Foot-lambert

A foot-lambert or footlambert (fL, sometimes fl or ft-L) is a unit of luminance in United States customary units and some other unit systems. A foot-lambert equals 1/π candela per square foot, or 3.426 candela per square meter (the corresponding SI unit). The foot-lambert is named after Johann Heinrich Lambert (1728–1777), a Swiss-German mathematician, physicist and astronomer. It is rarely used by electrical and lighting engineers, in favor of the candela per square foot or candela per square meter.

The luminance of a perfect Lambertian diffuse reflecting surface in foot-lamberts is equal to the incident illuminance in foot-candles. For real diffuse reflectors, the ratio of luminance to illuminance in these units is roughly equal to the reflectance of the surface. Mathematically,

$L_\mathrm v = E_\mathrm v \times R$,

where

$L_\mathrm v$ is the luminance, in foot-lamberts,
$E_\mathrm v$ is the illuminance, in foot-candles, and
$R$ is the reflectivity, expressed as a fractional number (for example, a grey card with 18% reflectivity would have $R = 0.18$).

The foot-lambert is used in the motion picture industry for measuring the luminance of images on a projection screen. The Society of Motion Picture and Television Engineers (SMPTE) recommended, in SMPTE 196M, a screen luminance of 16 foot-lamberts for commercial movie theaters, when measured "open-gate" (i.e. with no film in the projector). (Typical base density of 0.05 yields peak white of about 14 fL.) The current revision of SMPTE 196M specifies 55 candela per square meter (nits).

The foot-lambert is also used in the flight simulation industry to measure the highlight brightness of visual display systems. The minimum required highlight brightness varies based on the type and level of Flight Simulation Training Device (FSTD), but is generally 3–6 foot-lamberts for most devices qualified under Federal Aviation Administration (FAA) or Joint Aviation Authorities (JAA) regulations.[1][2][3]

Other units of luminance:

SI photometry units
QuantityUnitDimensionNotes
NameSymbol[nb 1]NameSymbolSymbol
Luminous energyQv [nb 2]lumen secondlm⋅sTJ [nb 3]units are sometimes called talbots
Luminous fluxΦv [nb 2]lumen (= cd⋅sr)lmJ [nb 3]also called luminous power
Luminous intensityIvcandela (= lm/sr)cdJ [nb 3]an SI base unit, luminous flux per unit solid angle
LuminanceLvcandela per square metrecd/m2L−2Junits are sometimes called nits
IlluminanceEvlux (= lm/m2)lxL−2Jused for light incident on a surface
Luminous emittanceMvlux (= lm/m2)lxL−2Jused for light emitted from a surface
Luminous exposureHvlux secondlx⋅sL−2TJ
Luminous energy densityωvlumen second per metre3lm⋅sm−3L−3TJ
Luminous efficacyη [nb 2]lumen per wattlm/WM−1L−2T3Jratio of luminous flux to radiant flux
Luminous efficiencyV1also called luminous coefficient