng. 25, 189 

(1981). 

17. (a) V. I. Saunders, R. W. Tyler, and W. West, Photogr. Sci. Eng. 

12, 90 (1968); (b) F. Trautweiler, Photogr. Sci. Eng. 12, 98 (1968). 

18. R. Matejec and E. Moisar, Photogr. Sci. Eng. 12, 133 (1968). 

19. L. Slifkin, Mater. Res. Soc. Bull. 36 (1989). 

20. H. E. Spencer, L. E. Brady, and J. F. Hamilton, J. Opt. Soc. Am. 

54, 492 (1964). 

21. (a) J. F. Hamilton, Photogr. Sci. Eng. 26, 263 (1982); (b) R. K. 

Hailstone, N. B. Liebert and M. Levy, J. Imaging Sci. 34, 169 

(1990). 



The Measurement of Diffuse Optical Densities. 

Part II: The German Standard Reference Densitometers 

E. Buhr, D. Hoeschen and D. Bergmann 

Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Bundesallee 100, Germany 

This article describes the design and performance of two densitometers used for high-accuracy measurements of visual diffuse 

optical transmission densities. The two densitometers were developed and constructed at the Physikalisch-T echnische 

Bundesanstalt (PTB), the German National Institute of Metrology. Both devices comply with the ISO standards 5-2 and 5-3 and 

are primarily used for the calibration of standard step tablets. One of these densitometers, the PTB’ s inverse square law 

densitometer, is the national standard reference densitometer capable of measuring with high accuracy optical densities up to 

D = 3.3. The other densitometer, called fiber densitometer, measures densities up to D = 6. For both densitometers, the expanded 

ISO uncertainty of density measurement (coverage factor k = 2) is 0.003 for densities below 1.5 and increases to 0.006 at density 

6 for the fiber densitometer with spectrally neutral samples. 


Introduction 

Accurate values of diffuse optical densities of scattering 

samples are needed for many purposes: quality 

assurance in medical x-ray diagnostics, industrial nondestructive 

x-ray testing, applications in molecular 

biology (DNA sequencing, for example), quality control 

in graphic arts, and, of course, for characterizing 

photographic materials. For the calibration and testing 

of densitometers, suitable test objects, e.g., standard 

step tablets, with well-known optical densities are used. 

Such step tablets are calibrated by calibration services 

which need reference standards. For reasons of 

traceability, these reference standards are calibrated 

with very high accuracy by National Institutes of 

Metrology such as NIST and PTB. They develop 

standard measuring equipment that is capable of 

measuring optical densities directly, without any step 

tablets being needed for calibration. The PTB has 

developed two such densitometers for the measurement 

of visual diffuse transmission densities. In this article 

we present the measuring arrangements and principles 

used in these two devices, discuss the performance of 

these densitometers and their measurement 

uncertainties. 

ISO Standards for the Measurement of Optical 

Densities 

The definition of optical density and the conditions of 

the measuring systems are given in the International 

Standards ISO 5, parts one to four. We present here only 



a very brief survey of these standards, especially with 

respect to the measurement of visual diffuse 

transmission density. 

According to ISO 5-1, 1 the optical transmission density 

D is defined as 

D =−log 10 T 

(1) 

where the transmittance factor T is the ratio of the 

measured flux transmitted by the specimen to the flux 

measured when the specimen is removed from the 

sampling aperture of the densitometer. 

The geometric measuring conditions are specified in 

ISO 5-2 2 and ISO/DIS 5-2 6 for transmission density and 

in ISO 5-4 4 for reflection density . The ISO standard 

diffuse transmission density is based on a method, where 

the sample is in “close contact” with the surface of a 

diffuse illuminating or receiving system. Because this 

surface is mostly realized by an opal glass, this method 

is usually called “opal glass” method. The term “close 

contact” means that there is a close proximity with an 

air gap to simulate conditions of the practice where 

inter-reflections between sample and opal glass are 

present. Because these inter -reflections influence the 

measurement result, ISO 5-2 specifies the reflection 

factor of the opal glass. ISO 5-2 also specifies the 

diffusion coefficient of the diffuser. In part I of this series 

of articles, 5 the ISO geometric conditions for determining 

diffuse transmission densities were discussed in detail. 

The spectral conditions for the measurement of optical 

densities are described in ISO 5-3, 3 where both the 

spectral energy distribution of the incident radiant flux 

and the spectral product of the measuring system (i.e., 

the product of the influx spectrum and the spectral 

response of the densitometer) are specified for various 

applications. For transmission density measurements, 

382

Figure 1. Set-up of inverse square law densitometer. 

Figure 2. (a) Modulation scheme applied in inverse square 

law densitometer. and (b) reference and sample beam, both 

signals have the same waveform which is out-of-phase by 180°. 

(c) detector output signal with the sample beam attenuated by 

sample. (d) and (e) chopper reference output signals. 

the spectral distribution of the influx is the CIE 

standard illuminant A, modified by the transmittance 

of a typical heat-absorbing filter to protect the specimen 

and the optical system from heat. The functional 

notation of this influx spectrum is S H according to ISO 

5-3. The spectral product required for the visual 

transmission density is defined as the product of S H and 

a spectral response of the receiver, V T , in order that this 

product be equal to the product of the spectral luminous 

efficiency function for photopic vision, V(λ), and the 

spectral distribution of CIE standard illuminant A. 

PTB’s Inverse Square Law Densitometer. The PTB’s 

inverse square law densitometer is the German national 

standard reference densitometer capable of measuring 

visual diffuse transmission densities according to 

ISO 5-2 and ISO 5-3. It applies the “diffuse efflux mode” 

measuring configuration, 2 where the film sample is 

illuminated directionally and the transmitted flux is 

measured by means of a diffuse receiver . 5 The 

densitometer is a dual-beam device: The luminous flux 

is time-shared by the reference and sample path, and it 

is detected by applying phase-sensitive lock-in 

techniques. Besides the well-known advantages of the 

dual-beam technique, the influence of low-frequency 

noise contributions is reduced. The densitometer uses a 

null-balance measuring configuration based on the 

fundamental photometric inverse square law , and 

therefore linearity of the optical detector system is not 

an indispensable prerequisite. 

Densitometer Set-Up and Measuring Principle. The 

diagram of the measuring set-up of the densitometer is 

shown in Fig. 1. The light of a tungsten halogen lamp is 

split into two beams, the reference and the sample beam. 

A mechanical chopper, equipped with a specially shaped 

chopping blade, is used to chop both light beams 

simultaneously. The resulting modulation waveforms 

are shown in Fig. 2. The two light beams show repetitive 

pulse groups, each of which consists of four equal squarewave 

light pulses. The repetition frequency of the pulse 

groups is f = 72 Hz, and the frequency of the single 

pulses is 8f. The frequencies are chosen so as to avoid 

any low-order harmonic of f and 8 f coinciding with a 

low-order harmonic of the power line frequency . The 

modulation frequencies f and 8 f are phase-locked to 

avoid possible low-frequency beating due to the same 

chopper blade being used to create these waveforms. The 

waveforms of the reference and the sample beam are 

out-of-phase by 180 ° with respect to each other , i.e., 

whenever light from the reference beam reaches the 

photodetector, light from the sample beam is blocked, 

and vice versa. 

The Measurement of Diffuse Optical Densities.Part II: ... Vol. 43, No. 4, July/Aug. 1999 383

Figure 3. Diffuser used in the inverse square law densitometer. 

The luminous flux of the reference beam, Φ R , passes 

neutral grey filters and a variable beam aperture (for 

intensity adjustment). It then directly reaches an 

integrating sphere (sphere diameter: 1 1 cm; coating: 

barium sulphate), which is provided with a 

photodetector (EMI 9558 photomultiplier). An optical 

filter combination mounted in front of the photomultiplier 

is used to meet the ISO spectral conditions 

for measuring visual densities. The sample is in contact 

with an opal glass that is located in another opening of 

the integrating sphere, see Fig. 3. The sample beam is 

directed onto the sample via two mirrors mounted on a 

long-travel linear translation-stage (length: about 6 m). 

Variation of the translation stage position leads to a 

change in the length of the sample beam path and, as a 

consequence, to a corresponding change of the incident 

luminous flux because of the photometric inverse square 

law. The length of the reference beam path is not altered 

if the translation stage position is varied. 

Because the photodetector captures both the reference 

beam flux Φ R and the transmitted sample beam flux Φ S , 

its output signal comprises the superposed contributions 

from the reference and sample beam signals. The 

photodetector output signal is amplified and 

subsequently fed to two equal digital lock-in amplifiers 

(Stanford SR 810). Lock-in amplifier No. 1, which is 

locked to the frequency f, detects the difference between 

reference and sample beam flux, Φ S – Φ R , whereas lockin 

amplifier No. 2, synchronized by the 8 f-reference 

output signal from the chopper , detects the sum of 

reference and sample beam flux, Φ S + Φ R . The digital 

lock-in output signals are transmitted to a computer that 

calculates the ratio of the sum and the difference of the 

two lock-in output signals, yielding Φ S / Φ R as the result. 

Density measurements are performed in two steps: 

1. The first measurement is made with the sample 

removed. An adjustment is made to ensure that the 

photodetector signal contributions coming from the 

reference beam and the sample beam are equal, i.e., 

Φ S / Φ R = 1. To attain this balance condition, the 

luminous flux of the sample beam is adjusted by 

positioning the translation stage on the optical bench. 

This stage position is measured and the corresponding 

sample path length, s 100% , is determined. 

2. The second measurement is performed with the 

sample arranged in front of the opal glass. The 

photodetector output signal contribution resulting 

from detecting the sample beam flux is reduced 

according to the transmittance factor T of the sample 

(see Fig. 2c), and the quantity computed from the 

two lock-in output signals, Φ S / Φ R , then directly 

yields the desired transmittance factor T. However, 

this value of T may be affected by possible 

nonlinearities of the characteristic curve of the 

photodetector/amplifier combination. In order to 

neglect this contribution to the measurement 

uncertainty, the translation stage is moved to a new 

position on the optical bench (closer to the lamp) 

where the null-balance condition, Φ S – Φ R = 0 or , 

equivalently, Φ S / Φ R = 1, is fulfilled as was the case 

without sample. If the length of this shorter sample 

path is denoted as s T , the sample transmittance 

factor is easily obtained by applying the inverse 

square law: 

sT 

T = ⎛ 2 

⎞ 

⎝ ⎜ s 

⎟ 

100% 

⎠ 

Therefore, the measurement of the optical density is 

reduced to two length measurements which can be 

performed with sufficient accuracy . The measuring 

range is limited to densities of up to about 1.65 because 

of the maximum and minimum sample path lengths 

possible. However, with the help of an auxiliary sample 

with a density of about 1.65 (which has to be well-known) 

and by attenuating the reference beam flux accordingly, 

it is possible to achieve the balance condition once again 

at large sample path lengths. This procedure renders it 

possible to measure sample densities up to twice the 

value of 1.65, i.e., up to 3.3. A third follow-up measurement 

is not possible because of a too low signal-to-noise 

ratio, which is due to the relatively weak radiation 

emitted by the tungsten lamp. 

