Calibration of Recorded Digital Counts to Radiance

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Charles Chase
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1 Graduate Radiometry, Laboratory No. 2 Fall Quarter, 2006 Calibration of Recorded Digital Counts to Radiance INTRODUCTION The goal of this experiment is to calibrate your digital camera, using a known source and reflectance standard, to radiance. That is, you will set up an experiment that will enable you to convert camera digital counts (DC) to radiance units. In this set up, you will take advantage of the radiometric expression Iρ W = π L r 2 m 2 sr (1) where I is the intensity of the source, ρ is the reflectance of the objects surface, and r is the distance from the source to the object. The idea is that for each distance r, we can derive an expected radiance and relate it, through a look-up-table, to a measured digital count from a captured image at that distance. MATERIALS CCD Camera 8.5 x 11 in white copy paper (3-4 sheets) Ruler Light source (supplied bulb or fiber optic source) 9V battery (for those using supplied bulb) PROCEDURE Using the Fiber Optic Light Source For those of you that have access to the CIS stockroom/facilities, you can use the following set up. 1. The overall set up for this experiment can be seen in Figure 1. We can see the specific set up using the fiber optic light source in Figure 2. We will be setting the sources output level to its lowest level. IMPORTANT: You will want to remember this setting for your particular light source for future Lab 3. At this setting, we will estimate the source intensity to be 10 W/sr. At some distance r away, the fiber optic source can act like a point source. Therefore we can take advantage of related radiometric relationships.

2 2. The source will illuminate a few sheets of standard 8.5 x 11 in copy paper at some distance r away. We will estimate the reflectance of this copy paper to be 85%. 3. You will then image the reflectance target with your digital camera as a function of distance r. To keep your measurements consistent, you should image the paper at an angle of 45 degrees at approximately the same distance, r camera away (see Figure 1). This will keep your field of view (FOV) the same for each image. For example, when designing this experiment, I needed to use an r camera distance of 30 cm for a given zoom level (i.e., focal length). Your FOV should capture a subset of your reflectance target (see Figure 4 for an example image). IMPORTANT: you will need the exposure to be the same for all your images (e.g., I found that f/4 at 1/8 sec worked for my camera). Also, you will need to disable the flash on your camera. 4. After your set up is complete, you should capture a series of images (in black and white, if possible) as a function of distance, r. Try to use the following distances (in cm): 50, 55, 60, 65, 70, 80, 90, 100, 110, 120, 130, 140, 150. You may find additional distance provide more resolution. 5. Repeat the entire process above as a second trial. r θ=45 r camera Figure 1 Basic set up for camera calibration.

Figure 2 Camera calibration set up using fiber optic light source. Using a Supplied Flashlight Bulb For those of you that do not have access to the CIS lab facilities (i.e., distance learning people) a light source (flashlight bulb) will be supplied or shipped to you (see Figure 3).

3 Figure 2 Camera calibration set up using fiber optic light source. Using a Supplied Flashlight Bulb For those of you that do not have access to the CIS lab facilities (i.e., distance learning people) a light source (flashlight bulb) will be supplied or shipped to you (see Figure 3). 1. The set up for the experiment is identical to that described in the previous section (see Figure 1) with the exception of the source type. 2. In this set up you will want to point the bulb in the direction of the reflecting target (i.e., paper). We will estimate the bulbs output (with a 9 volt battery) to be approximately 10 W/sr. A few points to mention when using this bulb as a source. a. The bulb is rated around 5 volts at 500mA. We are using a 9 volt battery. The bulb does not like this. Because of this high operating voltage, the bulbs life will be shortened significantly. Normally, we would have a ohm resistor in the circuit to limit the current which, both, preserves the bulb and decreases the drain on the battery. However, for our purposes this set up should be fine. b. That said, you should plan on capturing your data (images) in as short a period of time as possible. Once the bulb is on, the battery will start to drain thus changing the light output as a function of time. Over the time it should take you to typically acquire your images, the effect should be negligible. However, you should be aware of such effects. c. If possible, though not required, you could measure the voltage of your battery before and after your experiment to see if there has been any significant change in battery voltage. Remember, after disconnecting it from the circuit, the battery will slowly come back to some steady state voltage.

Figure 3 Flashlight bulb used as a source for calibration experiment. ANALYSIS 1.

You can do this by calculating a histogram over your image. Adobe Photoshop can do this.

2. An example image captured at distance r, can be seen in Figure 4 along with a histogram of the selected region.

4 Figure 3 Flashlight bulb used as a source for calibration experiment. ANALYSIS 1. Once your imagery is collected you will need to transfer the pictures to a software package where you can perform digital count estimation. You can do this by calculating a histogram over your image. Adobe Photoshop can do this. Additionally, a small, but fast and powerful, program called ImageJ can also perform this task (download free from 2. An example image captured at distance r, can be seen in Figure 4 along with a histogram of the selected region. From this you can estimate the mean and standard deviation of the region to use in your look up table. Figure 4 Sample image captured at distance r and histogram of selected region. 3. You should now be able to populate a look-up-table. An example of such a table can be seen in Table 1.

5 Table 1 Example look-up-table for relating digital count to predicted radiance. Distance (m) Average Digital Count (DC) Estimated Radiance, L REPORT 1. Where does Eq. (1) come from (i.e., derive Eq. (1)). 2. Explanation of your set up (i.e, what source you used, etc). 3. Your look-up-table values (i.e, Table 1 populated with numbers) for both trials. 4. A plot (your LUT) relating calculated radiance vs. measured digital counts for both trials. Include a model fit to your data. a. What is the expected trend of your results? And why do you anticipate this? b. What trend did you observe? c. Fit a model to your data. How good is the model at prediction? d. In general, comment on what your data looks like (i.e., scattered, not scattered, non-linear, linear, etc.). e. There is variation in each DC measured. Incorporate this in to your plot (i.e., error bars), if possible. 5. Since we are imaging a uniform object, we can calculate a signal-to-noise ratio. Include a plot of your SNR for both trials. a. Is this expected (i.e, can you explain your results)? b. Why is this not (averaging over the entire image) a true representation of the SNR? 6. What assumption have you made in performing this experiment (i.e., the set up and in using Eq. (1)). 7. What are the sources of error in this experiment? 8. How might you compensate for these sources of error?

Index of Refraction and Total Internal Reflection

$Index of Refraction and Total Internal Reflection$ Index of Refraction and Total Internal Reflection Name: Group Members: Date: TA s Name: Materials: Ray box, two different transparent blocks, two letter size white pages, pencil, protractor, two nails,