[Shiraz (Ray)]

That took a lot of thinking about Roger. Many good answers already and here is another try. apologies for such a large post - but here goes.

Optics comments

The aperture of a scope is a fundamental parameter, since it determines the number of photons collected from the external scene. Whatever happens after the aperture cannot increase the number of photons.

The focal length determines how big the physical image is. If the FL is long, the image will be large and the photons will be spread out, so the brightness will be low (where brightness is the number of photons passing through a fixed area of the image) - if the FL is short, the image will be small and bright. FL can be readily varied (eg with a Barlow or FR), so it is not a fundamental measure.

You don’t really need to use focal ratio, although it is useful for comparing optical systems. It is not a fundamental parameter.

If you have a good mount, the long integration resolution will be determined almost exclusively by the seeing blur due to atmospheric turbulence (except for very small apertures and discounting lucky imaging). Halfway decent optics above about 100mm aperture will have better resolution than the atmosphere in most Australian conditions - where the seeing limits you to a resolution of typically 1.5-2 arc sec FWHM at best. Even the 3.9m AAT will have about the same long integration resolution as the average on-axis Skywatcher 8 inch Newt under 2 arcsec seeing – the AAT will take a picture in a flash, but the image detail will not be better.

Extended objects in a physical image will not vary in brightness if the seeing-limited resolution changes, but the level of detail will change. However, star images get larger and dimmer as their energy is spread out by bad seeing.

Sampling

This is where it all happens in CCD imaging. What ends up in the digital image is determined primarily by how you sample the physical image when you place a CCD in the focal plane - and that is a function of the angular pixel size relative to the angular resolution of the atmosphere/optics (the sampling).

There are four basic approaches to choosing the angular pixel size:
1. Undersample. If the pixels are larger than the FWHM of the star blobs then dim stars fit within a single pixel – they are rarely lined up exactly on a pixel centre, so they put photons into ~4 pixels. Thus, most stars end up about the same size, but with varying brightness – only the brighter ones extend beyond ~4 pixels. Detail is lost in extended objects because small features in the physical image fit within a single pixel and are averaged out.
The two big advantages of undersampling are high sensitivity and wide field of view. For example, in 2 arc sec seeing, an undersampled system at 4 arcsec per pixel will have ~16 times the signal per pixel (4x the SNR) of a system that samples at the Nyquist optimum of ~1 arc sec per pixel (all else being equal). It will have 16 times the field of view as well. This sort of system is used by many who post on IIS and is ideal for imaging large faint nebulae, but it is not suitable for resolving the finest detail in galaxies or planetaries. Undersampling is the wide-field realm of the FSQ106/NP101 guys with 9 micron chips. Their huge images look very sharp because the available detail is determined entirely by the CCD pixel size and neither the scope resolution nor typical atmospheric seeing has much effect on apparent sharpness.
Example: 500mm fl system with 9 micron pixels.

2. Nyquist optimum. When you have 2-3 pixels across each FWHM of the image, you are able to record all of the detail present in the physical image and you get the best possible signal to noise ratio for that maximum detail. This is the optimum sampling for galaxy or planetary nebula imaging. In typical/good 2 arc sec seeing, this will require a little less than 1arcsec/pixel sampling.
Images taken in this realm have the most detail possible, but can often look less sharp than undersampled images because the finest detail, although present, has low contrast due to the rolloff of the atmospheric MTF at high spatial frequencies. Resolution is entirely determined by the atmospheric seeing and that can vary a lot. Stars will vary in size - determined by seeing PSF rather than CCD pixel size.
Sensitivity is much lower than for undersampled systems.
Examples: 2m fl system with 9 micron pixels or 1m fl system with 4.5micron pixels in 2 arcsec seeing.

3. Oversample. If the angular size of your pixels is much smaller than the Nyquist optimum, you will have decreased signal in each pixel, but no more detail in the image – you are looking with a fine grid for detail that has already been blurred out. There is no advantage in oversampling, except that such a system will be great on that night of exceptionally good seeing, where it can operate nearer Nyquist.
Eg, in 2 arcsec seeing, a system that has 0.5 arc sec resolution will have 1/4 the signal levels (1/2 the SNR) of a near-Nyquist sampled one (at 1 arcsec/pixel), but it will not record any additional information. The field of view will be small, stars will look bloated and the best processing strategy would be software binning to restore some of the SNR lost in the extra read noise. Images will look less sharp under almost all conditions, since even fine detail looks fatter when spread out over more pixels.
Example: 2m fl system with 4.5 micron pixels in 2 arcsec seeing.

4. Compromise. Many successful imagers operate in the no man’s land between about 1 and 2 arc sec per pixel, where they get better sensitivity than Nyquist, wider field of view, but still don’t lose too much detail in good seeing. Stars and extended object detail will look nice and tight with moderate undersampling, so aesthetics will be OK in average seeing. If you are more interested in aesthetics than in ultimate resolution and want images that look pleasingly sharp most of the time, this looks like a good approach.

In summary, for a given aperture, sampling determines how sensitive your system will be, how well it resolves detail, what your field of view will be and what your image aesthetics will be like.