ISO Geometric and Spectral Conditions. The 

densitometer complies with the geometric conditions 

specified in ISO 5-2, i.e., the diffusion coefficient value 

is larger than 0.90 and the reflectance factor of the 

diffuser is between 0.50 and 0.60. 

Figure 3 shows in detail the arrangement of the 

diffuser. It consists of an opal glass combined with an 

integrating sphere. This arrangement was chosen 

because the diffusion coefficient value of the 0.42 mm 

thick opal glass alone is not high enough. The thickness 

of the opal glass was selected to achieve a reflectance 

factor of 0.55 of the combination (sphere and opal glass) 

for a wavelength of about 570 nm which is the peak 

wavelength of the spectral product for visual density 

measurements. Due to light scattering, the reflectance 

factor of the diffuser decreases with increasing 

wavelength from 0,60 for a wavelength of 420 nm to 0.50 

for 710 nm. 

The geometrical distribution of the diffuse receiving 

system is shown in Fig. 4, together with the distribution 

of a perfect diffuse receiver that has a cosine spatial 

response, and, by definition, a diffusion coefficient of 1. 

The diffusion coefficient of the real diffuser is 0.945 

calculated according to Annex C of ISO 5-2. If the 

proposed new definition, given in the revised Draft ISO 

Standard ISO/DIS 5-2, 6 is applied, the diffusion 

coefficient is 0.909. Please note, that the value for the 

diffusion coefficient, stated in the first part of this series 

of papers, 5 no longer holds because the instrument was 

meantime modified. 

The measuring aperture (size: 5 mm × 3 mm) is 

defined by a diaphragm that is located between sample 

(2) 

384 Journal of Imaging Science and Technology Buhr et al.

Figure 5. Spectral product as specified in ISO 5-3 and 

measured for the inverse square law densitometer . The 

difference between both curves is also shown. 

Figure 4. Geometrical distribution of the diffuse receiving 

system of the PTB’s inverse square law densitometer. 

and opal glass. T o assure that sample and opal glass 

are in close contact with each other , the diaphragm is 

inlaid into the opal glass such that there is a smooth 

surface. 

Figure 5 shows the spectral product for visual 

densities according to ISO 5-3 together with the spectral 

product of the densitometer , that was obtained by 

multiplying the measured emission spectrum of the 

tungsten lamp by the spectral response of the complete 

diffuse receiver system. If the CIE error definition used 

for the specification of the spectral response of 

photometers is applied, 7 a value of 1.4% for f′ 1 is 

measured. 

Measurement Uncertainty. To determine the 

combined measurement uncertainty, the ISO Guidelines 

for the expression of uncertainty in measurement are 

applied. 8 The expanded uncertainty U(D) is specified, 

which is obtained by multiplying the combined standard 

uncertainty by a coverage factor k. The value of the 

coverage factor chosen is 2. 

The repeatability of measurement (repeated 

measurement of the same sample under unchanged 

conditions) was measured; the corresponding expanded 

uncertainty is U(D) < 0.001 for D < 1.65 and 

U(D) = 0.0025 for D > 1.65. 

Systematic uncertainty components originate from the 

uncertainty where the determination of the sample path 

lengths s 100% and s T are affected: Here, the problem is 

not the measurement of the translation stage position 

on the optical bench, but proper knowledge of the 

effective distance between lamp source and detector 

along the optical beam path. In practice, the problem is 

to accurately measure an “offset” distance which has to 

be added to the readings of the translation stage 

positions. We determine this offset distance by means 

of the inverse square law , by extrapolation to zero 

distance. For this measurement, a linear photodetector 

is needed. The possible non-linearity of the 

photodetector and the extrapolation to zero distance lead 

to an uncertainty of the offset distance. This in turn 

results in a corresponding uncertainty of the density 

measurement which is density dependent and can be 

described by U(D) = 0.0016•D. 

Another item concerns the photometric inverse square 

law itself. The largest dimensions of the tungsten light 

source and of the sampling aperture are 5mm, which is 

much smaller than the nearest distance between light 

source and detector (about 1700 mm). Therefore, the 

conditions for the applicability of the inverse square law 

are by far fulfilled; the uncertainty contribution due to 

this effect is far below 0.001. However, due to additional, 

undesirable signal contributions (e.g., stray light from 

the mirrors or other sources), small deviations from the 

ideal inverse square law occur. Careful measurements 

of these deviations show a stable and systematic 

behavior which is taken into account in the 

measurement evaluation. The residual uncertainty of 

measurement caused by this effect is density dependent, 

U(D) = 0.0007•D. 

Other sources of error are due to spatial nonuniformities 

of the radiation emitted by the lamp, and 

due to residual lock-in phase variations between the 

reference and the sample beam signals when the 

translation stage moves along the optical bench. The 

reason for both errors is that the solid angle of that part 

of the light beam that contributes to the signal, changes 

with the stage position. For instance, a larger distance 

between the sampling aperture and the lamp results in 

a smaller solid angle of the light beam falling onto the 

sampling aperture. Because the chopper blades hit the 

beam perpendicularly, the chopped light undergoes a 

phase variation. Other contributions to the uncertainty 

are the measurement uncertainties of the lock-in 

amplifiers. The total effect of all these uncertainties can 

be estimated to be below 0.002. 

The slight deviations of the spectral product of the 

densitometer from the ISO spectral product will lead to 

corresponding systematic measurement errors if the 

spectral transmission of the sample depends on the 


Figure 7. Spectral product as specified in ISO 5-3 and 

measured for the fiber densitometer. The difference between 

both curves is also shown. 

Figure 6. Set-up of fiber densitometer. 

wavelength. These systematic measurement errors can 

be corrected if the relative spectral transmission of the 

sample is known. For example, for medical x-ray films 

with their typical bluish base, the densitometer 

described here will indicate density values that deviate 

by about 0.001 from those of an ideal densitometer with 

exactly the spectral product specified in ISO 5-3. 

The effects of the diffusion coefficient value on the 

density values measured have already been discussed 

in detail in part I of this series of papers especially with 

respect to the inverse square law densitometer . 5 This 

discussion need not be repeated here, and the total 

uncertainty values stated below do not take this aspect 

into account. 

The resulting total measurement uncertainty for the 

ISO visual transmission density of spectrally neutral 

samples depends on density and can be expressed by 

U(D) = 0.0024 •D for densities above 1.5; for densities 

below 1.5 the uncertainty is U(D) = 0.003. 

PTB’s Fiber Densitometer. The fiber densitometer is 

specially designed for the measurement of high optical 

densities of neutral samples, and it thus complements 

the field of application of the inverse square law 

densitometer. 9 It is a single-beam densitometer that 

applies the “diffuse influx mode” configuration 2 using 

an opal glass as a diffuser. In this measuring mode, the 

sample is illuminated by diffuse light, and the 

transmitted luminous flux is detected with a directional 

receiver. 

Densitometer Set-Up and Measuring Principle. A 

diagram of the densitometer is shown in Fig. 6. The light 

of a tungsten halogen lamp, of which the IR radiation is 

removed with a heat-absorbing filter, is coupled into a 

so-called randomly mixed glass fiber cable (length: 1 m, 

diameter: 13 mm), where the input and output positions 

of the single fibers do not c orrelate. This ensures 

uniform light emission over the sectional area of the 

fiber cable output, despite the fact that illumination of 

the cable input area is not quite homogeneous. In 

addition, this arrangement also leads to a very high 

luminous flux at the sample, without necessity of 

removing the heat produced by the lamp. The opal glass 

(thickness: 0.50 mm) is located about 5 mm apart from 

the output end of the fiber cable. The sampling aperture 

(6 mm × 3 mm) is defined by a diaphragm which is placed 

at the side of the opal glass facing the sample; as in the 

case of the inverse square law densitometer , the 

diaphragm is inlaid into the opal glass to achieve close 

contact of sample and opal glass. The combination of fiber 

cable and opal glass makes it possible to meet the ISO 

conditions regarding uniformity, diffusivity (diffusion 

coefficient: 0.952 according to ISO 5-2 Annex C, and 0.918 

according to ISO/DIS 5-2) and reflectance (reflectance 

factor: 0.54 at 570 nm) of the diffuse illuminator. 

The transmitted luminous flux is collected within a 

cone with a half angle of about 8° (maximum permissible 

half angle according to ISO 5-2: 10°). After collimation, 

the flux is filtered by means of an optical filter 

arrangement and detected with a silicon photodiode 

(Hamamatsu S1227-1010BQ). The spectral product of 

the densitometer is not as good as that of the PTB’ s 

inverse square law densitometer (see Fig. 7); the value 

of the f’ 1 error parameter is 6.5%. Because the device is 

intended primarily for the measurement of spectrally 

neutral samples, this is actually no disadvantage. 

Optional grey filters (one filter or two filters in tandem 

arrangement) serving as spectrally neutral attenuators 

can be positioned in front of the photodetector. The grey 

filters are glass plates coated with a durable metallic 

alloy. These plates ensure uniform attenuation of the 

radiation over a wide spectral range. The filters are used 

to attenuate the luminous flux obtained without a 

sample, which renders it possible to reduce the ratio 

between the signals recorded with and without a sample 

to values ranging between 1 and 30. This has the 

advantage that the same amplifier setting can be used 

for both signals. The attenuation provided by the grey 

filters must be known with high accuracy . These 

calibrations are performed in situ, with all densitometer 

386 Journal of Imaging Science and Technology Buhr et al.

components present to include possible effects of interreflections. 

The measurement procedure is straightforward. First, 

the measurement with the sample is performed using 

an appropriate amplifier setting. The second 

measurement is conducted with the sample removed and 

with a suitable grey filter inserted. The density value 

obtained corresponds to the difference between sample 

density and the known grey filter density . The signalto-noise 

ratio is high enough to measure diffuse densities 

up to about D = 6 with sufficient accuracy . The light 

flux emitted by the tungsten lamp is recorded with an 

additional photodiode to detect possible changes of the 

light flux that might occur between the measurement 

with and without a sample. 

