OK let's consider photometry, using the aperture method, because SNR is well defined since the object is known (it's a point source). In the aperture method, you have a circle of a certain angular size that you overlay on the star image. Add up all the ADU counts of all the pixels in the circle. Then, outside the circle and separated by a small gap, you make a ring (a donut) around the circle. Add up all the ADU counts of all the pixels in the donut. That provides the measure of the sky background. Now, you know that inside the circle, you have both star flux plus sky flux. In the donut you have sky flux only. So the SNR is the ratio of the counts you measured in the circle to the square root of the sum of the circle counts plus the donut counts (also you normalize the the area of the donut and the area of the ring).
So the smaller you make the circle, the more you get of star only and not sky. You can do that when you have good seeing and high resolution. If your circle is five arc seconds in diameter, you are getting a lot of sky flux added in. If your circle is only one arc second in diameter, you get 25x less sky flux so your SNR is (IIRC) sqrt 25 or 5x higher.
Even if you're not doing photometry you can easily see this on images where when the seeing is good, faint details suddenly become visible. That is because there is more information in those images = higher SNR. The SNR of a complex image is not really well defined because you never know what the noise-free image is. But with a star you know exactly what the noise free image is and it's super easy to calculate and many tools do this for you automatically.
You can mostly discard the camera performance when you do not have heroically good skies or if you're doing narrowband; the sky flux is going to dominate for most of us if we are using good cameras, which we mostly have now.
see 6.5.2 in the paper below
https://www.stsci.ed...osuretime6.html
So you need to share what FHWM you are getting for stars, what you are binning to (either in camera or processing), and what your sky background is. ASTAP can calculate the sky background for you. A 10" SCT can go very faint under the right conditions, a lot fainter than a 6" refractor.
Edited by 555aaa, 16 April 2025 - 03:20 PM.