Night visual range

night visual range

(
Also called nighttime visual range, transmission range.) The maximum distance at which a normal observer can see a particular point light source under given atmospheric conditions.

For a light source of luminous power P_v (in lumens), uniform atmospheric extinction coefficient σ along the viewing direction, and threshold illuminance E_thresh for the observer, the night visual range x is

Unlike the daytime visual range, the night visual range is determined by both the inverse-square law and atmospheric extinction. Note that for a light to be seen at a distance x > 0, its illuminance at the observer (P_v/x²) must exceed E_thresh. Even if σ is known, there is no unique night visual range because x also depends on P_v and the observer's dark adaptation.
See Allard's law

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