Measurement Uncertainty 

Intercomparison measurements between the inverse 

square law densitometer and the fiber densitometer 

have shown that the values indicated by both devices 

agree for spectrally neutral samples within the 

measurement uncertainty of the inverse square law 

densitometer. This is confirmed by the measurement 

uncertainty analysis. The repeatability of measurements 

(k = 2) is better than 0.002 for densities below 2, for 

densities between 2 and 4, U(D) = 0.002, and for 

densities above 4, U(D) = 0.004. The linearity of the type 

of photodetector used in this densitometer has been 

tested to be better than 0.1% within a range of two 

decades; 10 the contribution to uncertainty due to this 

effect is therefore below 0.001 in optical density. The in 

situ calibration of the attenuation provided by the 

neutral grey filters is another source of measurement 

uncertainty: U(D)=0.002 for densities below 4, and 

U(D) = 0.004 for D > 4. For spectrally neutral samples 

the total measurement uncertainty ( k = 2) is 

U(D) = 0.003 for densities below 2, U(D) = 0.004 for 

24. 

In the case of non-neutral samples the densities 

measured with the fiber densitometer may differ 

significantly from that measured with the inverse 

square law densitometer; these differences might be due 

to the worse match of the spectral product of the fiber 

densitometer. 

Conclusions 

We have developed and set up two densitometers that 

fulfill the ISO geometric and spectral conditions for the 

measurement of visual diffuse optical densities. 

However, relatively great effort was necessary to meet 

the ISO geometric conditions; an opal glass alone serving 

as the diffuser was not sufficient to meet both the 

reflectance and the diffusivity conditions. Thin opal 

glasses may have the proper reflectance factor, but their 

diffusion coefficient is low, whereas thick opal glasses, 

where diffusion coefficients are large enough have 

reflectance factors that exceed the specified value of 0.55 

by more than the permissible tolerance. 

The intercomparisons between both PTB densitometers 

have shown that the single-beam instrument 

which is not a null-balance device, furnishes the same 

results as the sophisticated dual-beam inverse square 

law densitometer. It is possible to build a standard 

reference densitometer with the much simpler geometric 

and optical arrangement of a single-beam device. This 

device should be able to meet the customer ’s demands 

with regard to measuring range, measurement accuracy 

and also calibration cost. 

Intercomparison measurements with NIST’ s newly 

established standard densitometer 11 have been 

performed. The results of these intercomparison 

experiments will soon be submitted for publication in 

this Journal. 

References 

1. ISO 5-1: Photography - Density measurements - Part 1: Terms, symbols 

and notations, 1984. 

2. ISO 5-2: Photography - Density measurements - Part 2: Geometric 

conditions for transmission density, 1991. 

3. ISO 5-3: Photography - Density measurements - Part 3: Spectral conditions, 

1984. 

4. ISO 5-4: Photography - Density measurements - Part 4: Geometric 

conditions for reflection density, 1983. 

5. E. Buhr, D. Hoeschen and D. Bergmann, The Measurement of Diffuse 

Optical Densities. Part I: The Diffusion Coefficient, J. Imaging 

Sci. Technol. 39, 453 (1995). 

6. Revision of ISO 5-2, ISO/DIS 5-2, 1998. 

7. CIE publication no. 53 (TC-2.2): Methods of characterizing the performance 

of radiometers and photometers, Paris, 1982, sect. 3.2.3. 

8. Guide to the expression of uncertainty in measurement, ISO, Geneva, 

1993. 

9. D. Bergmann, Entwicklung und Realisierung eines Einstrahldensitometers 

für hohe optische Dichten, Diploma thesis, Fachhochschule 

Iserlohn, 1993. 

10. K. Stock, PTB department Light and Radiation, private communication, 

see also in: PT Jahresbericht 1997, Braunschweig, 1998, sect. 

2.4.1, p. 222. 

11. E. A. Early, T. R. O’Brian, R. D. Saunders, and A. C. Parr, Film Step 

Tablet Standards of Diffuse Visual Transmission Density - SRM 1001 

and SRM 1008, NIST Special Publication 260-135, Washington, 

1998; E. A. Early, C. L. Cromer, X. Xiong, D. J. Dummer, T. R. O’Brien, 

and A. C. Parr, J. Imaging. Sci. Technol. 43, 388 (1999). 



NIST Reference Densitometer for Visual Diffuse Transmission Density 

Edward A. Early, Christopher L. Cromer, Xiaoxiong Xiong, Daniel J. Dummer, Thomas R. O’Brian, and Albert C. Parr 

Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 

The Optical Technology Division of the National Institute of Standards and Technology has developed a new reference densitometer 

for measuring visual diffuse transmission densities using the diffuse influx mode. This densitometer is used to calibrate both 

x-ray and photographic film step tablet Standard Reference Materials. The design, characterization, and operation of the densitometer 

are detailed. The densitometer was fully characterized both to verify compliance with the applicable documentary standards 

and to determine the combined uncertainty in transmission density associated with the calibrations. 


Visual diffuse transmission density is an important 

physical property for exposed films, and therefore has 

great industrial demand for process control in the fields 

of medicine, non-destructive testing, photography, and 

graphic arts. Standards for visual diffuse transmission 

density are provided by the National Institute of Standards 

and Technology (NIST) in the form of Standard 

Reference Materials (SRMs). These standards are film 

step tablets, 254 mm long by 35 mm wide, with steps 

extending the width of each film and equally spaced 

along its length. A double emulsion x-ray film is used 

for SRM 1001, while a single emulsion photographic film 

is used for SRM 1008. The steps have increasing visual 

diffuse transmission densities from approximately 0.1 

to 4 from one end of the film to the other. SRM 1001 has 

17 steps, while SRM 1008 has 23 steps. 

The visual diffuse transmission densities of film step 

tablets for both SRMs are determined with a new reference 

densitometer using the diffuse influx mode. Diffuse 

illumination is achieved with a lamp, filter , and 

flash opal, while directional detection is accomplished 

with a lens, filter, and photodiode system. The densitometer 

is designed to automatically measure many films 

using computerized data acquisition and control. 

This article states the relevant measurement equations 

for determining visual diffuse transmission density, 

describes the densitometer’s design and operation, 

and details the characterization of the densitometer and 

the resulting uncertainties in the measurement. Additional 

details can be found in Ref. 1. 

Measurement Equations 

The purpose of the measurement equation derived in 

this section is to obtain a mathematical description of 

the measurement of visual diffuse transmission density. 

This is useful for calculating the transmission density 

Original manuscript received December 7, 1998 


from the experimental results, for determining the uncertainty 

in these values, and for relating measurements 

made with the densitometer to those that would be made 

by an ideal densitometer—one that exactly conforms to 

all the relevant documentary standards. 

As specified in the documentary standards, 2–4 visual 

diffuse transmission density is essentially a photopic 

transmission measurement using a hemispherical/directional 

geometry, with the added complication that the 

transmission is determined with the sample in contact 

with an opal. Therefore, the nomenclature and equations 

from photometry and spectrophotometry will be 

used as much as possible to derive the measurement 

equation. 

Following the nomenclature given in Refs. 2 and 5, 

visual diffuse transmission density is determined from 

two luminous fluxes, the aperture flux Φ j and the transmitted 

flux Φ τ . The first is the flux emerging from the 

sampling aperture in the directions and parts of the 

spectrum used in the measurement; the second is the 

flux that passes through the sample, emerging from a 

surface other than that on which the incident flux falls, 

and then used in the measurement. In terms of these 

fluxes, the visual diffuse transmittance factor T v is given 

by 

T V 

= Φ Φτ 

and the visual diffuse transmission density D T is defined 

by 

j 

(1) 

D T = – log 10 T V . (2) 

To this point, neither the spatial nor spectral properties 

of the fluxes have been specified. For the spatial 

properties, some nomenclature must first be defined. 

The incident flux is referred to as the influx, while the 

transmitted flux is referred to as the efflux. These fluxes 

can either be hemispherical (in all directions) or directional 

(in one specified direction). For visual diffuse 

transmission density, there are two possible equivalent 

measurement geometries, with equivalence being as- 

388

sumed by the Helmholtz reciprocity theorem. 

6 

In the 

diffuse influx mode the influx is diffuse and detection 

of the efflux is directional; in the diffuse efflux mode 

the influx is directional and detection of the efflux is 

diffuse. 3 Using the terminology from spectrophotometry, 

these geometries are hemispherical/directional and directional/hemispherical, 

respectively. 

For visual diffuse transmission density, the spectral 

product of the influx and the detector are specified 4 so 

that the integral is a luminous flux. In general, luminous 

flux Φ v [lm] is defined as 

Φ V = K m • ∫ dλ S(λ) • V λ (λ), (3) 

where K m = 683 lm/W is the maximum spectral luminous 

efficacy for photopic vision, λ [nm] is the wavelength, 

S(λ) [W/nm] is the spectral flux distribution, and 

V λ (λ) is the spectral luminous efficiency function. For 

visual diffuse transmission density , the spectral flux 

distribution of the incident flux is denoted by S H (λ) and 

the relative spectral response function V(λ) of the detection 

system is denoted by V T (λ). Note that V(λ) is a 

normalized, unitless function, as is V λ (λ). S H (λ) is based 

on the spectral flux distribution of CIE Standard 

Illuminant A, S A (λ), modified at infrared wavelengths 

to protect the sample and optical elements from excessive 

heat, and V T (λ) is defined so that 

S H (λ) • V T (λ) = S A (λ) • V λ (λ). (4) 

Therefore, because the spectral product on the righthand-side 

of Eq. 4 is the same as that integrated in Eq. 

3, visual diffuse transmission density is determined from 

luminous fluxes. 

In terms of the definitions and concepts presented in 

the previous paragraph, the densitometer measures visual 

diffuse transmission density using the diffuse influx 

mode. The important components of the densitometer are 

shown in Fig. 1, as well as a spherical coordinate system. 

