hi Rick.
Interesting observation. I suspect that Richard's analysis assumes that the main FP noise is due to the interaction of the target signal with the CCD non-uniformity, whereas the big problem is actually FPN due to the much brighter sky. His noise equation (in the reference in an earlier post) has an FPN term of Signal*NU, so that is possibly the case. If so, you would need more accurate flats to compensate, since Sky*NU presents you with much more noise amplitude than Signal*NU. Will have to look a bit more closely at Richard's maths - I skimmed over a bit of his work
. Might send him an email.
Of course there is also the added complication of spectral variability - unless the spectrum of the flats matches that of the dark sky light, the flat calibration cannot be totally accurate, since the response of the sensor has variability with wavelength as well as intensity. Sky light at dusk will not be the same colour as dark sky light and could add noise due to pixel level spectral sensitivity variations. This is a real can of worms and I don't have any feel for how significant it is, but there may be a good case for using a white LED source for flats. Have you tried any alternative light sources for flats?
Regards Ray