2.3.1

Overview: Semi-Conductor Physics and Using a Silicon Photodiode

This first lab is used to get the students familiar with the key component of their radiometers (to be constructed in the next lab), the silicon photodiode. The lab is basically a handout the students read, followed by a series of questions. In the lab we first discuss some background information about semi-conductor physics followed by the construction of a silicon photodiode. We illustrate how the photodiode can be used in a broad-band radiometer. The semi-conductor background discusses how we dope silicon to create n- and p-type semiconductors, at least to the level pertinent in the class. Of course, an entire course can be devoted to this subject matter so we only touch up what is essential. We then talk about how we put these semiconductors together to create a pn-junction. We note that the simplest device that incorporates a pn-junction is called a diode and that a light sensitive variant of the diode is called a photodiode. This is followed by discussion on how we can amplify the output of the photodiode using an operational amplifier. Lastly, we briefly introduce the concepts of photodiode spectral response, responsivity and quantum efficiency. The lab handout ends with a series of 14 questions to be answered and handed in.

2.3.2

Building a Radiometer

Once we have exposed the students to the basic workings of photodiodes and how they can be used to sense light, we actually have them construct a working radiometer. The radiometer utilizes a UDT silicon photodiode with a BNC connection, an LM741 operational amplifier, two 9-volt batteries, a series of feedback resisters, a digital multi-meter, and a 5-position DIP switch. The entire assembly is fabricated on a breadboard using the circuit design shown in Figure 3(a). The operational amplifier is powered by a bi-polar supply, though this is not completely necessary, and is connected to the photodiodes cathode terminal. The resister network allows for a large range of gains when operating the device. That is, low gains for high light levels and high gains for low light levels. The output voltage is read directly from a multi-meter with a saturation value around 9-volts (i.e., the power supply voltage). Currently, the UDT photodiode does not have a diffuser attachment associated with it (i.e., for cosine correction behavior and hemispherical irradiance measurements). We simply expose the bare 1cm² active surface to illumination. This, along with hardware to form a solid angle for radiance measurements, will show up in our next round of improvements.

Figure 3.

Radiometer (a) circuit and (b) breadboard layout.

Before students come to lab, we encourage them to get familiar with the circuit before hand by exploring AutoDesk’s TinkerCAD online. This website allows students to assemble and play with the circuit in a virtual world and has been found to be quite useful.

2.3.3

Using your Radiometer

Once the radiometer has been constructed and tested for operation (i.e., it responds to light appropriately), we ask the students to quantify its behavior. This is accomplished by examining the radiometers gain and linearity as a function of illumination. We also examine dark current noise. For gain, there is a fixed light level incident on the radiometer followed by recording the output voltage, for each feedback resister setting. The voltage should change by orders of 10, since this is how the feedback resister values were selected (i.e., differing by orders of 10). Given the measured resistance and known voltage, they can also calculate the current to see how this changes or doesn’t change. Linearity is examined by reducing the light level in a predictable manor and examining the voltage output. Since the source is not calibrated, we set the source to a particular level and reduce the light onto the detector through use of known neutral density (ND) filters, since the relationship between ND and transmission is well known as ND = − log(τ). In the end, the student can create a plot of voltage out of the detector versus ND (though it is really log ND to make it linear on the x-axis). From this, students can see if the changes in light level correspond to linear steps in output voltage.

2.3.4

Verification of the Inverse Square Law (ISL) with your Radiometer

Without a doubt, one of the cornerstone principles in radiometry is the falloff in radiation as a function of distance. The falloff experiment is fairly straight forward in that students simulate a bright point source and take voltage reading as a function of distance. There are some additional variables that are explored like non-point source behavior and using LED’s as a source. Students plot the actual measured voltage from the un-calibrated radiometer, the predicted voltage (using the ISL), and a curve fit with a power model to see how close the exponent is to 2.0 (see Figure 4).

Figure 4.

Results from inverse square law experiment using a student constructed radiometer.

