Allard's law

An equation used in predicting the night visual range of self-luminous targets. Assume a light source at distance x from an observer and having (monochromatic) luminous power P_v in that person’s direction. Then for uniform extinction coefficient σ, the illuminance E_v reaching the observer is

When E_v equals the threshold illuminance for a given background luminance and detection probability, x is the night visual range, or maximum distance for detecting the light source.