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Is there a simple way to know the signal-to-noise ratio of a certain star on a FITS image? Is it possible to be as simple as by just clicking on the object?

If you run imexamine on your fits image, put the cursor on your star, and
hit the "r" key, you will see a bunch of numbers displayed.
The third of these is the integrated number of counts of the star after
background has been removed. Let's call that F.
The fourth is the average number of counts
in the background. Let's call that B.
These numbers will be meaningful as long as you have
set reasonable values in "rimexam" for the object radius (R), background buffer
width, and background width.Assuming that your "fits image" is a CCD frame for which you know the
gain "g" [electrons/ADU] and read noise r [in electrons] then the
"signal" will be the F*gainWhat will the noise be? One component will be the photon statistics of the
star itself: sqrt(F*gain). Another will be the photon noise from the sky:
sqrt(N*B*gain), where N is the number of pixels in your aperture, i.e.,
3.14159*R**2.
Another will be due to the readout noise in your aperture, sqrt(N)*R.
All of these sources of noise are independent, so you have to add them
in quadrature, i.e.,
noise = sqrt [ F*gain + N*B*gain + N*R**2]You might want to read through some photometry guides, such as the
"How to do stellar photometry with IRAF" in the documentation section.

Thank you for your detailed description, massey! It's very helpful.