2.3.5

Detector Broadband Radiometric Calibration with your Radiometer

Up to this point, none of the previous labs required the student constructed radiometers to be calibrated. In this lab we illustrate the concept of generating a radiometric calibration look-up-table (LUT) that maps voltage to known irradiance, for all the radiometer feedback resistor gain settings. For this lab we do not have a calibrated light source, however, we do own a calibrated International Light Technologies (ILT) radiometer that measures irradiance (with the cosine corrector), thus we measure the irradiance of the (point) source at a distance of say, 30cm. We position the student constructed radiometer at this location (as well as a few other distances, say, 60, 90, and 120cm) and capture voltage readings (as a function of distance). As mentioned in lab 2, we currently do not employ a cosine corrector on the device. This will appear in our next round of improvements. None-the-less, we can still effectively convey concepts related to calibration.

We use the neutral density (ND) filters to help generate a large number of data points (since we know the predicted transmissions of the filters, see the“Using your Radiometer” lab). Finally, we use the inverse square law (since it was so accurate in the previous lab) to predict the irradiance-like behavior at the various distance/ND pairs. The end result is a LUT (and calibration equation) that maps voltage to irradiance, as shown in Figure 5 for the 10k ohm feedback resistor gain setting.

Figure 5.

Calibrating the student-constructed radiometer. LUT mapping of radiometer voltage to irradiance.

2.3.6

Concept of Diffraction Gratings

The goal of this lab is to introduce the concept of diffractions gratings and spectral radiometry, which is also the subject of labs 7 and 8. We introduce the grating equation, mλ = d(sin θ_i ± sin θ_r) and use it in both transmission and reflection grating set ups. For the transmission set up, we estimate the wavelength of a laser. Once this is known, the same laser is used to determine the groove spacing between tracks in a compact disc (CD) followed by a DVD. Basically, we are demonstrating how these ruled surfaces act like reflective diffraction gratings. The set up for the laser and track spacing determination can be seen in Figure 6. Turns out, this experiment provides fairly accurate results for the track spacing. In one experiment, the CD track spacing was found to be 1.65 μm (or 606 LPM), an error of 3.1% from the industry standard spacing of 1.6μm. For the DVD, example results were shown to be 712 nm (1404 LPM) which resulted in an error around 3.7% from the standard spacing of 740 nm.

Figure 6.

Diffraction grating set ups for determining (a) laser wavelength and (b) CD/DVD track spacing.

2.3.7

Spectrometer Spectral Calibration

This lab addresses the concept of spectral wavelength calibration of a point spectrometer. Students learn how to spectrally calibrate their Ocean Optics USB650 (of which we have five) using specialized, commercially available, light sources that emit sharp spectral lines at very well known wavelengths (which are published in the literature). The sources are measured with the USB650 and students eventually determine the relationship between pixel number (i.e., detector element) and wavelength using an n-degree polynomial. This is captured as a look-up-table (LUT) mapping pixel index to wavelength. The sources we use for this lab are Argon and Mercury-Neon which provide sharp emission lines across the full region from 300 to 1000 nm, as seen in Figure 7(a). The polynomial we end up using is of degree three and takes on the form λ(p) = α₁p + α₂p² + α₃p³ + b where we have wavelength, A, as a function of pixel number, p. The coefficients, α₁, α₂, α₃ along with intercept, b, need to be determined based on a programmed regression routine. The intercept, b, in our wavelength vs. pixel index LUT, would be the wavelength of pixel one, for example. The coefficients have units of nm/pixel, nm/pixel² and nm/pixel³, respectively.

Figure 7.

(a) Emission lines from Argon and Mercury-Neon sources and (b) 3rd order polynomial LUT mapping pixel to wavelength.

2.3.8

Spectrometer Radiometric Calibration and Determining the Distribution Temperature of an unknown Source

Concepts learned in this lab involve utilization of a hand-held spectrometer, radiometrically calibrating the spectrometer, programming the Planck function and estimating the distribution temperature of an unknown incandescent source. Students first use the Ocean Optics USB650 to measure the (un-calibrated) spectrum (in digital counts) of a tungsten light bulb, often reflecting off a 100% reflecting Lambertian Spectralon plaque. They then use a known calibrated radiance source to calibrate or “transfer the calibration” to the spectrometer, as illustrated in Figure 8.

Figure 8.

Transfer calibration. The un-calibrated (but stable from measurement-to-measurement) spectrometer is first used to measure a known radiance output in digital counts. This is followed by measuring the unknown sample, in digital counts, in which the spectral radiance can be determined.

