We are using co-add mode - that is, we take stacks of 100 images and co-add them to increase the SNR. Since there is RON (read Out Noise) in each frame - about 2 ADU/pixel, tests have shown - it is important to know whether a sequence of added frames have a mean that converges.
We now test this directly on the stack of 100 images: "2456015.7742682MOON_V_AIR". We extract a small square of size (2*w+1) around regularly spaced points covering the image plane and calculate a mean subframe (averaging along the stack direction), the average value of that mean subframe (a scalar for each of n coadded subframes), and plot these. These are shown in the PDF file:
The top panel in each page shows where the point was chosen. w was 4 so subframes are 9 pixels by 9 pixels, centred on the point. Second panel in each page shows how the mean value of the average subframes evolves, along with estimates of the +/-1 sigma error bounds (calculated based on the value the series converges to, or at least evolves to, in the last 10 steps of the series; the known RON (about 2.4 ADU/pixel in all observations, estimated from bias frames differences), the number of pixels in each subframe and the number of subframes co-added). Last panel shows the mean value of each sub-frame used (along the stack direction).
What do we see? In page 1 a point on the sky has been selected and we see a mean value that evolves inside the expected error bounds, and we see that the subframes have mean values with some spread, but no trend.
Page 11 shows a point on the DS. Nice evolution.
Page 24 is on the BS and is very hard to explain. This holds also for points 'near the BS'.
It seems we have little to worry about on the sky and on the DS, but on the BS we see strange evolution of the running mean! We have before touched on such subjects in this blog, when we tested effects of alignment of images - perhaps this problem was hiding inside the other problem?
[added later:] Chris asked a good question. Here is a plot of the running mean of the whole frame, as frames are taken from the stack. The value is expressed as a percentage deviation from the middle value on the curve - about 1378 counts. A small drift is seen at the 0.05% level from one frame at left to all frames at right. I think this could be due to sky variations - or slight drift of the Moon inside the frame causing 'light to fall off the edge'. If drift is the explanation we may have an answer for why the mean in a much smaller sub-frame, when near the BS, drifts so much more - image brightness gradients are being sampled in a small subframe. Experiment at top should be redone but with drifts taken out. No large drift was evident sp I guess we are learning that a small drift can be very important!
This has an implication for how we measure the albedo - if we use 'DS patch divided by BS patch' we run a risk . if we use 'DS patch divided by total flux' we are much better off.