Allard's law

From Glossary of Meteorology
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 Pv in that person's direction. Then for uniform extinction coefficient σ, the illuminance Ev reaching the observer is
ams2001glos-Ae15
When Ev 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.
Copyright 2024 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.