A foot-lambert or footlambert (fL, sometimes fl or ft-L) is a unit of

luminance Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls with ...

United States customary units United States customary units form a system of measurement units commonly used in the United States and U.S. territories since being standardized and adopted in 1832. The United States customary system (USCS or USC) developed from English uni ...

and some other unit systems. A foot-lambert equals 1/π or 0.3183

candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous t ...

per

square foot The square foot (plural square feet; abbreviated sq. ft, sf, or ft2; also denoted by '2) is an imperial unit and U.S. customary unit (non- SI, non- metric) of area, used mainly in the United States and partially in Canada, the United Kingdom, B ...

, or 3.426 candela per square meter (the corresponding

SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

). The foot-lambert is named after

Johann Heinrich Lambert Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made important contributions to the subject ...

(1728–1777), a Swiss-German mathematician, physicist and astronomer. It is rarely used by electrical and lighting engineers, who prefer the candela per square foot or candela per square meter units. The luminance of a perfect Lambertian diffuse reflecting surface in foot-lamberts is equal to the incident illuminance in

foot-candle A foot-candle (sometimes foot candle; abbreviated fc, lm/ft2, or sometimes ft-c) is a non- SI unit of illuminance or light intensity. The foot-candle is defined as one lumen per square foot. This unit is commonly used in lighting layouts in par ...

s. For real diffuse reflectors, the ratio of luminance to illuminance in these units is roughly equal to the

reflectance The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...

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 A film also called a movie, motion picture, moving picture, picture, photoplay or (slang) flick is a work of visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, feelings, beauty, or atmosphere ...

industry for measuring the luminance of images on a

projection screen A projection screen is an installation consisting of a surface and a support structure used for displaying a projected image for the view of an audience. Projection screens may be permanently installed, as in a movie theater; painted on the ...

. The

Society of Motion Picture and Television Engineers The Society of Motion Picture and Television Engineers (SMPTE) (, rarely ), founded in 1916 as the Society of Motion Picture Engineers or SMPE, is a global professional association of engineers, technologists, and executives working in the m ...

(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 A projector or image projector is an optical device that projects an image (or moving images) onto a surface, commonly a projection screen. Most projectors create an image by shining a light through a small transparent lens, but some newer typ ...

). (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 National Institutes of Technology (NITs) are the central government-owned-public technical institutes under the ownership of Ministry of Education, Government of India. They are governed by the National Institutes of Technology, Scienc ...

). 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 The Federal Aviation Administration (FAA) is the largest transportation agency of the U.S. government and regulates all aspects of civil aviation in the country as well as over surrounding international waters. Its powers include air traffic ...

(FAA) or

Joint Aviation Authorities The Joint Aviation Authorities (JAA) was an associated body of the European Civil Aviation Conference representing the civil aviation regulatory authorities of a number of European States who had agreed to co-operate in developing and implemen ...

(JAA) regulations.JAR-FSTD H 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.

References

Units of luminance Customary units of measurement in the United States {{optics-stub

See also

References