The film step tablet is in contact with the opal that 

provides an influx with a hemispherical geometry and 

a spectral flux distribution S H (λ). The efflux is collected 

within an acceptance cone at normal incidence to the 

film surface and having a half-angle κ less than 10 °, 

and with a relative spectral response function V T (λ). The 

aperture stop of the optical system is the collecting lens, 

while the opal is the aperture that defines the aperture 

flux. Using the functional notation specified in Refs. 2, 

3, and 5, the measured visual diffuse transmission density 

is described by 

D T (90° opal; S H :≤ 10°;V T ). (5) 

The aperture flux Φ j measured by the densitometer is 

given by 

Ij 

Φj = Km ⋅∫ 

dAj∫ 

dΩj∫ 

dλLj( Aj, θj, φ j; λ) ⋅ V( λ) 

= 

R 

, (6) 

j 

where A j [m 2 ] is the area over which the aperture flux 

emerges, Ω j [sr] is the projected solid angle over which 

the aperture flux is collected, θ j and φ j are the polar and 

azimuth angle, respectively, of the aperture flux, L j 

[W/(m 2 sr nm)] is the aperture spectral radiance from 

the opal, I j [A] is the current from the photodiode for 

the aperture flux, and R j [A/lm] is the photometric 

responsivity of the detector. For a Lambertian spectral 

radiance, the integrals over A j and Ω j yield the throughput 

of the densitometer. An immediate simplifying assumption 

for Eq. 6 is that the spectral radiance L j is 

Figure 1. Schematic diagram of the important components of 

the visual diffuse transmission densitometer. 

uniform over the area A j , and that A j is small enough so 

that Ω j is the same at all points of this area. This is 

reasonable because the flux from the opal varies by less 

than 8% from its value at the center and the opal is 

much smaller than the aperture stop of the detection 

system. Then, Eq. 6 becomes 

Ij 

Φj = Km ⋅Aj⋅∫ 

dΩj∫ 

dλLj( Aj, θj, φ j; λ) ⋅ V( λ) 

= 

R 

. (7) 

j 

Similarly, the transmitted flux Φ τ measured by the densitometer 

is given by 

Ω 

Iτ 

= Km ⋅A ⋅∫ 

dΩ 

∫ d λL ( θ , φ ; λ) ⋅ V( λ) 

= 

R 

, (8) 

τ τ τ τ τ τ 

where A τ [m 2 ] is the area over which the transmitted 

flux emerges, Ω τ [sr] is the projected solid angle over 

which the transmitted flux is collected, θ τ and φ τ are the 

polar and azimuth angle, respectively, of the transmitted 

flux, L τ [W/(m 2 sr nm)] is the transmitted spectral 

radiance from the sample, I τ [A] is the current from the 

photodiode from the transmitted flux, and R τ [A/lm] is 

the photometric responsivity of the detector . The 

transimpedance amplifier with gain G [V/A] converts 

the current from the photodiode to a voltage signal N [V] 

for both fluxes. 

The sample has a spectral hemispherical/directional 

transmittance τ(2π; θ τ , φ τ ; λ), where 2π indicates that the 

incident flux is over the entire hemisphere. This transmittance 

is related to the bi-directional transmittance 

distribution function (BTDF) f t (θ i , φ i ; θ τ , φ τ ; λ) [sr –1 ] by 

τ 

NIST Reference Densitometer for Visual Diffuse Transmission Density Vol. 43, No. 4, July/Aug. 1999 389

1 

τ( 2π; θτ, φτ; λ) = ⋅∫ f t ( θ i , φ i ; θτ, φτ; λ) 

dΩ i , (9) 

π 

where the integral of the projected solid angle is over 

the entire hemisphere. Note that the BTDF is the transmittance 

analog of BRDF, and relates the incident irradiance 

to the transmitted radiance. As specified in the 

documentary standards, the sample is in contact with 

the opal, 3 and therefore the radiant flux transmitted by 

the sample also includes flux from the inter-reflections 

between the sample and the opal. This situation is described 

by the spectral hemispherical/directional transmittance 

factor T(2π; θ τ , φ τ ; λ), that depends on both the 

spatial and spectral variables and is given by 

τ( 2π; θτ, φτ; λ) 

T( 2πθ ; τ, φτ; λ) 

= 

1 − ρo( 2π; θτ, φτ; λ) ⋅ ρ( 2π; θτ, φτ; λ) 

. (10) 

The spectral hemispherical/directional reflectance of the 

opal and sample are ρ o (2π; θ τ , φ τ ; λ) and ρ(2π; θ τ , φ τ ; λ), 

respectively. Thus, the transmitted spectral radiance L τ 

is 

Lτ( θτ, φτ; λ) = Lj( 2π; λ) ⋅T( 2 π; θτ, φτ; λ) 

, (11) 

where L j (2π; λ) is the spectral radiance incident on the 

sample from the entire hemisphere. As with transmittance, 

the spectral hemispherical/directional transmittance 

factor is related to the bi-directional transmittance 

factor distribution function (BTFDF) f T (θ i , φ i ; θ τ , φ τ ; λ) 

[sr –1 ] by 

1 

T( 2πθ ; τ, φτ; λ) = ⋅∫ fT( θi, φi; θτ, φτ; λ) 

dΩ i . (12) 

π 

Combining Eqs. 7, 8, and 11, the visual diffuse transmittance 

factor T v measured by the densitometer is given 

by 

T 

v 

Φτ 

= = 

Φ 

j 

Aτ ⋅ ∫ dΩτ∫ 

dλ Lj( 2π; λ) ⋅T( 2 π; θτ, φτ; λ) ⋅V( λ) 

N Gj 

R 

τ 

j .(13) 

= ⋅ ⋅ 

A ⋅ ∫ dΩ 

∫ dλ L ( θ , φ ; λ) ⋅ V( λ) 

N G R 

j j j j j j 

The analysis is simplified by assuming that the spatial 

and spectral variables can be separated in Eq. 13, which 

is equivalent to assuming that the spatial properties of T 

and L j 

are independent of wavelength. Therefore, Eq. 13 

becomes 

A ∫ dΩ 

lj 

⋅T 

τ τ ( 2π) ( 2π; θτ, φτ) 

∫ d λS( λ) ⋅T( λ) ⋅V( λ) 

Tv 

= ⋅ 

⋅ 

Aj 

∫ dΩ 

jlj( θj, φj) ∫ dλS( λ) ⋅V( λ) 

, (14) 

where l j (2π) and l j (θ j , φ j ) [1/(m 2 sr)] are the relative spatial 

radiance distributions over the entire hemisphere 

and within the acceptance cone, respectively, T(2π; θ τ , φ τ ) 

is the spatial transmittance factor, and T(λ) is the spectral 

transmittance factor. 

For the ideal densitometer, the relative spatial radiance 

distribution l j (θ i , φ i ) is constant for all angles, the 

spectral flux distribution is S A (λ), and the relative spectral 

response function is V λ (λ). The ideal visual diffuse 

transmittance function T v,id is then given by 

τ 

τ 

T 

v,id 

Aτ ∫ dΩτ T( 2πθ ; τ, φτ) 

∫ d λSA( λ) ⋅To( λ) ⋅Vλ 

( λ) 

= ⋅ ⋅ 

, (15) 

Aj 

∫ dΩ 

j ∫ dλSA 

( λ) ⋅Vλ 

( λ) 

where T o (λ) is the spectral transmittance factor for an 

opal with a reflectance specified in the documentary 

standards. The spatial and spectral terms of Eqs. 14 

and 15 are given by the first two fractions and the last 

fraction, respectively. For the spectral term, the spectral 

correction factor C s is given by 

Tv,id 

∫ d λSA( λ) ⋅To( λ) ⋅Vλ 

( λ) 

∫ d λS( λ) ⋅V( λ) 

Cs 

= = 

⋅ 

Tv 

∫ d λS( λ) ⋅T( λ) ⋅V( λ) 

∫ dλSA 

( λ) ⋅Vλ 

( λ) . (16) 

For the spatial terms, the geometrical correction factor 

C g is given by 

Tv,id 

∫ dΩτ T( 2πθ 

; τ, φτ) 

∫ dΩ 

jlj( θj, φj) 

Cg 

= = 

⋅ 

, (17) 

Tv 

∫ dΩτ lj( 2π) ⋅T( 2π; θτ, φτ) 

∫ dΩ 

j 

which in terms of the BTFDF from Eq. 12, is 

∫ dΩτ ∫ dΩi fT( θi, φi; θτ, φτ) 

∫ dΩ 

jlj( θj, φj) Cg 

= 

⋅ 

. (18) 

∫ dΩτ ∫ dΩi lj( θi, φi) ⋅ fT( θi, φi; θτ, φτ) 

∫ dΩ 

j 

Therefore, C g depends on both the relative spatial radiance 

distribution of the incident radiant flux and on the 

transmitting properties of the sample. 

Consider two extreme examples. First, assume that 

the sample does not scatter the incident flux, but simply 

absorbs it. Then, f T is given by 

2 2 

T i i 

f 

= 2 ⋅T( λ) ⋅δ(sin θτ −sin θ ) ⋅δ( φτ − π ± φ ), (19) 

where δ(x) is the Dirac delta-function. Performing the 

integrals over dΩ i with this expression for f T , Eq. 18 

becomes 

∫ dΩτ 

∫ dΩ 

jlj( θj, φj) Cg 

= ⋅ 

, (20) 

∫ dΩτ lj( θτ, φτ) 

∫ dΩ 

j 

which, for the reasonable assumption that the acceptance 

cones for the aperture and transmitted fluxes are 

the same, becomes C g = 1. Second, assume that the 

sample is a Lambertian diffuser, so that f T = 1/π. Then, 

C g becomes 

C 

g 

∫ dΩi 

∫ dΩ 

jlj( θj, φ j) 

= ⋅ 

, (21) 

∫ dΩi lj( θi, φi) 

∫ dΩ 

j 

where, assuming that the relative spatial radiance distribution 

is Lambertian within the acceptance cone, reduces 

to 

∫ dΩi 

1 

Cg 

= = , (22) 

∫ dΩ i lj( θi, φi) 

d 

where d is the diffusion coefficient for the opal. From 

these two extreme cases, the range of C g is 1 ≤ C g ≤ 1/d. 

Finally, the visual diffuse transmittance of the sample 

measured with an ideal densitometer, τ v,id , is given by 

τ 

v,id 

∫ d λSA 

( λ) ⋅τ( λ) ⋅Vλ 

( λ) 

= 

, (23) 

∫ dλSA 

( λ) ⋅V 

( λ) 

λ 

390 Journal of Imaging Science and Technology Early et al.

where τ(λ) is the spectral transmittance of the sample. 

The transmittance correction factor C t is then given 

by 

C 

t 

τv,id 

d SA 

V 

= = 

∫ λ ( λ) ⋅τ( λ) ⋅ λ ( λ) 

T ∫ dλS ( λ) ⋅T( λ) ⋅V 

( λ) . (24) 

v,id 

Combining, Eqs. 13, 16, and 17, the visual diffuse 

transmittance factor of a sample measured on an ideal 

densitometer in terms of the measurements and characteristics 

of the actual densitometer is given by 

A 

T = T ⋅C ⋅C 

v,id V S g 

N G R 

τ j j 

= ⋅ ⋅ ⋅ 

N G R C S⋅ 

C 

j 

τ 

τ 

λ 

g 

(25) 

and, including Eq. 24, the visual diffuse transmittance 

of a sample measured by an ideal densitometer without 

an opal in contact with the sample is given by 

τ 

= T ⋅C 

N G 

v,id v,id t 

R 

R C C C . (26) 

τ j j 

= ⋅ ⋅ ⋅ S⋅ g ⋅ t 

Nj 

Gτ 

τ 

Note that because all three correction factors are ratios, 

only relative values of the integrated quantities 

are needed. 

