optical

OPTICS
INTRODUCTION
The optics lab consists of three experiments: (1) blackbody radiation from a tungsten
filament, (2) optical absorbance and (3) photoluminescence (PL) of light-sensitive (dye)
molecules in a solution. The experiments use contemporary technology, with laser diodes,
optical fibers, charge-coupled-devices (CCD), etc.
EQUIPMENT
Ocean Optics HR2000+ High-speed Fiber Optic Spectrometer (operation,
data sheet, system sensitivity, grating efficiency, ccd array)
Ocean Optics SpectraSuite software
Ocean Optics HG-1 Mercury Argon Calibration Light Source
Ocean Optics LS-1 Calibration Light Source
Ocean Optics CUV-UV Holder for 1-cm Cuvettes
Ocean Optics CVD-UV Disposable Cuvettes
Ocean Optics P400-1-SR Optical Fiber (general information)
Ocean Optics 74-UV Collimating Lens (general information)
ThorLabs Laser Diode (HL6322G 635 nm, HL7851G 785 nm,
LD2000 APC Laser Diode Driver, LT220P-B Collimation Tube)
ThorLabs Cage System (ER8 Construction Rods, CP02T Cage Mounts,
HPT1 XY Translation Mount, SM1SMA Fiber Adapter)
Indocyanine Green (ICG)
Hexamethyl indotricarbocyanine tetrafluoroborate (HITC-BF4)
Agilent E3633A DC Power Supply (User Guide, Service Guide)
Coherent LaserCheck laser power meter
WARNING! Visible and invisible laser radiation in used in this optics lab. Avoid direct
exposure to the beam and scattered light. The power of the diode laser is ∼10 mW, which
can blind you! Safety goggles must be worn when these lasers are in use.
A photograph of some of the equipment is shown in Fig. 1. The optical components are
contained in an ∼1 m opaque enclosure.
1

Fig. 1. Photograph of some of the equipment used in the optics experiments.
INSTRUMENT CALIBRATION
The Ocean Optics HR2000+ Fiber Optic Spectrometer measures a light intensity distribution
density (light intensity per unit band of wavelength, with units microwatts per square
centimeter per nanometer, µW/cm 2 -nm) as a function of wavelength. Both the wavelength
axis and the light intensity distribution density axis must be calibrated. An Ocean Optics
HG-1 Mercury Argon Calibration Light Source is used for for calibrating the wavelength,
and an Ocean Optics LS-1 Calibration Light Source is used for calibrating the light intensity
distribution density. After using these calibration sources, be sure to turn them off, because
the bulbs have a finite lifetime.
THEORY
The Photon
The photon is the most abused concept in all of science. The truth of the matter may be
seen in a quote from Albert Einstein:
“All these fifty years of conscious brooding have brought me no nearer to the answer to the
question, ‘What are light quanta?’ Nowadays every Tom, Dick and Harry thinks he knows
it, but he is mistaken.” (1954)
Virtually all “modern physics” textbooks and “photon” web sites claim that Einstein and the
photoelectric effect (and other experiments) showed the particle nature of light. However,
the “particle nature of light” and the “photon” were thought up by others after Einstein’s
2

