Sky background, SNR and saturation

Sky background

sky = night background of the site + twilight + scattered moonlight

Term	Model
Night background	Site value (mag/arcsec²), zenith on a dark night
Twilight	Zenith sky brightness interpolated against the Sun’s elevation, from 21.6 mag/arcsec² at −18° to 18.3 at −12°, 13.1 at −6° and 8.6 at 0°
Moonlight	Krisciunas & Schaefer (1991), from the Moon’s phase, elevation, separation from the satellite and the extinction
From orbit	22.5 mag/arcsec² (zodiacal light at mid ecliptic latitudes)

Signal-to-noise ratio

Aperture photometry in a circle of radius r = max(seeing FWHM, pixel scale), which holds about 90 % of a seeing spot. The satellite is assumed tracked.

S   = F0 · 10^(−0.4 m) · A_eff · η · t · 0.9
B   = F0 · 10^(−0.4 m_sky) · A_eff · η · t · π r²
SNR = S / sqrt( S + B + n_pix · RN² )

with F0 = 8.8 × 10⁹ photons s⁻¹ m⁻² for V = 0, A_eff the collecting area (central obstruction removed), η the total efficiency (optics × quantum efficiency), t the exposure, n_pix the pixels in the aperture and RN the effective read noise. The limiting magnitude is the magnitude that gives SNR = 5.

Saturation

The brightest pixel receives the share of the signal that falls in the pixel the Gaussian seeing spot is centred on, plus the sky of that pixel:

peak = S/0.9 · erf( p / (2√2 σ) )² + sky per pixel,   σ = FWHM / 2.3548

Above the full well of the (binned) pixel, the verdict shows saturated.