By combining Eqs. 2 and 13, the visual diffuse transmission 

density measured by the densitometer is given 

by 

D 

T 

⎛ Φ j⎞ 

Nj 

G R 

=− TV 

= ⎜ ⎟ 

⎝ ⎠ 

= ⎛ 

N 

⋅ G 

⋅ 

⎞ 

τ τ 

log10 log10 log10 

Φ 

⎜ 

⎝ j R 

⎟ , (27) 

τ τ j⎠ 

which is used both to calculate D T from the experimental 

values and to determine the uncertainty in D T from 

the uncertainties in the variables. By combining Eqs. 

25 and 27, the visual diffuse transmission density for 

an ideal densitometer D T,id is given by 

D T,id = D T – log 10 (C S ) – log 10 (C g ), (28) 

which is also used to calculate the uncertainty in D T 

due to the non-ideal characteristics of the actual densitometer. 

Finally, the visual diffuse transmittance density 

for an ideal densitometer without an opal, from Eqs. 

25 to 28, is given by 

D τ,id = D T – log 10 (C S ) – log 10 (C g ) – log 10 (C t ). (29) 

For convenience, visual diffuse transmission density will 

often be referred to simply as transmission density for 

the remainder of the paper. 

Description and Operation of the Densitometer 

The densitometer was designed and built to automatically 

measure the visual diffuse transmission density of each 

step of film step tablets using computerized data acquisition 

and control. A side view of the mechanical, optical, 

and electrical components of the densitometer, as well as 

the connections between them and the optical path from 

the lamp housing to the detector, is shown in Fig. 2. The 

densitometer is conveniently divided into three systems: 

source, film transport, and detector. 

The source system provides diffuse illumination to the 

film step tablet with spectral flux distribution S(λ), using 

a lamp and housing, an infrared filter assembly , a 

shutter, and an opal. A 100 W quartz-tungsten-halogen 

lamp is contained in the lamp housing and operated at 

a constant dc current from the lamp power supply . An 

elliptical reflector focuses the light from this lamp at 

approximately the position of the opal. The infrared filter 

consists of a flow of chilled water between two glass 

plates; the top optical filter is chosen so that the transmittance 

of the infrared filter modifies the spectral flux 

distribution from the lamp to one closely approximating 

S H (λ). The lamp housing is also cooled with chilled 

water, and if the flow of water is interrupted, the flow 

meter disables the power supply, preventing the infrared 

filter from overheating. An electronically controlled 

shutter blocks all light from reaching the opal for a 

measurement of the dark signal. A flash opal with a diameter 

of 3 mm and a thickness of 1.5 mm is the source 

of diffuse illumination. The opal is mounted in a sleeve 

and the top is centered in and flush with the vacuum 

plate described below. Black enamel paint is applied to 

the sides of the opal so that all the influx originates 

from the top of the opal, which defines the sampling 

aperture. 

The film transport system picks up film from a tray 

using a holder, positions the film to measure the transmission 

density of each step, and drops the film in another 

tray. A top view of this system is shown in Fig. 3. 

The film holder is attached to a vertical spring-loaded 

stage on a vertical translation stage, that in turn is attached 

to a horizontal translation stage. The film holder 

and translation stages move the film to the appropriate 

locations. A vacuum holds the film on the holder and 

brings the film into direct contact with the opal. The 

vacuum is applied through solenoids, and an additional 

solenoid brings air into the holder when the film is 

dropped in the tray. The film holder has a groove along 

its outer edge, so that when the holder is in contact with 

a film and vacuum is applied to this groove, the film is 

attached to the holder and can be moved. When a film is 

on the vacuum plate and a vacuum is applied, small holes 

in the vacuum plate pull the film down onto the opal. 

The detector system collects and detects the radiant 

flux from the opal or the step. The lenses collect the 

flux within the acceptance cone, collimate it through a 

photopic filter, and focus it onto a Si photodiode detector. 

A transimpedance amplifier converts the current from the 

photodiode to a voltage, that is then measured with a 

digital voltmeter. A baffle with a diameter of 10 mm reduces 

scattered light in the detector system. The spectral 

transmittance of the photopic filter is such that, in 

combination with the spectral responsivity of the photodiode, 

the spectral response function of the detector 

system closely approximates V λ (λ). The photopic filter 

is slightly tilted so that the light reflected from it does 

not travel back down to the opal. The 4 mm by 4 mm Si 

photodiode is contained in a package that provides thermoelectric 

temperature control and transimpedance amplification 

with a gain that can be selected either 

manually or automatically. The aperture stop of the 

optical system is the collecting lens that defines an acceptance 

cone with a half-angle κ = 9.5°. If the opal is 

included in the optical system, it is the field stop; if it is 

not, the photodiode is the field stop. W ith this second 

choice for defining the field stop, the field of view has a 


Figure 2. Schematic diagram of all the components of the visual diffuse transmission densitometer and their electrical and 

mechanical connections. 

Figure 3. Top view of the film transport system of the visual diffuse transmission densitometer. 

392 Journal of Imaging Science and Technology Early et al.

diameter of 10 mm at the plane of the opal, which is 

large enough to capture the entire area from where flux 

exits a step. 

The films of a batch to be measured are loaded into 

the film holder. For each film, the holder is moved on 

top of it and the vacuum is applied, attaching the film 

to the holder. While the steps of the film are centered in 

their longitudinal direction (parallel to the short dimension 

of the film) by the position of the holder perpendicular 

to its horizontal direction of travel, centering 

the steps in their transverse direction is accomplished 

by optical means. The location of the boundary between 

the first and second steps is found by measuring the 

signal as the film is moved horizontally just above the 

opal; a 5% decrease in the signal indicates the boundary. 

The positions of the centers of the steps are then 

referenced from the location of the boundary. 

The film is moved away from the opal and the aper - 

ture signal N j is measured at an amplifier gain G j = 10 5 

V/A. The transmitted signal N τ is measured by moving 

the film horizontally to center the step on the opal, lowering 

the film until it is on top of the opal, and applying 

a vacuum to the vacuum plate while releasing the 

vacuum on the film holder. The amplifier gain G τ is selected 

to yield a signal between 1 V and 12 V. After the 

last step is measured, the film is moved over the other 

film tray, the vacuum on the holder is released and air 

is introduced into the line, and the film falls onto the 

tray. The aperture signal is measured again as described 

previously. Dark signals are measured at each amplifier 

gain with the shutter closed, and these are subtracted 

from the signals obtained at that gain to yield 

net aperture and transmitted signals. The two aperture 

signals are averaged, and Eq. 27 is used to calculate 

the transmission density of each step, assuming that 

the photometric responsivity of the detector was constant 

for all the measurements. Note that only the amplifier 

gain ratio, G τ /G j , is needed for Eq. 27, not the 

absolute values of the gains. 

A batch of films is measured on three separate occasions, 

and the average transmission density of each step 

is reported on the calibration certificate that accompanies 

each film step tablet SRM. The standard deviation 

of the transmission density must be less than the expanded 

uncertainty due to random effects detailed below. 

Proper operation of the densitometer is verified by 

including in each batch several check standard films 

that were measured previously. 

Densitometer Characterization and Uncertainties 

The densitometer was thoroughly characterized, not 

only to ensure proper operation, but also to verify compliance 

with the applicable documentary standards for 

measuring visual diffuse transmission density. 2–4 These 

standards specify both the geometrical and spectral conditions 

for this measurement. The characterization also 

determines the uncertainties in the measurements, that 

are analyzed following the guidelines given in Ref. 7. 

In general, the purpose of a measurement is to determine 

the value of a measurand y. This result may be 

obtained from n other quantities x i through the functional 

relationship f, given by 

y = f (x 1 , x 2 ,...,x i ,...,x n ). (30) 

The standard uncertainty of an input quantity x i is the 

estimated standard deviation associated with this quantity 

and is denoted by u(x i ). The relative standard uncertainty 

is given by u(x i )/x i . The standard uncertainties 

may be classified either by the effect of their source 

or by their method of evaluation. The effects are either 

random or systematic; the random effect arising from 

stochastic temporal or spatial variations in the measurement, 

and the systematic effect from recognized effects 

on a measurement. The method of evaluation is either 

Type A, which is based on statistical analysis, or T ype 

B, which is based on other means. 

To first order, the estimated standard uncertainty u(y) 

in the measurand, due to a standard uncertainty u(x i ) 

is 

∂f 

uy ( ) = ⋅ 

x 

ux ( i) 

∂ 

, (31) 

where ∂f/∂x i is the sensitivity coefficient. The combined 

standard uncertainty u c (y) in the measurand is the rootsum-square 

of the standard uncertainties associated 

with each quantity x i , assuming that these standard uncertainties 

are uncorrelated. The expanded uncertainty 

U is given by k·u c (y), where k is the coverage factor and 

is chosen on the basis of the desired level of confidence 

to be associated with the interval defined by U. 

The components of uncertainty are conveniently divided 

into those arising from the operation of the densitometer, 

compliance with the standards, and the 

properties of the densitometer and the films. In the first 

case, the appropriate form of the measurement equation 

is Eq. 27. Expressing Eq. 27 as 

i 

D T = log 10 (x) (32) 

where D T is the transmission density and x can be a 

signal or the gain ratio, the sensitivity coefficient is 

∂D 

∂x 

T = 

0. 434 ⋅ 

1 . (33) 

x 

Therefore, the standard uncertainty u(D T ) due to the 

standard uncertainty u(x) is 

ux ( ) 

uD ( T ) = 0 . 434 ⋅ . (34) 

x 

Note that the standard uncertainty of D T is proportional 

to the relative standard uncertainty of x. 

There are several components of uncertainty associated 

with operation of the densitometer and calculating 

transmission density from Eq. 27. These components 

are the accuracy of the digital voltmeter , signal noise, 

lamp stability, detector linearity, and the ratio of the 

gains. 

The uncertainty arising from the accuracy of the digital 

voltmeter is a systematic effect with a Type B evaluation. 

