small telescopes and low intensities

I spent some research time on the weekend working on the question that Joe Hennawi (MPIA) asked me on Friday: What is the sensitivity of a telescope and detector to very faint features on the sky as a function of aperture diameter and focal ratio? There are various regimes to consider. In one, the object is much smaller than a resolution element on the focal plane (the point source limit). In another, much larger, but still much smaller than the detector as a whole. In another, larger even than the detector array. There are slightly different answers in each case, but the large telescope does better in the first two cases, and even in the third if the faint object has any structure on the scale of the detector. I wrote words about this and wondered if there was something to publish (informally or otherwise). Of course small telescopes often have much better optics and scattered light properties, so this isn't the end of the story!

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