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CALCULATION OF RETINAL<br />
IMAGE QUALITY FOR<br />
POLYCHROMATIC LIGHT<br />
SOWMYA RAVIKUMAR, LARRY N. THIBOS, ARTHUR BRADLEY<br />
Wavefront Congress 2008, San Francisco
The human eye is subject<br />
to substantial chromatic<br />
aberration<br />
Objective and subjective<br />
measurements of LCA agree well.<br />
2.2 D<br />
Most natural scenes have broadspectral<br />
content and thus their<br />
retinal images are subject to<br />
chromatic aberrations
Campbell & Gubisch 1967<br />
Contrast sensitivity<br />
2.5 mm pupil<br />
Spatial Frequency in cycled per degree<br />
Open circles: 578 nm;<br />
Filled circles: Tungsten Lamp white light
CHALLENGE #1:<br />
How to calculate ocular optics at<br />
all wavelengths while only<br />
measuring the optics at perhaps<br />
one wavelength
STEP 1<br />
TCA can be included in model: TCA = d x LCA
STEP 2<br />
n=1<br />
n′(λ)<br />
OPD ≈ QS* (1 - n′ λ cos θ)
Combining monochromatic PSF to create polychromatic<br />
images.<br />
Monochromatic<br />
Wavefronts (LCA<br />
defocus + HOA)<br />
Monochromatic<br />
PSF<br />
| IFT | 2<br />
Polychromatic PSF<br />
Σ PSF λ<br />
Not all wavelengths have the<br />
same diffraction -<br />
Should we assume a common<br />
diffraction limit
STEP 3<br />
2.5 mm EP<br />
Log M T F<br />
Diffraction-limited MTF<br />
MTF in an eye with LCA<br />
MTF in an eye with HOAs MTF in an eye with LCA +<br />
monochromatic aberrations<br />
5 mm EP<br />
SF Cycles per degree
Combining monochromatic PSF to create polychromatic<br />
images.<br />
Monochromatic<br />
Wavefronts (LCA<br />
defocus + HOA)<br />
Monochromatic<br />
PSF<br />
D65 White<br />
Spectrum<br />
V-Lambda<br />
| IFT | 2<br />
Polychromatic PSF<br />
Σ PSF λ
STEP 4<br />
Blue TV<br />
phosphor<br />
Font et al, Journal of Modern <strong>Optics</strong>, 1994.<br />
Polychromatic Point Spread Function: Calculation Accuracy
• Under-sampling the visible spectrum as well as the source spectrum<br />
creates large changes in poly PSF<br />
• The effect is more enhanced when visually important wavelengths are not<br />
sampled<br />
• For systems with larger LCA, this effect is more Obvious (Font et al, J.<br />
Modern <strong>Optics</strong>, 94)
Methods<br />
Computational Fourier <strong>Optics</strong> are used to<br />
calculate polychromatic image quality.<br />
Monochromatic<br />
Wavefronts (LCA<br />
defocus + HOA)<br />
Monochromatic<br />
PSF<br />
D65 White<br />
Spectrum<br />
V-Lambda<br />
| IFT | 2<br />
Polychromatic PSF<br />
Σ PSF λ<br />
IQ<br />
FT<br />
Polychromatic OTF<br />
IQ
Challenge #2:<br />
Limitations on the general utility<br />
of a Polychromatic PSF.
Constraints on convolving a Polychromatic Object and PSF<br />
Monochromatic PSF Monochromatic Object Monochromatic Image<br />
*<br />
Convolution Extrapolated to polychromatic domain<br />
*
An Example of spectrally in-homogenous convolution<br />
Colored Object<br />
Grayscale homogenous<br />
• 7 mm pupil diameter<br />
• Model eye with LCA<br />
• 600 nm in focus<br />
• Target: 1.5 deg * 3.75 degrees<br />
• Blur circle width ~ 10 arc min<br />
*<br />
Single polychromatic<br />
convolution<br />
Blurred Image
*10^-4<br />
4.50<br />
RGB spectra for Macintosh LCD<br />
Radiance (W/sr*m*m per nm)<br />
4.00<br />
3.50<br />
3.00<br />
2.50<br />
2.00<br />
1.50<br />
1.00<br />
5.00<br />
Green<br />
Red<br />
Blue<br />
0<br />
300 400 500 600 700 800<br />
Wavelength (nm)
Red-Green-Blue<br />
decomposition and<br />
individual convolution<br />
RED<br />
*<br />
=<br />
GREEN<br />
+<br />
*<br />
=<br />
BLUE<br />
+<br />
*<br />
=
Red-Green-Blue<br />
Composite Blurred<br />
Image<br />
≠<br />
Homogenous<br />
convolution
Thank You<br />
“Calculation of retinal image quality for polychromatic light”<br />
In Review - JOSA, 2007<br />
Email me for copy at sravikum@indiana.edu
Reflectance of flower petal and leaf<br />
Red layer<br />
Wavelength in nm<br />
Green layer<br />
Blue layer
~700 nm<br />
Diffraction-limited<br />
Only LCA<br />
Monochromatic<br />
aberrations<br />
alone<br />
Monochromatic<br />
aberrations +<br />
LCA<br />
~470 nm<br />
Typical Eye data from IAS dataset<br />
6 mm pupil from Thibos et al 2002
Impact of chromatic aberrations (TCA + LCA) in<br />
eyes with monochromatic aberrations<br />
The aberrated eyes were chosen from a population database (Thibos et al). All the eyes<br />
had total rms < mean magnitude of the population and individual modes did not differ<br />
significantly from the population.
The influence of chromatic aberration is also dependent on the<br />
interaction between monochromatic aberrations<br />
Contrast Sensitivity<br />
Campbell and Gubisch, 1967<br />
30<br />
10<br />
1<br />
3<br />
2.5 mm<br />
Mono<br />
Poly<br />
10 20 30 40 50<br />
SF c/deg<br />
4.0 mm<br />
30 40 50<br />
“SA, which increases with pupil diameter,<br />
could account for the smaller differences.”<br />
Contrast Sensitivity<br />
Yoon and Williams, 2002<br />
100<br />
10<br />
1<br />
1<br />
6mm<br />
w/ HOA<br />
Mono<br />
Poly<br />
3<br />
SF c/deg<br />
10<br />
w/o HOA<br />
“The presence of monochromatic aberrations<br />
greatly reduces the benefit of avoiding chromatic<br />
aberration.”<br />
30
Fixed sampling resolution<br />
Normalised PSF intensity<br />
To add with accuracy, we need corresponding samples
Small, uniform sampling resolution corresponds to<br />
short wavelength
Polychromatic Image Quality<br />
Results for an un-aberrated eye<br />
Wavelength in focus 550 nm; Sampling resolution of 10nm
Pupil Function<br />
λ<br />
| IFT | 2<br />
Point<br />
Spread<br />
Function<br />
*<br />
=<br />
FT<br />
FT<br />
Inverse FT<br />
Optical 1<br />
Transfer<br />
Function o<br />
π<br />
0<br />
× Letter Spectrum = Defocused letter<br />
spectrum
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