explanation of the photoelectric effect, and Einstein did not care for these concepts. The
truth is that there is absolutely no experiment which requires that light behave like a particle;
it is completely sufficient that charges (including those in “detectors”) behave according to
quantum mechanics. There is the greatly reduced concept that a photon is related to the
quantization of the electromagnetic field. It is a greatly reduced concept because in all
of physics there are only a few phenomena which actually require the quantization of the
electromagnetic field (which remains absolutely not particle-like): 1) spontaneous emission
from atoms, 2) the Lamb shift, 3) the anomolous magnetic moment of the electron, and a few
other more obscure effects. Virtually all experiments in optics can be explained completely
with classical electromagnetic fields, and there is no need for a “photon”. The photon can
be a useful concept in perturbation approximations (as in Feynman diagrams), but Nature
does not have any need for perturbation approximations. If you want to be a practitioner
of rigorous physics, don’t be like Tom, Dick and Harry; if you simply stop using the term
photon, or in very rare cases refer to “the quantized electromagnetic field”, you will be right
every time. [?]
Blackbody Radiation
Blackbody radiation [?,?] is electromagnetic radiation from a particular type of source. In
the laboratory, blackbody radiation is approximated by the radiation from a small hole
entrance to a large cavity. Any radiation entering the hole would reflect off the walls of the
cavity multiple times and would be unlikely to again find the entrance hole and escape; such a
perfect absorbance of light would make the cavity and hole appear to be “black”. Arguments
invoking thermal equilibrium show that the ideal absorbance is independent of wavelength
and shape of the cavity and depends only on the temperature of the cavity walls, and also
shows that the blackbody will emit the same amount of radiation as it absorbs. The escaping
radiation is characterized by an intensity distribution density as a function of wavelength λ
(and parameterized by the temperature T): ε e (λ; T). Because this quantity is a function of
wavelength, it is often referred to as a “spectral” density, or sometimes simply “spectrum”.
Its units are intensity per band of wavelength, conveniently expressed as microwatts per
square centimeter per nanometer, or µW/cm 2 -nm. It is a “density” in that it must be
multiplied by a wavelength bandwidth in order to obtain an actual radiation intensity (in
µW/cm 2 ); thus ε e (λ; T)dλ gives the intensity of the radiation having wavelengths between
λ and λ + dλ. In 1901 Max Planck showed that for an ideal blackbody
ε e (λ; T) = 2πhc2
λ 5 1
e hc/λk BT
− 1
(1)
where h = 6.626×10 −34 J-s is Plank’s constant, c = 3.00×10 8 m/s is the speed of light, and
k B = 1.38×10 −23 J/K is Boltzmann’s constant. Plots of ε e (λ; T) versus λ for several values
of T are shown in Fig. 2.
3

Fig. 2. Blackbody spectral density versus wavelength for several temperatures.
By integrating the spectral density (Eq. 1) over all wavelengths, one obtains the total radiated
intensity (power per unit area) S e (T) at the temperature T :
S e (T) = 2π5 k 4 B
15c 2 h 3T4 = σ B T 4 (2)
where σ B = 2π 5 k 4 B /15c2 h 3 = 5.67×10 −8 W/m 2 -K 4 is the Stefan-Boltzmann constant.
From the plots in Fig. 2, it can be seen that ε e (λ; T) has a maximum at some λ = λ max for
each T. Taking the derivative of Eq. 1 with to respect to λ and setting it equal to zero gives
an equation which can be solved for λ max as a function of T :
This is known as the Wien displacement law.
λ max = ( 2.90 × 10 −3 m-K ) T −1 (3)
Actual thermal radiation devices are not quite ideal, theoretical blackbodies. Real devices do
not have perfect absorbance but reflect some fraction of any incident radiation. The deviation
from perfect absorbance by a particular material is given by a function a e (λ; T) < 1; because
of the balance between absorption and emission of radiation, this quantity is referred to as
either absorptivity or emissivity. For real devices approximating a blackbody, the formulas
for ε e (λ; T) and S e (T) must be multiplied by the absorptivity a e (λ; T) characterizing the
device. In the optics lab experiment on blackbody radiation, the radiator involves a tungsten
filament; the absorptivity function for tungsten is shown in Fig. 3.
4

