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]

Military specifications for illuminated switches, panels, and displays, such as MIL-PRF-22885 and SAE AS7788, also require luminance measurements in foot-lamberts. Luminance levels can vary from hundreds of foot-lamberts for sunlight readable switch displays per MIL-PRF-22885 to only a few foot-lamberts in night conditions for panels in accordance with SAE AS7788.

See also

Other units of luminance:

• Lambert (L)
• Nit (nit)
• Stilb (sb)
• Apostilb (asb)
• Blondel (blondel)
• Skot (sk)
• Bril (bril)

SI photometry quantities

Quantity		Unit		Dimension	Notes
Name	Symbol[nb 1]	Name	Symbol	Symbol
Luminous energy	Qv [nb 2]	lumen second	lm⋅s	T⋅J [nb 3]	Units are sometimes called talbots.
Luminous flux / luminous power	Φv [nb 2]	lumen (= cd⋅sr)	lm	J [nb 3]	Luminous energy per unit time.
Luminous intensity	Iv	candela (= lm/sr)	cd	J [nb 3]	Luminous power per unit solid angle.
Luminance	Lv	candela per square metre	cd/m^2	L^−2⋅J	Luminous power per unit solid angle per unit projected source area. Units are sometimes called nits.
Illuminance	Ev	lux (= lm/m^2)	lx	L^−2⋅J	Luminous power incident on a surface.
Luminous exitance / luminous emittance	Mv	lux	lx	L^−2⋅J	Luminous power emitted from a surface.
Luminous exposure	Hv	lux second	lx⋅s	L^−2⋅T⋅J
Luminous energy density	ωv	lumen second per cubic metre	lm⋅s⋅m^−3	L^−3⋅T⋅J
Luminous efficacy	η [nb 2]	lumen per watt	lm/W	M^−1⋅L^−2⋅T^3⋅J	Ratio of luminous flux to radiant flux or power consumption, depending on context.
Luminous efficiency / luminous coefficient	V			1
See also: SI · Photometry · Radiometry

1. Standards organizations recommend that photometric quantities be denoted with a suffix "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
2. Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ or K for luminous efficacy.
3. "J" here is the symbol for the dimension of luminous intensity, not the symbol for the unit joules.

References

1. 14 CFR Part 60
2. JAR-FSTD A
3. JAR-FSTD H