Light reaching the sensor per unit area: H = q L t / N² (q = 0.65, L scene luminance, t shutter time, N f-number). Doubling t, halving N² or doubling ISO all change the picture by one stop; EV = log₂(N²/t) − log₂(ISO/100). The sensor signal as a fraction of saturation is H·ISO/78 (ISO 12232 saturation speed).

Photon noise is Poisson: signal e electrons has standard deviation √e, plus read noise σ_r, so SNR = e / √(e + σr²). That is why a longer exposure at low ISO beats a short exposure at high ISO for the same brightness. Stars drift at the sidereal rate ω = 7.29×10⁻⁵ rad/s; a star at angular distance θ from the celestial pole leaves a trail of f ω t sinθ / p pixels (p = pixel pitch 6 µm). The 500 rule t ≈ 500/f[mm] limits trails to a few pixels.

Simplifications: a fictional aurora model with luminance chosen for realistic exposures (peak 0.003, 0.03 or 0.3 cd/m²), a fixed 6 µm full-frame-like sensor, 50 % quantum efficiency, no colour filter array, no lens aberrations beyond a vignette, preview shown at reduced resolution with native-pixel noise.