Dark Current as a Function of Temperature

As we discussed above in Section 3.3, the dark current is a function of both exposure time and temperature. We can quantify these values by taking ``dark'' images (i.e. taking images while keeping the shutter closed) and varying the exposure time and/or temperature and then subtracting out the bias from the image.

Figure 4: Here are two histogram plots of the dark current at the same exposure time at varying temperature. Note that the temperature here is measured in $^{\circ }$C. You can see that at the higher temperature (b) the mean increases by a bit and the standard deviation increases by a lot. You can also see that the frequency of pixel values at any specific is almost uniform. Here, I actually did not subtract out the bias for our data so we can view the true values in our pixel array.

First we can examine how the dark current varies as we vary the temperature. We can see from Figure 4 that at a higher temperature, the mean is slightly higher and the standard deviation is much higher than at lower temperatures. The temperatures that we made our cool and warm dark currents were -20$^{\circ }$C and 11.96$^{\circ }$C respectively. We saw an increase in the mean by about 30% for the warm dark current and an increase of about 2700% for the standard deviation. If we examine the data for the cool dark current (Figure 4a) more closely, we see that the mean of the dark current at -20$^{\circ }$C is very close to the value that we got for the mean of the bias image. Therefore, we can see that the noise contributed from the thermal energy at -20$^{\circ }$C is very small. On the other hand, for the warm dark current at a temperature of 11.96$^{\circ }$C (Figure 4b), we see that the mean is increased by a pretty significant amount. Additionally, the large standard deviation tells us that the contribution of noise of the thermal energy is very random and it confirms that the thermal fluctuations are fairly high for a temperature of 11.96$^{\circ }$C.

Interestingly, the dark current of the cool CCD has some pixels that is lower than the bias of our CCD. This means that there is some variation in the readout of each pixel. Thus if we examine how much the measurement fluctuates from the mean of the bias we get a measure of the amount of readout noise of the CCD. I wont discuss this here because I will provide a more accurate discussion of the readout noise later in Section 4.3.3.

Another point of interest is the small peak in the warm dark current histogram at about 1400 DN. This peak occurs close to the value of the mean of the bias. This is probably a count of the dead pixels in our CCD. Since the dead pixels are unable to collect photoelectrons, when it is read out at the A/D converter, it will only measure the value contributed by the bias.