Stage Lighting Beam and Throw
Theatrical fixture photometry: beam (pool) diameter at a throw distance (2 x throw x tan(beam angle / 2)) and center-beam illuminance by the inverse-square law (E = candela / distance^2, or candela estimated from lumens + beam angle), in footcandles and lux (first-principles point-source photometry, distinct from the architectural lumen-method average).
Formula and source
Beam (pool) diameter = 2 x throw x tan(beam angle / 2); center illuminance E = candela / distance^2 (inverse-square). Candela from lumens = lumens / (2*pi*(1 - cos(beam angle / 2))). 1 fc = 10.764 lux.
First-principles theatrical photometry - beam spread and the inverse-square illuminance the form fixture photometric charts (manufacturer cut sheets) publish, by name; public domain.
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