Rogelio, I like your idea.
Geoff, those threads seem to make the case that there is no benefit to binning once your subs are sky limited. I think there is. What I have here is a project that I think shows that binning does have a benefit. You can download it from Endor Forum Shared Files mschuster/Binning.zip.
Earlier this year I was trying to collimate a Cassegrain and took four 300 second subs of M53, two binned 1x1 and two binned 2x2. Looking at the subs, the 2x2 does not look any better than the 1x1 in terms of SNR, at least subjectively. But is there an objective way to tell?
The median ADU of the 2x2 subs is about four times larger than the median of the 1x1 subs. Drag the icon Bin1x1Calibration onto one of the 1x1 subs and note that the result's median is 408 ADU. Drag the icon Bin2x2Calibration onto one of the 2x2 subs and note a median of 1741 ADU. These icons basically subtract the bias master from each sub and take the average.
Of course all subs have captured roughly the same number of photons, their exposure times were all the same. But the 2x2 pixels are four times larger and so have captured four times as many photons as the 1x1 pixels. As a result their ADUs are four times larger. The gain of all four subs is the same, so this factor of four is in fact signal (electrons) not just ADUs.
The noise in the 2x2 subs is about twice as large as the noise in the 1x1 subs. Drag the icon Bin1x1Difference onto one of the 1x1 subs and run the NoiseEvaluation script on the result, you will get 7.4e-4. Drag the icon Bin2x2Difference onto one of the 2x2 subs and run the script, you will get 1.4e-3.
These icons just subtract the two subs from one another and add 0.5 to avoid clipping. Subtracting removes the bias, dark current, fixed pattern and also the signal. What is left is roughly noise (read noise, dark current shot noise, signal shot noise) and the script measures this. You can also look at the histogram of the difference, zoom in around 0.5. You will see the histogram is roughly a Gaussian profile, the bin 2x2 profile is wider than the bin 1x1 profile.
I think photon statistics accounts for the factor of two increase in noise. Noise goes up with the square root of the signal. Four times the signal in each pixel, twice the noise in each pixel.
So signal is four times larger in the 2x2 and noise is two times larger in the 2x2. Hence signal to noise is twice as large in the 2x2. Binning does improve SNR.
As I mentioned, subjectively there does not seem to be much difference between the subs. Maybe the reason for this is that the image here is basically high signal to noise ratio stars (high SNR due to their brightness) and so the improved SNR is not visible. But suppose there was a faint spiral arm or tidal tail you wanted to capture. The improved SNR of binning might help you do so. In this project the median pixel is a sky background pixel, and its SNR is twice as big when binned. Add a weak signal to this background and the improved SNR of binning will help resolve it.
If I have made a mistake here please let me know.
Regards,
Mike
Update: Hopefully the math below is correct.
Gain in all subs is 0.45 e-/ADU. Median 1x1 signal is 408 * 0.45 = 184 e-, median 2x2 signal is 1741 * 0.45 = 783 e-. Bin 1x1 noise is 7.4e-4 * 65535 * 0.45 / sqrt(2) = 15 e- rms, bin 2x2 noise is 1.4e-3 * 65535 * 0.45 / sqrt(2) = 29 e- rms. The 65535 factor here converts normalized units to ADUs. The sqrt(2) factor accounts for the quadrature addition of the sub's noise in the difference, assuming equal noise in the two subs.
So bin 1x1 median SNR is 184 / 15 = 12 and bin 2x2 median SNR is 783 / 29 = 27. Median SNR gain by binning is 27 / 12 or about 2.
Note, as a double check, taking the square root of the signal gives for bin 1x1 sqrt(184) = 14 e- rms and for bin 2x2 sqrt(783) = 28 e- rms. These are noise estimates simply based on photon statistics. They match the noise estimate above closely.
