Theory

In a CCD the signal is measured in terms of the charge that is stored on to each pixel, however in converting this charge into a signal, the number of ADUs found is not directly proportional to the number of photon events that happen. Two main effects that are responsible for this are the 'bias level in ADU' (B), which is usually approximated to an average of a dark frame of 0 second exposure time array, and the read noise (RN) of the camera, which is a well documented value for a given CCD chip.

One would expect that a 0 second exposure time would produce an array full of zeros, but this is not the case. Each pixels will have a number that will represent the bias level, and these numbers do not have to be equal, because of read out noise which in principle introduces noise into readings. An average over this array should give us the bias level, B. Additionally, B is considered to be a constant which becomes less important for higher exposure times. However, one has to make sure that the camera is sufficiently cool for B to be a constant.

To investigate B we took five 0 second dark frames. Each image array was averaged to get the value for B, and then the five B values were averaged together.

The basic equation for the measured ADU number is:

N_ADU = Gain * N_photons + B + RN

The gain measures the amount of photoelectrons you get per ADU.

Since we have N_ADU and we can determine B and find RN from documentations, we should be able to use this to find the actual amount of photon events that occured, and see if the standard deviations from fitting the actual number of photon events still deviates from Poissonian.

Last week's analysis

The plot below shows what we did last week, please see the corresponding section.

The plot shows the difference between the standard deviation found from the fit and the standard deviation found from Poisson such that standard deviation is square root of the mean. The negative deviation at short exposure times could be due to a constant offset between N_ADU and N_photoelectrons, whereas higher exposure deviation could be due to electric noise. We wanted to see if we account for these using the formula above and this is done below.

Analysis

The bias level was found to be 107.456260541. The read out noise was found from documentations to be 15e- rms for our CCD.

These values were used to calculate the actual number of photon events for each image. Each image was then plotted as a histogram, and an exaple of this can be seen below.

As can be seen, the mean is now close to 0. This is because one would expect no photon events when taking a dark frame if there is no noise, which is what we corrected for. So this seems good.

We were still able to fit a Gaussian, and therefore use the found standard deviation from the fit and compare it to Poisson standard deviation as defined by the square root of the fitted mean. Our results can be see below.

This plot for this is not good.This would mean that maybe our assumption of the effects on the readout of ADU is not exactly correct. As an alternative, maybe Poisson assumption is not valid for high exposure times, and this would give the larger difference. We know that if one takes the total amount of data to infinite, the Poisson distribution turns Gaussian.

Some of the corrected means were negative, due to the fact that we took away constant B and RN. In order to compute the Poisson standard deviation, we chose to take the absolute magnitude of the mean.

Bias only

If the number of ADUs is corrected only for the bias effects, then the following plot is made.

The plot is not good in comparison to the original plot. We need to explore this more.

Read noise only

If the number of ADUs is corrected only for the read noise effects, then the following plot is made.

This plot is more like the one we found before, as well as the difference is only around 0.5 pixels. However, it is negative, which means that the standard deviation found from fitting is smaller than the one defined by the Poisson distribution.

-- ElenaCukanovaite - 27 Oct 2015