Using the manufacturer’s specifications, the relative 

standard uncertainty of N j is 23·10 –6 , while the maximum 

relative standard uncertainty of N τ is 77·10 –6 . The 

combined relative standard uncertainty of the ratio 

N j /N τ is therefore 80·10 –6 which, by using Eq. 34, results 

in a standard uncertainty u(D T )

Figure 4. Relative responsivity (measured signal divided by 

actual flux) of the photodiode and amplifier as a function of 

current at the amplifier gains given in the legend. The horizontal 

dotted line indicates the ideal value. T ypical limits of 

the current measured by the densitometer are also indicated. 

Figure 5. Normalized signal of the efflux from the opal, 

divided by the cosine of the angle as a function of polar 

angle. The dotted line indicates the values for a Lambertian 

diffuser. 

ture flux over the time required to measure a film is 

0.002. 

The linearity of the photodiode-amplifier combination 

was measured using the beam addition method. 

8 

The 

relative responsivity, defined as the ratio of the measured 

signal to the incident flux, was determined at several 

amplifier gains and is shown in Fig. 4 as a function 

of current from the photodiode. Also shown are typical 

maximum and minimum measured currents. The relative 

responsivity is close to the ideal value of one over the 

entire range of measured currents. The uncertainty arising 

from the detector linearity is a systematic effect with 

a Type A evaluation. The maximum relative standard deviation 

of the relative responsivity is 0.0028 at a gain of 

10 9 V/A, resulting in a standard uncertainty u(D T ) = 0.001. 

The gain ratios for successive gains were determined 

by measuring the voltage output of the amplifier at both 

gains with the same input current. Combinations of 

these ratios were then used to calculate the ratio of each 

gain to the gain of 10 5 V/A. These calculated gain ratios 

that are not exactly powers of ten, are used in Eq. 27. 

The uncertainty arising from the gain ratio is a systematic 

effect with a Type A evaluation. The maximum standard 

uncertainty in the gain ratios is 10 –4 , resulting in 

a standard uncertainty u(D T )

Figure 6. 6°/hemispherical reflectance of the opal as a function 

of wavelength. The dotted line indicates the value specified 

in the documentary standard. 

The final properties to consider are spectral, which 

result in uncertainties in D T from Eq. 28 through the 

spectral correction factor C s . The spectral reflectance of 

the opal ρ o (λ) is specified 4 to be 0.55 ± 0.05. The 6°/hemispherical 

reflectance of flash opals of the same type used 

in the densitometer was measured in the Spectral Trifunction 

Automated Reference Reflectometer facility , 9 

and is shown in Fig. 6 as a function of wavelength. The 

spectral reflectance decreases monotonically with wavelength 

and is within the values specified by the standard 

for wavelengths longer than 490 nm. 

The spectral flux distribution of the source, S H (λ), is 

also specified in Ref. 4. This distribution depends upon 

the opal, infrared filter, and current through the lamp. 

With the type of opal, lamp, and filter fixed, as well as 

the thickness of the filter, the only adjustable parameter 

is the current. Therefore, the optimal current to achieve 

a close approximation of S H (λ) was determined experimentally 

using the spectroradiometer in the Low-Level 

Radiance facility. 11 The best agreement between S H (λ) and 

the measured spectral flux distribution S(λ) was obtained 

with a lamp current of 7.8 A. The two distributions, normalized 

at 560 nm, are shown as a function of wavelength 

in Fig. 7(a). The spectral flux distribution S(λ) was relatively 

insensitive to changes in lamp current of 0.1 A. 

Because the lamp power supply maintains a constant 

current to within 1 mA, this distribution is not expected 

to change during measurements. 

The relative spectral response function of the detector 

system, V T (λ), is specified in Ref. 4 to satisfy Eq. 4. 

The spectral responsivity of the photodiode was measured 

in the Spectral Comparator facility , 12 while the 

spectral transmittance of the photopic filter was measured 

in the Regular Spectral Transmittance facility. 13 

The relative spectral response function V(λ) of the densitometer, 

from the product of the responsivity and 

transmittance, is shown as a function of wavelength in 

Fig. 7(b), as well as V T (λ). The relative spectral response 

function closely approximates V λ (λ). Because V λ (λ) is 

widely used, and because no filter could be readily found 

to correctly modify the relative spectral response function, 

no attempt was made to obtain V T (λ). The spectral 

product of the normalized spectral flux distribution and 

the relative spectral response function, S(λ)·V(λ), is 

shown in Fig. 7(c) as a function of wavelength, as well 

as the specified product S H (λ)·V T (λ). 

Figure 7. Normalized spectral flux distribution (a), relative 

spectral response function (b), and spectral product (c) as a 

function of wavelength. The dashed lines are the values specified 

by the documentary standards, and the solid lines are the 

values measured for the densitometer. 

To calculate the spectral correction factor from Eq. 16 

and the transmittance correction factor from Eq. 24, the 

spectral transmittance and reflectance of the steps must 

be known to calculate the spectral hemispherical/directional 

transmittance factor from Eq. 10. These properties 

were measured using a commercial spectrophotometer 

for both types of film step tablets in unexposed areas 

and are representative of the base films. The spectral 

directional/hemispherical reflectance and spectral regular 

transmittance for both types of films are shown in 

Fig. 8 as a function of wavelength. There is spectral 

structure in these properties for the x-ray film, giving 

it a blue tint, while the neutral photographic film has 

no such spectral structure. The spectral transmittance 

will, of course, vary between steps, although its spectral 

shape is expected to remain similar for all steps of 

the same type of film. The spectral reflectance, on the 

other hand, should remain the same for all steps of a 

given film type. Therefore, while the correction factors 

are calculated using the properties of the base films, 

there is a possibility of some dependence of these factors 

on the transmission density of the step. 

The spectral correction factor given by Eq. 16 uses 

the actual values for both the opal spectral reflectance 

and spectral product, and compares them with the ideal 


TABLE I. Components of Uncertainty and the Resulting Standard 

Uncertainties in Visual Diffuse Transmission Density. 

Standard Uncertainty u(D T ) 

X-Ray Photographic 

Component of Uncertainty Effect a) Type b) Film Film 

Voltmeter Accuracy S B

yielding log 10 (C t ) = –0.018 and –0.021, respectively, 

which, from Eq. 10 are independent of transmission density 

if the reflectance of the film is likewise independent. 

Therefore, the transmittance density is always 

greater than the transmission density because it does 

not include the effects of inter -reflections between the 

opal and the step. 

Comparisons with other instruments that measure 

transmission density by an absolute method (without 

relying upon calibrated standards) are important for 

verifying the performance of the densitometer described 

here. While few such densitometers exist, several comparisons 

have been performed due to the new NIST instrument 

becoming operational, and are described in 

detail elsewhere. Briefly, a round-robin comparison 

among laboratories in the United States resulted in differences 

in transmission density 14 of less than 0.04, 

while a comparison with the Physikalisch –Technische 

Bundesanstalt, the national metrology institute of Germany, 

found systematic differences 15 of less than 0.015. 

This later comparison is particularly significant because 

it demonstrates good agreement between national metrology 

institutes, although the differences in transmission 

density are slightly greater than the combined 

expanded uncertainty for the comparison. 

Conclusions 

A densitometer is operational at NIST for measuring 

the visual diffuse transmission density of both x-ray 

and photographic film step tablet Standard Reference 

Materials using the diffuse influx mode. It is fully automated 

so that many films can be measured in one 

batch run. Comprehensive characterizations of the densitometer 

were performed to ensure that it complies 

with the relevant documentary standards for these 

measurements with the result that the expanded uncertainty 

(k = 3) for visual diffuse transmission density 

is 0.006. 

Acknowledgments. Design, construction, and characterization 

of the densitometer benefited from discussions 

with Michael R. Goodwin and Philip W ychorski of the 

Eastman Kodak Co. 

References 

1. E. A. Early, T. R. O’Brian, R. D. Saunders, and A. C. Parr, Standard 

Reference Materials: Film Step Tablet Standards of Diffuse Visual 

Transmission Density – SRM 1001 and SRM 1008, Natl. Inst. Stand. 

Technol., Spec. Publ. 260–135 (1998). 

2. ISO 5–1: Photography – Density Measurements – Part 1: Terms, Symbols, 

and Notations (1984). 

3. ISO 5–2: Photography – Density Measurements – Part 2: Geometric 

Conditions for Transmission Density (1991). 

4. ISO 5–3: Photography – Density Measurements – Part 3: Spectral 

Conditions (1995). 

5. C. S. McCamy, Concepts, Terminology, and Notation for Optical Modulation, 

Photogr. Sci. Eng. 10, 314 (1966). 

6. H. Helmholtz, Handbuch der Physiologischen Optik, Leoplold Voss, 

Leipzig, 1867, p. 168. 

7. B. N. Taylor and C. E. Kuyatt, Guidelines for Evaluating and Expressing 

the Uncertainty of NIST Measurement Results, Natl. Inst. Stand. 

Technol. Tech. Note 1297 (1994). 

8. A. Thompson and H.-M. Chen, Beamcon III, a Linearity Measurement 

Instrument for Optical Detectors, J. Res. Natl. Inst. Stand. Technol. 

99, 751 (1994). 

9. P. Y. Barnes, E. A. Early and A. C. Parr, NIST Measurement Services: 

Spectral Reflectance, Natl. Inst. Stand. Technol. Spec. Publ. 250–48 

(1998). 

10. E. Buhr, D. Hoeshen and D. Bergmann, The Measurement of Diffuse 

Optical Densities. Part I: The Diffusion Coefficient, J. Imag. Sci. 

Technol. 39, 453 (1995). 

11. J. H. Walker and A. Thompson, Spectral Radiance of a Large-Area 

Integrating Sphere Source, J. Res. Natl. Inst. Stand. Technol. 100, 

37 (1995). 

12. T. C. Larason, S. S. Bruce and A. C. Parr, Spectroradiometric Detector 

Measurements: Parts I and II - Ultraviolet and Visible to Near Infrared 

Detectors, Natl. Inst. Stand. Technol., Spec. Publ. 250–41 

(1997). 

13. K. L. Eckerle, J. J. Hsia, K. D. Mielenz, and V. R. Weidner, Regular 

Spectral Transmittance, Natl. Bur. Stand. (U.S.), Spec. Publ. 250–6 

(1986). 

14. E. A. Early and T. R. O’Brian, NIST Transmission Density Instrument, 

Analytica Chimica Acta 380, 143 (1999). 

15. E. Buhr, D. Bergmann, E. A. Early, and T. R. O’Brian, Intercomparison 

of Visual Diffuse Transmission Density Measurements, (in preparation). 