Fig. 3. Absorptivity for tungsten as a function of wavelength and temperature.
In the derivation of the blackbody formulas, it is assumed that the blackbody is in equilibrium
with (and hence at the same temperature as) its environment. However, in the optics
lab blackbody experiment, the device approximating the blackbody is heated to a temperature
T significantly above its environment, which is at room temperature T 0 ≃ 300 K; thus
the formula for blackbody power radiation must be modified, as will be shown below. Furthermore,
the experimental blackbody will also lose energy due to heat being removed by
convection in the surrounding air; this power loss is linearly proportional to the difference
in the device temperature T and the environment temperature T 0 . The total power lost by
the blackbody device due to being out of thermal equilibrium with its environment must be
supplied by an external source; in the case of the optics lab blackbody device, this is the
electrical power delivered to the tungsten filament. By conservation of energy we have
I dc V dc = κ (T − T 0 ) + 〈a e 〉 (T)σ B A ( )
T 4 − T0
4 (4)
where I dc is the DC current passing through the tungsten filament, V dc is the voltage drop
across the filament, κ is the effective thermal conductivity due to convection in the air,
〈a e 〉 (T) is an average of a e (λ; T) over wavelengths for which data are taken, and A is an
estimate of the area of the tungsten filament.
With the above formulas, the goals of the optics lab blackbody experiment may be outlined
as follows:
(a) By measuring the spectral density of the radiation from the tungsten filament and com-
5

paring with the appropriate formula, the temperature T of the filament may be determined.
By adjusting the electrical power delivered to the filament, different temperatures may be
measured.
(b) Using several values of T, the electrical power I dc V dc may be plotted versus T 4 , and the
slope of a fitted line may be used to determine a value for σ B .
Optical Absorbance by Light Sensitive Molecules and Beer’s Law
The Beer-Lambert Law [?], more commonly known as Beer’s law, states that the optical
absorbance by a light-sensitive molecule (e.g., a dye molecule) in a transparent solvent varies
linearly with both the sample cell path length and the concentration of the molecules in the
solvent. In practice, Beer’s law is accurate enough for a range of light-sensitive molecules,
solvents and concentrations, and is a widely used relationship in quantitative spectroscopy.
Absorbance is measured in a spectrophotometer by passing a collimated beam of light at
wavelength λ through a plane parallel slab of material that is normal to the beam. For
liquids, the sample is held in a an optically flat, transparent container called a cuvette.
Optical absorbance OA is calculated from the ratio of the spectral density transmitted
through the sample ε ′ e (λ) to the spectral density that is incident on the sample ε e (λ) (with
T = room temperature).
ε ′ e (λ)
OA = − log 10 (5)
ε e (λ)
For a sample with an optical pathlength l and a molar concentration C m [with units of
molarity (M), defined as a mole per liter (mol/L)], Beer’s law can be stated as
OA = α m (λ)lC m (6)
where α m (λ) is the coefficient of molar absorptivity (also known as the extinction coefficient)
of the molecule at wavelength λ. α m (λ) has units M −1 m −1 , and is a property of the material
and the solvent.
In an absorbance experiment, light is attenuated not only by the light-sensitive molecule
but also by reflections from the interface between air and the cuvette, the cuvette and the
sample, and absorbance by the solvent. These factors can be quantified separately, but
are often removed by defining ε e (λ) as the light intensity passing through a sample blank
or reference sample (e.g., a cuvette filled with solvent but with zero concentration of the
light-absorbing molecule).
In the optics lab, the transmitted spectral density ε e ′ (λ) of various samples with different
concentration and the sample blank spectral density ε e (λ) are measured so as to determine
the absorbance OA. By fitting the absorbance OA versus the concentration C m , which should
have linear relation, Beer’s law may be verified. The measurements will be performed on
solutions of two different dye molecules, indocyanine green (ICG) [?] and hexamethylindotricarbocyanine
tetrafluoroborate (HITC-BF4) [?] solutions.
6

