Thanks Dominic. Well beyond the call of duty to be doing stats at 2am!
That all looks reasonable. M/(M-1) and (M+1)/M aren’t quite the same but they are very similar and in any case tend to unity for the real situation of largish M. For the photon noise SG makes sense when G is defined as ADU/photon.
One further practical question about estimating G from the image. I am using the magnitude zero point derived by fitting an ensemble of stars to a catalogue. This links the magnitude (and hence photon flux) to the ADU count. Is there an alternative/better way of doing this?
I’ll try this later and will see if I can start getting some consistent SNR estimates.