Image scale of the telescope / Nyquist-Shannon-Sampling-Theorem
The image scale gives a statement about how much sky section (in arc seconds) can be represented on one pixel.
The Nyquist-Shannon-Sampling-Theorem comes from signal and control engineering and roughly states that an analog frequency f (in this case the object signal) must be digitally sampled with a frequency greater than 2*f in order to be able to reconstruct the output signal exactly.
The section of the sky theoretically mapped on one pixel must therefore be scanned with two pixels instead of one. In other words, the resolving power must be twice as good.
The image scale of the telescope-camera system is calculated using the following formula: (https://astrofotografie.hohmann-edv.de/aufnahmetechniken/grundlagen.fokale.projektion.php)
β – image scale in [°]
P – pixel size in [µm]
f – telescope focal length
To obtain a value in arcseconds/pixel, the units must be converted accordingly, and the result is:
In Germany, a FWHM of 2" - 4" prevails. So that the diffraction discs "inflated" by seeing can always be sampled with two pixels, the resolving power β must therefore lie between 1" - 2". In astrophotography, the smaller value is often sampled with three pixels, so that a value range of 0.67" - 2" is applied for this FWHM.
A suitable combination of telescope and camera can be determined via the calculation tool 'Deep Sky' in the menu point 'Tools'.