Photoluminescence
Photoluminescence (PL) [?] is a process in which a chemical compound absorbs electromagnetic
radiation, makes a transition to a higher electronic energy state, and then re-emits
electromagnetic radiation upon returning to a lower energy state. In stricter terms it is “luminescence
arising from photoexcitation”. The time delay between absorption and emission
is typically extremely short, on the order of 10 nanoseconds. Under special circumstances,
however, this period can be extended into minutes or hours.
In this experiment, the concentration dependence of photoluminescence will be measured for
indocyanine green (ICG) and hexamethylindotricarbocyanine tetrafluoroborate (HITC-BF4)
solutions.
PROCEDURE
Calibration
The HG-1 Mercury Argon Calibration Light Source is used to calibrate the x-axis (wavelength
axis) of the HR2000+ spectrometer. Connect the HG-1 to the HR2000+ with a
fiber optic cable, and take a spectrum with the SpectraSuite software. Fit each peak in the
spectrum with an appropriate function (Gaussian, Lorentzian, or other?) to determine the
wavelength at the peak, λ fit . Make a plot of (λ − λ fit ) versus λ, where the values of λ are
the accepted values of the spectral lines for the HG-1. What is the mean apparent error for
the range of 200 to 1000 nm?
The LS-1 Calibration Light Source is used to calibrate the y-axis (spectral density axis) of
the HR2000+ spectrometer. Make a measurement as with the HG-1, but also make a measurement
with the LS-1 off to obtain a background spectrum; in the data analysis, subtract
the background from the measured LS-1 spectrum. Determine the HR2000+ calibration
curve by comparing the measured LS-1 spectrum with the actual LS-1 spectrum which is
given by a blackbody spectrum at 2000 K, multiplied by an absorptivity curve given by:
where the coefficients are given by
a e (λ) = C 0 + C 1 λ + C 2 λ 2 + C 3 λ 3 + C 4 λ 4 + C 5 λ 5 + C 6 λ 6 (7)
C 0 -1.07983×10 0
C 1 1.58273×10 −2
C 2 -6.41915×10 −5
C 3 1.33611×10 −7
C 4 -1.51662×10 −10
C 5 8.90834×10 −14
-2.12064×10 −17
C 6
The calibration can be used from 400 nm to 900 nm. Check to see if your calculated
calibration is in reasonable agreement with a value predicted using the available optical fiber
properties, the HC1 grating efficiency curve, and the properties of the charge-coupled-device
(CCD) used in the HR2000+, which together contribute to an “instrument function”.
7

Blackbody Radiation
An illustration of the setup for the blackbody experiment is shown in Fig. 4, and a photograph
is provided in Fig. 5.
Fig. 4. Schematic of the blackbody radiation setup
Fig. 5. A photograph of the blackbody radiation setup
8

In Fig. 5, the tungsten lamp is inside the enclosure to the left. An adjustable iris just
outside the enclosure is used to vary the amount of light falling on the fiber connected to
the HR2000+ spectrometer.
For estimating the surface area of the filament A, use the photographs of the filament shown
in Fig. 6. The dimensions of the filament coil region are 4.06×2.22×1.00 mm, and the
filament wire diameter is 0.229 mm. The leads below the coil are 8.0 mm long.
Fig. 6. Pictures of the tungsten 12 V, 100 W lamp filament. On the left is the front view
and on the right is the side view.
1. Set up the experiment according to the schematic in Fig. 4 and align the optics.
2. Set the tungsten filament at a certain power (make sure the input power and voltage
are smaller than 100 W and 12 V), and collect the blackbody spectrum with HR2000+
spectrometer. You may find that the intensity of the light radiated by the filament is so
high that the spectrum always saturates even for the minimum integration time. If this
happens, change the iris size and/or change the integration time of the spectrometer.
Take a background spectrum for subtraction when you analyze the data.
3. Change the input power for the filament and repeat step 2 to get several spectra at
different input powers.
4. Using Eq. 1 to fit your spectra, you should be able to determine the temperature of
the filament at a certain input power. You will need to account for the absorptivity as
a function of both wavelength and temperature (provided in Fig. 3). You will want to
fit the data in Fig. 3 in order to come up with an analytical absorptivity function as
an approximation.
5. Once you determine the temperature for each power, you can plot the power supplied
to the lamp I dc V dc versus T 4 . Using Eq. 2, determine a value for the Stefan-Boltzmann
constant.
Optical Absorbance by Light Sensitive Molecules and Beer’s Law
An illustration of the setup for the absorbance experiment is shown in Fig. 7, and a photo-
9

graph is provided in Fig. 8.
Fig. 7. Schematic of the absorbance setup
Fig. 8. A photograph of the absorbance setup
The CUV-UV Holder for 1-cm Cuvettes couples to lamps and spectrometers to create an
absorbance or transmission measurement system. Two 74-UV lenses are mounted across the
cell holder for square 1-cm cuvettes. The base includes channels for connection to a water
bath for temperature regulation, and the unit also accepts filters. The 74-UV lens uses fused
10