Self-Excited Vibration Induced in Paper-Feed-Roller in 

Electrophotography Copy Machine 

Hiroyuki Kawamoto* 

Corporate Research Laboratories, Fuji Xerox Co., Ltd., Kanagawa, Japan 

Theoretical and experimental investigations have been performed to clarify the mechanism of a self-excited chatter vibration 

induced in a paper-feed-roller system in an electrophotography copy machine. From results of the investigation, the following 

points were deduced: (1) The chatter vibration is induced only when a platen cover is pushed with a certain force and a paper 

does not exist between the roller and a platen glass, i.e., the roller slips against the platen glass. The experimental observation 

suggests that the vibration is a stick-slip vibration induced by the negative speed dependence of the friction coefficient. 

(2) Calculated results based on the present model qualitatively agreed with experimental observations, and several methods to 

suppress the vibration were proposed. (3) The paper-feed-roller system must be designed to be (a) high damping, (b) low negative 

speed dependence of the friction coefficient, (c) small press force, and (d) low arm angle. The resonance frequency of the platen 

cover must be designed to be away from the resonance frequency and its ultraharmonic ones of the roller system. 


Introduction 

A paper-feed-roller system, shown in Fig. 1, is used to 

feed manuscripts automatically onto a platen glass in 

an electrophotography copy or facsimile machine. Friction 

force between a paper and the roller made of rubber 

is utilized to feed the paper initially set on an upper 

tray. Images written on the paper are read by an image 

sensor located under the platen glass. The rollers attached 

to a shaft are driven by a motor through gears 

and a belt. The shaft is connected to a cover through 

arms hinged at both ends of the shaft. The shaft is 

pressed to the platen glass by two springs inserted between 

the cover and the arms at the both ends of the 

shaft to induce the friction force. The low-frequency 

chatter vibration takes place in the roller system when 

the roller slips on the platen glass. This condition typically 

occurs in the case that no paper exists between 

the roller and the platen glass because the motor is operated 

and the roller is forced to rotate even if the paper 

is not fed. The abnormal chatter vibration is also 

observed when the paper sticks and slips to the roller . 

The vibration induces the intolerable large acoustic 

noise and image defect due to misread of a document. 

Many papers have been published on the self-excited 

chatter vibration due to the friction force but, to the 

author’s knowledge, there has been no literature on this 

kind of system as of today . 1–4 The objectives of the 

present investigation are to clarify the vibration mechanism 

and to propose effective countermeasures against 

its cause in order to realize highly reliable copy machine. 


* Current address: Dept. of Mechanical Engineering, W aseda University, 

Tokyo, Japan. 


Figure 1. Schematic of paper-feed-roller system. 

Characteristics of Vibration 

Before conducting a quantitative experiment, qualitative 

characteristics of the vibration were investigated 

experimentally in order to construct a reasonable theoretical 

vibration model. 

1. Small normal noise due to the operation of the motor 

and gear was observed but any chatter vibration did 

not take place when the paper was properly fed. Here, 

398

the proper feed means that the roller does not slip on 

the paper. 

2. The vibration took place when the cover was pressed 

with more than a certain force and the paper was not 

fed or the paper was stuck even though the roller was 

driven. The characteristics 1 and 2 suggest that the 

chatter vibration is a stick-slip vibration due to the 

dry friction between the roller and the platen glass 

or the paper. 

3. The vibration was steady and continuous while the 

cover was pressed. 

4. The acoustic noise sounded uncomfortable, low 

frequency, and like a single-tone. 

5. Major portions of the vibration were the roller , the 

shaft, and the arms. 

Modeling 

Vibration Equation. Based on the experimentally observed 

characteristics of the vibration, a vibration model 

shown in Fig. 1 was introduced. A vibration equation of 

the model is derived by the Lagrange’s equation. 

d ⎛ ∂T 

⎞ ∂T 

∂U 

∂V 

Q 

dt 

⎜ 

q 

∂q˙ 

⎟ 

s ∂qs ∂qs ∂q˙ 

s 

. 

⎝ ⎠ 

− + + = (1) 

s 

where ( •• ) = d 2 /dt 2 , ( • ) = d/dt, t is time, C 0 ≡ C+cl 2 cos 2 Θ, 

and K 0 ≡ K+kl 2 cos 2 Θ. Because the friction coefficient is 

generally not constant but a function of the slip speed 

s, it is assumed to be linear with the speed. 3,4 

( ) = 

µ=µ( s) =µ V + x˙ 

µ+ sgn( sl ) θ ˙(sinΘ+ 2θcos Θ) µ ' ( µ ' ≡ dµ 

/ dt), 

where V is a process speed, sgn(s) ≡ s/|s|, and µ′ is usually 

negative when the slip speed is slow. Substitution 

of Eq. 4 into Eq. 3 gives 

I ˙˙ 2 2 

( C ' kl y sin ) ˙ 2 

θ + 0 +µ 0 Θ θ + ( K0 

+µ kl sinΘcos Θ) 

θ + 

3 2 

' kl sin cos θθ ˙ 2 2 2 

µ Θ Θ +µ kl cos Θθ 

+ 

(5) 

3 2 

µ ' kl sin cos θθ ˙ 2 3 3 

+ µ ' kl cos θθ ˙ 3 

3 Θ Θ 2 Θ = −µ kly0 

sin Θ. 

Here, the sign sgn( s) of µ is omitted, because the slip 

speed is always positive in the present system. Because 

the fifth, sixth, and seventh terms of the left hand side 

of Eq. 5 are negligibly small compared to the other terms 

with the given parameters cited in the Calculation 

section below, Eq. 5 is simplified as 

(4) 

The kinetic energy T, the potential energy U, the dissipation 

function V, and the non-conservative force Q are 

1 2 1 

2 1 2 1 2 1 2 

T = Iθ ˙ × U = K − + ky V = C + cy 

2 2 

( θ0 

θ ) 2 

, θ ˙ 2 2 

˙ , 

Q =−µ Fl sin( Θ + θ ) ( F = ky), 

where 

C total viscous torsion damping constant of the arms, 

c total viscous damping constant of the rollers, 

F total press force of the rollers to the platen glass (= 

ky), 

I total inertia of the rollers, the shaft, and the arms, 

K total torsion stiffness of the arms induced by the two 

springs, 

k total stiffness of the rollers due to the Hertz contact, 

l length of the arms, 

q s generalized coordinate, 

y vertical displacement of the roller (defined as positive 

in the lower direction), 

µ friction coefficient, 

θ vibration angle from the statically equilibrium 

position (defined as positive in the anti-clockwise 

direction), 

Θ angle from the horizontal line to the statically 

equilibrium position of the arm, 

θ 0 angle from the free position to the statically 

equilibrium position of the arm. 

Substitution of Eq. 2 into the Lagrange’s Eq. 1 yields 

the following vibration equation with respect to the 

angle θ that is assumed to be the generalized coordinate 

q s of the Lagrange equation. 

I˙˙ C ˙ 2 2 2 2 

θ + 0θ + ( K0 

+µ kl sinΘcos Θ) θ +µ kl cos Θθ 

= 

−µ kly sin Θ, 

0 

(2) 

(3) 

⎧ 

˙˙ ' k l y sin cos 

θ ( ' ) 

˙ 

a + ζ + ζ ωn 

− µµ 2 4 3 

⎪ 

⎫⎪ 

⎨2 

0 Θ Θ 

⎬θ 

a + 

2 2 

⎩⎪ 

I ω n ⎭⎪ 

' kl sin cos 

ω θ 

θ˙ n a + µ 3 2 

2 

Θ Θ 

aθa 

= 0, 

I 

where θ a is an angle from the statically equilibrium position 

under friction force, θ a = θ + µkly 0 sinΘ/(K 0 + 

µkl 2 sinΘcosΘ), ω n 

2 

= (K 0 + µkl 2 sinΘcosΘ)/I, 2ζω n = C 0 /I, 

and 2ζ’ω n = µ’kl 2 y 0 sin 2 Θ/Ι. Equation 6 is the basic vibration 

equation. 

Dynamic Stability. The condition for dynamic stability 

against the stick-slip vibration can be derived by examining 

the damping term, the second term in the left 

hand side of Eq. 6. For dynamic stability, this term must 

remain positive. 

⎛ kl 

C+ cl > −µ kl y − µ 2 ⎞ 

2 2 2 2 sin Θcos 

Θ 

cos Θ ' 0 sin Θ⎜1 

2 ⎟. 

(7) 

⎝ Iω 

n ⎠ 

The value in the parenthesis of the right hand side 

of Eq. 7 is positive in the present system (about 0.9 for 

the given parameters in the Calculation section below). 

This implies an interesting characteristic that the 

friction stabilizes the system. The system is prone to 

being dynamically unstable under condition of (a) small 

damping C + cl 2 cos 2 Θ, (b) large negative speed dependence 

of the friction coefficient µ′, (c) large press force 

of the rollers to the platen glass ky 0 , and (d) large arm 

angle Θ. The characteristic (b) was supported by the 

experimental evidence that the chatter vibration was 

suppressed when a tape made of polytetraflorethylene 

whose speed dependence of the friction coefficient is 

positive was stuck on the platen glass. The characteristic 

(c) was also confirmed by the experiment that the 

chatter vibration took place when the cover was pressed 

with more than a certain force, 1.0 N. It is evident that 

(6) 

Self-Excited Vibration Induced in Paper-Feed-Roller in Electrophotography Copy Machine Vol. 43, No. 4, July/Aug. 1999 399

Natural Frequency. The stiffness term, the third term 

in the left hand side of Eq. 5, consists of the stiffness K 0 

that is independent of the friction and the stiffness due 

to the friction µkl 2 sinΘcosΘ. This means that the natural 

frequency with friction is larger than that without 

friction, i.e., the frequency of the chatter vibration is 

higher than the frequency when the chatter vibration 

does not take place. Although this characteristic was 

not quantitatively confirmed by the experiment because 

of a large experimental dispersion, the qualitative tendency 

that the frequency becomes slightly high under 

chatter vibration was observed in the experiment. 

Static Displacement. Static displacement θ a0 is dependent 

on the friction. The roller shifts up under high 

friction. 

Figure 2. Calculated free vibration without friction ( µ = 

µ′ = 0). 

µ kly0 

sin Θ 

θ a 0 ≅− 

( < 0). 

2 

K0 

+µ kl sin Θcos 

Θ 

(8) 

Figure 3. Calculated vibration response with constant friction 

(µ′ = 0). 

Figure 4. Calculated vibration response (µ′ = –5 s/m). 

Figure 5. Calculated vibration response (µ′ = –30 s/m). 

a simplest and easiest countermeasure to suppress the 

stick-slip vibration is to lower the press force. However, 

this method is limited by the condition that a cer - 

tain press force µ p F = µ p ky 0 (p: paper) must be 

maintained to feed the paper. 