Given the measurement scenario in Figure 8, we have three known quantities and one unknown quantity (i.e., the radiance of the sample in question). This can be expressed as

To be more complete and accurate, we should subtract off the noise measurement, thus we have

We can then solve for the calibrated absolute spectral radiance of the sample as

This is essentially transferring the calibration from the known source to the USB650 and is often called transfer calibration. What is happening here is, we are using the ratio L_calsrc/DC_calsrc to appropriately scale our initial, un-calibrated, digital count measurement of our source (DC_sample) so as to produce a calibrated measurement of our sample (L_sample).

Following this calibration, students measure the spectral distribution of an unknown tungsten source. They then program (MatLAB, Python, etc.) the Planck function, normalize the source measurement and Planck function data, followed by iterative curve fitting by varying the Planck temperature until and RMS error is minimized. Once minimized, it is fairly straight forward to determine what the distribution temperature value was for the unknown source, which should be around 2800 - 3000 K.

2.3.9

Making Spectral Measurements: Sources, Transmission, and Reflection

This lab gives students hands-on experience using spectrometers to make spectral measurements of light sources, as well as measurements of transmissive and reflective materials. To start, we repeat the process of radiometrically calibrating the spectrometer, as was illustrated in the previous lab. Once calibrated, students then measure a variety of light sources (though they are not told what they are measuring) including a black light, blue LED, CFL, fiber optic light source, green LED, red LED, room/ceiling lights, standard tungsten bulb, and a white LED. Questions are posed about what types of sources they are examining in addition to the physics of operation (i.e., how do these sources generate light).

The spectrometer is then used to perform transmission measurements of a variety of filters. These include ND filters, cut-off filters, cut-on filters, and the V-lambda filter (i.e., the human visual response). The filter descriptions are not provided to the students ahead of time. The students first measure the stable light output from a small integrating sphere with a 1-inch port. The second measurement is of the integrating sphere port but with the filter in the light path. It is explained that the ratio of these two measurements provides us with an estimate of the spectral transmission. Furthermore, is explained that the spectrometer need not be absolutely radiometrically calibrated for such measurements since this is ratio. Lastly, sources of error, including BRDF effects, are explained.

The last station is set up to perform (rough) spectral reflectance measurements. We say rough because proper total reflectance measurement requires the use of a certain integrating sphere set up, which we do not have for this experiment. In lecture, we would have already discussed issues related to specularity and the use of a goniometer to measure the reflectance at every exiting angle in the hemisphere above the sample, which is in contrast to what we are doing in this exercise. In this lab, we approximate hemispherical reflectance measurements by using a 45/0 measuring geometry. That is, we illuminate the sample at 45 degrees while measuring the signal from the sample at zero degrees. In this way, we avoid measuring any specular highlights. Here, the reflectance is computed as the ratio of two measurements: one of the illuminated sample and one from an illuminated 100% reflecting Lambertian Spectralon surface (i.e., a measurement of the source only). We discuss the pitfalls of performing these measurements outdoors where the source (i.e., the sun) is constantly changing and may not be exactly the same in both measurements and the need for the spectrometer to be stable but not necessarily calibrated in an absolute radiometric sense, again, since this is a ratio measurement.

2.4.1

Determine the Relative Spectral Response (RSR) of a Photodiode

At the core of the student-built radiometers is the UDT silicon photodiode. The essence of this lab would be to have students actually measure the spectral response of the detector using the OL-750 monochromator. Armed with this response information, they can perform band-effective calculations such as determining the band-effective sensor radiance/iradiance given a spectral radiance/irradiance distribution, for example. This can then be compared to what the calibrated detector (i.e., photodiode) is actually reading.

2.4.2

Source Based Calibration using and FEL Lamp

This lab will teach students about calibration using a calibrated source. Namely, our 1000 watt calibrated FEL lamps in combination with a Spectralon plaque. This calibration set up is an alternative to using an expensive integrating sphere for radiometric calibration but does have some caveats. The idea is to give students the experience in setting up an FEL lamp (lab set up, alignment, use of special jig, operation of power supply, etc.) at the given calibrated distance (i.e., 50 cm), to a Spectralon plaque so as to generate a source of spectral radiance. This source of radiance can then be used to calibrate detectors or imaging systems. Results can be cross-compared to using the integrating sphere as a means of stable spectral radiance, for example.