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So we want to compute, for each field and for each observing opportunity, a zenith-angle and sky-brightness adjusted 5 sigma point source magnitude, m5. The signal to noise ratio for a point source scales as
for a fixed integration time and in the sky-dominated regime. Taking the log of both sides, and incorporating the zenith-dependence of FWHM and also passband-dependent extinction A(zenith), and incorporating the attenuation due to clouds AC (in magnitudes), we compute a change in m5 relative to nominal conditions of
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Some references
LSST science book
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