Calculation 

Because it is not possible to derive an analytical solution 

of Eq. 5 without neglecting the nonlinear terms, 

numerical calculations were conducted using the Runge– 

Kutta method. This was done to investigate the characteristics 

of the vibration and the effect of speed 

dependence of the friction coefficient. Here the following 

system parameters were used for calculations: l = 

51 mm (designed), Θ = 19 deg (designed), µ = 0.4 (measured), 

k = 6 × 10 4 N/m (calculated by Hertz ’s contact 

theory), y 0 = 1.63 × 10 –4 m (derived from the measured 

threshold press force, 1.0 N), I = 0.0003 kgm 2 (designed), 

K = 25 Nm/rad (measured), C + cl 2 cos 2 Θ = 0.008887 Nsm 

(derived from the measured damping ratio, 0.02). Initial 

conditions are assumed to be ( θθ , ˙) = (0, 0) at t = 0 

except for the case of no friction. External force due to 

the friction, the right hand side of Eq. 5, induces transient 

vibration even if the initial displacement and velocity 

are assumed to be zero. Calculated results are 

shown in Figs. 2 through 5. The ordinates of the figures 

are vertical vibration of the roll, –y = – θlcosΘ. 

Figure 2 shows the vibration response without friction. 

This case corresponds to the normal condition that 

the paper is fed without stick or slip. The initial condition 

is assumed to be ( θθ , ˙) = (0.003 rad, 0) at t = 0, 

because no external force is applied in this case. Static 

displacement is not induced because no friction force is 

applied to the roller . The vibration is a simple linear 

damping response. The natural frequency and the damping 

ratio are 117.8 Hz and 0.02, respectively, which are 

calculated by the least square method applied to peaks 

of the vibration response. These values deservedly coincide 

with theoretical ones. 

Figure 3 shows the vibration response for the case 

that the friction coefficient is not zero but constant. 

Static displacement, 17.1 µm to the upper side, is induced 

in this case because friction force is applied to 

the roller. The vibration is also a simple linear damping 

response. The system is dynamically stable, because 

the speed dependence of the friction coefficient is assumed 

to be zero. The natural frequency is 124.5 Hz, 

which is a little higher than that of the no-friction case, 

117.8 Hz, as analytically predicted in the Modeling 

section above. Because the system is linear, the numerically 

calculated natural frequency and the damping ratio 

also coincides with the theoretical values. 

Figure 4 indicates the vibration response for the case 

that the speed dependence of the friction coefficient is 

−5 s/m which was estimated by data measured with glass 

and an automotive wiper made of rubber. 5 This case corresponds 

to the actual system in which the self-excited 

vibration takes place. The static displacement and the 

frequency is almost the same with those of Fig. 3, but 

the system is dynamically unstable with a negative 

damping ratio, –0.00685, which is derived by the least 

square method applied to peaks of the calculated vibration 

response in the approximately linear region. 

400 Journal of Imaging Science and Technology Kawamoto

Figure 6. Nonlinearity with respect to vibration amplitude. 

Figure 7. Nonlinearity with respect to period. 

Figure 5 finally shows the vibration response for the 

case that the speed dependence of the friction coefficient 

is extremely large, –30 s/m, that is six times larger 

than that of Fig. 4. Although the vibration is linearly 

increased when the vibration amplitude is small, it suddenly 

diverges to the lower direction when the vibration 

amplitude exceeds about 400 µm. 

Parametric calculations taking µ′ as a parameter are 

conducted to investigate this kind of nonlinear characteristics. 

Figure 6 shows a relationship between the cycle 

number and the logarithm of vibration peaks. It is recognized 

that the vibration is linearly increased from the 

static displacement, 17.1 µm, when the vibration amplitude 

is small but it gradually deviates from the linearity 

in accordance with the increase of the vibration 

amplitude. A period of vibration between adjacent peaks 

indicates the similar characteristics as shown in Fig. 7. 

Although the period is constant, 8.03 ms, which corresponds 

to the natural frequency 124.5 Hz in the linear 

region, it becomes long as the vibration amplitude becomes 

nonlinearly large. These characteristics are due 

to the nonlinearlity of the system. That is, a consequence 

of the vibration increase is the decrease of the effective 

stiffness and hence increase of the vibration amplitude 

and the period, because the forth nonlinear term of the 

left hand side of Eq. 6 becomes relatively large compared 

to the third linear stiffness term. When the fourth 

term exceeds the third term, the effective stiffness falls 

in negative and thus the system is statically unstable. 

The roller goes down when the vibration amplitude exceeds 

the threshold indicated in Fig. 6. 

Experimental 

Experimental Procedure. A series of experiments was 

performed to clarify characteristics of the vibration and 

to demonstrate the adequacy of the model. Figure 8 

shows an experimental set-up. The platen cover and 

glass with the paper -feed roller system was used for 

experiments. The acoustic noise was detected by a microphone 

located at about one meter from the roller and 

the vibration of the drum was measured by a laser displacement 

sensor. Transducer signals of the noise and 

the vibration were introduced to an oscilloscope and to 

an FFT analyzer. Data were recorded on a hard disc in 

a personal computer and then analyzed. Noise measurement 

was conducted in an anechoic room. 

Acoustic Noise. Figure 9 shows measured spectra of 

sound pressure levels under chatter vibration and with- 

Figure 8. Experimental set-up. 

out chatter vibration. The measured main resonance frequency 

under chatter vibration was 117 Hz which coincided 

fairly well with the calculated natural frequency, 

124.5 Hz. Resonance frequencies in parentheses, 182 

and 281 Hz, were not due to the self-excited vibration 

but probably a forced vibration of the motor and gears, 

because these were also observed without the chatter 

vibration. Other higher peeks, 229, 346, 463, 580, and 

697 Hz, were superharmonic ones. These peaks were 

substantially large compared with the main frequency, 

probably because these coincided with eigen frequencies 

of the platen cover. Avoidance of the resonance with 

respect to not only the main but also superharmonic frequencies 

is not a countermeasure of the self-excited vibration 

but effective in order to reduce the acoustic noise 

when the self-excited vibration takes place. 

Self-Excited Vibration. Measurement of vibration response 

is more straightforward than the noise measurement 

to investigate characteristics of the chatter 

vibration. Measured vibration responses of the arm are 

shown in Fig. 10. Here the ordinates are the vertical 

vibration of the roller . Although the vibration is not 

strictly stationary but random, typical and quasi-stationary 

responses are shown in Fig. 10. It is observed 

that the magnitude of the chatter vibration was a limit 

cycle in the order of 10 µm, as a result of the nonlinearity 

of the stiffness and/or the damping. In either case the 

fourth nonlinear term in the left hand side of Eq. 6 is 

negligible, because the vibration magnitude is much 

smaller than the threshold shown in Fig. 6. Therefore, 

Self-Excited Vibration Induced in Paper-Feed-Roller in Electrophotography Copy Machine Vol. 43, No. 4, July/Aug. 1999 401

Figure 9. Measured spectra of sound pressure level. 

Figure 11. Measured spectra of vibration. 

Figure 10. (a) Measured vibration without chatter vibration; 

(b) measured vibration under chatter vibration. 

only Eq. 7 is the practical stability condition. The nonlinear 

terms must be taken into consideration when the 

negative speed dependence of the friction coefficient is 

extremely large under very low speed region even if the 

vibration magnitude is small. 

Figure 11 shows measured vibration spectra under 

chatter vibration and without chatter vibration. Resonance 

frequencies in parentheses, 38, 166, and 258 Hz, 

were not due to the self-excited vibration, because these 

were also observed without the chatter vibration. Except 

for these peaks, a peak at 1 18 Hz was most predominant 

and coincided fairly well with the calculated 

natural frequency, 124.5 Hz, and the measured resonance 

frequency of noise, 117 Hz. Other higher peaks, 

226, 338, and 448 Hz, were superharmonic. We conclude 

from these results that chatter vibration was self-excited 

vibration of the main resonance frequency 18 Hz. 

Conclusions 

Theoretical and experimental investigation has been 

performed to clarify the mechanism of the self-excited 

chatter vibration induced in the paper -feed-roller system 

in the electrophotography copy machine. From results 

of the investigation, the following points were 

deduced: 

1. The chatter vibration is induced only when the platen 

cover is pushed with a certain force and a paper does 

not exist between the roller and the platen glass, i.e., 

the roller slips against the platen glass. The 

experimental observation suggests that the vibration 

is the stick-slip vibration induced by the negative 

speed dependence of the friction coefficient. 

2. Calculated results based on the present model 

qualitatively agreed with experimental observations, 

and several methods to suppress the vibration were 

proposed. 

3. The paper-feed-roller system must be designed to be 

(a) high damping, (b) low negative speed dependence 

of the friction coefficient, (c) small press force, and 

(d) low arm angle. The resonance frequency of the 

platen cover must be designed to be away from the 

resonance frequency and its ultraharmonic ones of 

the roller system. The characteristics (b) and (c) were 

experimentally confirmed. The chatter vibration 

problem has been overcome by sticking a tape made 

of polytetraflorethylene which makes the speed 

dependence of the friction coefficient positive and 

reducing the press force of the springs. 

Acknowledgment. The author wishes to thank Y. 

Nakayama, Y. Ichikawa, and K. Watanabe (Fuji Xerox) 

who supported the work and to N. Kojima (Nagaoka University 

of Technology) who helped to carry out the experiment. 

The author would also like to express his 

thanks to Prof. M. Yoshizawa at Keio University for his 

helpful suggestion. 

References 

1. A. Watari and T. Sugimoto, Vibrations Caused by Dry Friction, Trans. 

Japan Soc. Mech. Eng. 29, 769 (1963). 

2. A. Bhattacharyya, A. B. Chatteerjee, A. Bhattacharyya and B. K. 

Mallick, Analysis of Stick-Slip Motion of a Vander–Pol Model, CIRP, 

2011, 81 (1971). 

3. H. Kawamoto, Chatter Vibration of a Cleaner Blade in Electrophotography, 

J. Imaging Sci. Technol. 40, 8 (1996). 

4. H. Kawamoto, Self-Excited Vibration of a Lap Spring Clutch Used in 

Electrophotography Fuser, Nonlinear Dynamics, 16, 153 (1998). 

5. R. Suzuki and K. Yasuda, Analysis of the Chatter Vibration in an Automotive 

Wiper Assembly (Derivation of Approximate Solution and 

Study of Vibration Characteristics), Trans. Japan Soc. Mech. Eng. 

61, 3203 (1995). 

402 Journal of Imaging Science and Technology Kawamoto

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404 Journal of Imaging Science and Technology

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