The Gain of our CCD

Now that we have cleared up which mean and variance to use, we can calculate our gain using Equation 2. Note that we can make the assumption that we made in Section 3.4 that our data obeys Poisson statistics because we have isolated the noise of the images which are only due to quantum fluctuations of the emitted photons. In Figure 6 we plotted the bias subtracted mean against the variance. After fitting a line to the data using the method explained in Section 4.2.3, we can determine the gain from the inverse of the slope of the best fit line since Equation 2 says that the gain is the mean over variance. The slope of our plot comes out to be 0.6662 so the gain for our CCD is about 1.5 $\frac{\char93 \; e^{-}}{DN}$.

Figure 6: Here is a plot of the bias subtracted mean versus the variance of the sequence of images that we took. Notice that there is a linear relation between the mean and the variance as expected (Section 3.4). Also, notice that even with the bias subtracted, the variance does not go to zero as the mean goes to zero.

Now that we know the gain of the CCD, we can calculate how many photoelectrons are needed to saturate a pixel in our CCD. We know that digital saturation occurs when we obtain a readout of 65,535 DN. Multiplying this by the gain gives us the corresponding value in number of electrons. We find that saturation occurs when the pixels inside our CCD capture about 98,300 electrons. According to the specifications of the CCD camera, the pixel well capacity is 100,000 electrons. We can see that digital pixel saturation occurs slightly before the pixel well is fully saturated. This is the optimal operation for such a device.