Hi James,
The signal to noise ratio will be affected by both the number of photons, and how those photons are spread across the detector pixels (amongst other things). However, the SNR by itself is not everything, for example you also need to keep systematic errors to a minimum.
I think you already know this, but it is useful to state it anyway. Assuming a constant aperture, then the number of photons from a star will remain the same at different focal ratios. The focal ratio will then only affect the size of the star image and so how many pixels those photons will fall onto.
Taking an extreme case where the focal ratio is sufficiently short that the photons from an individual star fall onto a single pixel. In this scenario the signal from the star on that pixel will be at its maximum possible value and it will be as under sampled as it is possible to be. While this might sound good, it means you are relying on a single pixel to tell you everything about the star. While flat fields and dark frames remove the majority of pixel to pixel variations, then do not remove it all, and you will also get random noise. By spreading the photons from the star across several pixels you help to ‘smooth’ out this variation, and particularly any systematic differences from pixel to pixel. For example one technique to improve photometry is to defocus star images slightly so that the photons are spread across a larger number of pixels.
Hence for photometry, getting the sampling right should give you the best results. In some cases this might even mean oversampling (more pixels per star) though I have never tested this myself.
A couple of other point to consider:
- If you use comparison stars across a wide field of view then applying transformations to your measurements becomes more important as you are looking at stars passing through a different length of atmosphere.
- As you go fainter so there are more stars and so crowding of fields can become a problem. In this scenario you want a larger image scale so you can separate stars. Though of course you also need better seeing to do this properly.
This is not to say don’t go for a Hyperstar, but if you do then I would advise an imaging chip with small pixels so you don’t end up under sampling.
Cheers,
Andy