silica for a wavelength range of 200 to 2000 nm. When focused for collimation, the beam
divergence is 2 degrees or less, depending on the optical fiber diameter.
1. Set up the experiment according to the schematic in Fig. 7. The light source here is
the same tungsten filament used for the blackbody radiation experiment.
2. Align the optics so that sufficient light goes into the fiber.
3. Prepare ICG and HITC-BF4 solutions with various concentrations. You may find that
low concentrations (less than 10 −3 M) are preferable for this experiment. A CVD-UV
Disposable Cuvette should be filled with a sample.
4. Put the cuvette with a solution in the CUV-UV Holder and collect the spectra for both
sample spectral density ε e ′ (λ) (with the solution that you want to measure) and blank
spectral density ε e (λ) (with only solvent as a reference).
5. Determine the optical absorbance OA by Eq. 5.
6. Repeat steps 4 and 5 for each of the various concentrations.
7. Using Eq. 6, determine the molar absorptivity of your sample.
In your lab report, you should comment on the optical properties of the various components
(the cuvette, the cuvette holder and its lenses, etc.) used in the measurement, and how they
might affect the performance of the apparatus.
Photoluminescence
An illustration of the setup for the photoluminescence (PL) experiment is shown in Fig. 9,
and a photograph is provided in Fig. 10.
Fig. 9. Schematic of the photoluminescence setup
11

Fig. 10. A photograph of the photoluminescence setup
In the photoluminescence experiment,
diode lasers at wavelengths of 635 nm and
785 nm are used. You must follow the
safety procedures for using lasers. The
diode lasers are held in a LT220P-B Collimator
Tube and operated with a LD2000
APC Laser Diode Driver. The driver is
contained in a unit made by the Physics
Department Electronics Shop; a photograph
of a laser diode with collimator,
holder and driver is shown in Fig. 11.
Fig. 11. Photograph of a laser diode with collimator,
holder and locally fabricated driver
unit.
12

1. Set up the experiment according to the schematic in Fig. 9.
2. Put on safety goggles and align the optics carefully. The PL intensity from the solution
can be very weak depending on the quality of your alignment and the concentration
of your solution. Use the special spanner wrench to adjust the lens in the front of the
collimation tube. A cage system is used to align the lenses for collecting the light for
the PL spectra. The optical axis of the cage should be perpendicular to the direction
of the incident laser. For this geometry, use the cuvette holder that is designed for a
PL experiment. For 785 nm infrared (IR, which is almost invisible) laser, use the IR
sensitive card to check the laser spot and align the optics. (Note: as a safety measure,
the laser will not be lasing if the laser head is not mounted on the laser holder.)
3. Using appropriate excitation (635 nm and/or 785 nm), record the PL spectra of both
ICG and HITC-BF4 solutions with different concentrations.
Acknowledgement: The original experiment design, lab guide, diagrams and photographs
were prepared by Duming Zhang (c. 2005).
References
[1] M. O. Scully and M. Sargent, Physics Today, March 1972, p 38-47, “The concept of the
photon”
[2] F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York,
1965), pp. 373-388.
[3] Daryl W. Preston, Eric R. Dietz, The Art of Experimental Physics (John Wiley & Sons,
New York, 1991).
[4] J. D. J. Ingle and S. R. Crouch, Spectrochemical Analysis (Prentice Hall, New Jersey,
1988)
[5] M. L. J. Landsman, G. Kwant, G. A. Mook and W. G. Zijlstra, J. Appl. Physiol.,
40, 575-583 (1976). “Light absorbing properties, stability, and spectral stabilization of
indocyanine green”.
[6] Marvin J. Weber, Handbook of Lasers (CRC Press, Boca Raton, FL, 2001).
[7] Donald A. McQuarrie and John D. Simon, Physical Chemistry, a Molecular Approach
(University Science Books, Sausalito, CA, 1997).
13