Gain

The gain of the CCD can be determined, as we saw in Section 3.4 by plotting the mean of the images against the variance. I have plotted this in Figure 6. To increase the mean of each image we could have either increased the intensity of the light source or increased the exposure time in small steps. We decided to increase the exposure time because it is much easier to control and quantify. In Figure 6 we increased the exposure time in increments of 0.1 seconds starting at 0.1 seconds. We took a series of 35 images with different exposure times, so the range in the plot is from 0.1 s to 3.5 s. We can take the means of each of these images to get our $\bar{x}$. The images that we took were of a uniformly lit white board.

We ran into a problem at first with our plots when we plotted the mean versus the variance of our data and we found that it was not linear like we expected it to be. After some thought, we found that the variance of one of our images does not show the true variance in the data since the image itself has low and high intensities corresponding to the brightness of the image itself. What we want is how the measured intensities at each pixel varies due to noise. By subtracting two identical images taken at different times we can remove the variations in intensity due to just the image itself and isolate the sum of the noise. Now we can calculate the variation of the images by using the difference image which only contains the noise. However, when we take the difference between the two images we have to remember to take into account how the error propagates when we combine two sets of data, each with its own inherent errors. This will be discussed in Section 4.3.1.