Afoot-lambert orfootlambert (fL, sometimes fl or ft-L) is a unit ofluminance inUnited States customary units and some other unit systems. A foot-lambert equals 1/π or 0.3183candela persquare foot, or 3.426candela per square meter (the correspondingSI unit). The foot-lambert is named afterJohann Heinrich Lambert (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 perfectLambertian diffuse reflecting surface in foot-lamberts is equal to the incidentilluminance infoot-candles. For real diffuse reflectors, the ratio of luminance to illuminance in these units is roughly equal to thereflectance of the surface. Mathematically,where
The foot-lambert is used in themotion picture industry for measuring the luminance of images on aprojection screen. TheSociety 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 theprojector). (Typical base density of 0.05 yields peak white of about14 fL.) The current revision of SMPTE 196M specifies 55candela per square meter (nits).
The foot-lambert is also used in theflight simulation industry to measure the highlight brightness of visual display systems. The minimum required highlight brightness varies based on the type and level ofFlight Simulation Training Device (FSTD), but is generally 3–6 foot-lamberts for most devices qualified underFederal Aviation Administration (FAA) orJoint 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.
| cd/m2(SI unit) ≡ nit≡ lm/m2/sr | stilb (sb)(CGS unit) ≡ cd/cm2 | apostilb (asb) ≡ blondel | bril | skot (sk) | lambert (L) | foot-lambert (fL) = 1 ⁄π cd/ft2 | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 cd/m2 | = | 1 | 10−4 | π ≈ 3.142 | 107π ≈ 3.142×107 | 103π ≈ 3.142×103 | 10−4π ≈ 3.142×10−4 | 0.30482π ≈ 0.2919 | ||
| 1 sb | = | 104 | 1 | 104π ≈ 3.142×104 | 1011π ≈ 3.142×1011 | 107π ≈ 3.142×107 | π ≈ 3.142 | 30.482π ≈ 2,919 | ||
| 1 asb | = | 1 ⁄π ≈ 0.3183 | 10−4 ⁄π ≈ 3.183×10−5 | 1 | 107 | 103 | 10−4 | 0.30482 ≈ 0.0929 | ||
| 1 bril | = | 10−7 ⁄π ≈ 3.183×10−8 | 10−11 ⁄π ≈ 3.183×10−12 | 10−7 | 1 | 10−4 | 10−11 | 0.30482×10−7 ≈ 9.29×10−9 | ||
| 1 sk | = | 10−3 ⁄π ≈ 3.183×10−4 | 10−7 ⁄π ≈ 3.183×10−8 | 10−3 | 104 | 1 | 10−7 | 0.30482×10−3 ≈ 9.29×10−5 | ||
| 1 L | = | 104 ⁄π ≈ 3,183 | 1 ⁄π ≈ 0.3183 | 104 | 1011 | 107 | 1 | 0.30482×104 ≈ 929 | ||
| 1 fL | = | 1 ⁄ 0.30482 ⁄π ≈ 3.426 | 1 ⁄ 30.482 ⁄π ≈ 3.426×10−4 | 1 ⁄ 0.30482 ≈ 10.76 | 107 ⁄ 0.30482 ≈ 1.076×108 | 103 ⁄ 0.30482 ≈ 1.076×104 | 10−4 ⁄ 0.30482 ≈ 1.076×10−3 | 1 | ||
Other units of luminance:
| Quantity | Unit | Dimension [nb 1] | Notes | ||
|---|---|---|---|---|---|
| Name | Symbol[nb 2] | Name | Symbol | ||
| Luminous energy | Qv[nb 3] | lumen second | lm⋅s | T⋅J | The lumen second is sometimes called thetalbot. |
| Luminous flux, luminous power | Φv[nb 3] | lumen (= candelasteradian) | lm (= cd⋅sr) | J | Luminous energy per unit time |
| Luminous intensity | Iv | candela (= lumen per steradian) | cd (= lm/sr) | J | Luminous flux per unitsolid angle |
| Luminance | Lv | candela per square metre | cd/m2 (= lm/(sr⋅m2)) | L−2⋅J | Luminous flux per unit solid angle per unitprojected source area. The candela per square metre is sometimes called thenit. |
| Illuminance | Ev | lux (= lumen per square metre) | lx (= lm/m2) | L−2⋅J | Luminous fluxincident on a surface |
| Luminous exitance, luminous emittance | Mv | lumen per square metre | lm/m2 | L−2⋅J | Luminous fluxemitted from a surface |
| Luminous exposure | Hv | lux second | lx⋅s | L−2⋅T⋅J | Time-integrated illuminance |
| Luminous energy density | ωv | lumen second per cubic metre | lm⋅s/m3 | L−3⋅T⋅J | |
| Luminous efficacy (of radiation) | K | lumen perwatt | lm/W | M−1⋅L−2⋅T3⋅J | Ratio of luminous flux toradiant flux |
| Luminous efficacy (of a source) | η[nb 3] | lumen perwatt | lm/W | M−1⋅L−2⋅T3⋅J | Ratio of luminous flux to power consumption |
| Luminous efficiency, luminous coefficient | V | 1 | Luminous efficacy normalized by the maximum possible efficacy | ||
| See also: | |||||
