In radiometry, radiance is the radiant flux emitted, reflected,
transmitted or received by a given surface, per unit solid angle per
unit projected area. Spectral radiance is the radiance of a surface
per unit frequency or wavelength, depending on whether the spectrum is
taken as a function of frequency or of wavelength. These are
directional quantities. The SI unit of radiance is the watt per
steradian per square metre (W·sr−1·m−2), while that of spectral
radiance in frequency is the watt per steradian per square metre per
hertz (W·sr−1·m−2·Hz−1) and that of spectral radiance in
wavelength is the watt per steradian per square metre, per metre
(W·sr−1·m−3)—commonly the watt per steradian per square metre
per nanometre (W·sr−1·m−2·nm−1). The microflick is also used
to measure spectral radiance in some fields.[1][2]
Contents 1 Description 2 Mathematical definitions 2.1 Radiance 2.2 Spectral radiance 3 Conservation of basic radiance 4 SI radiometry units 5 See also 6 References 7 External links Description[edit]
L e , Ω = ∂ 2 Φ e ∂ Ω ∂ A cos θ , displaystyle L_ mathrm e ,
where ∂ is the partial derivative symbol; Φe is the radiant flux emitted, reflected, transmitted or received; Ω is the solid angle; A cos θ is the projected area. In general Le,Ω is a function of viewing direction, depending on θ through cos θ and azimuth angle through ∂Φe/∂Ω. For the special case of a Lambertian surface, ∂2Φe/(∂Ω ∂A) is proportional to cos θ, and Le,Ω is isotropic (independent of viewing direction). When calculating the radiance emitted by a source, A refers to an area on the surface of the source, and Ω to the solid angle into which the light is emitted. When calculating radiance received by a detector, A refers to an area on the surface of the detector and Ω to the solid angle subtended by the source as viewed from that detector. When radiance is conserved, as discussed above, the radiance emitted by a source is the same as that received by a detector observing it. Spectral radiance[edit] Spectral radiance in frequency of a surface, denoted Le,Ω,ν, is defined as[3] L e , Ω , ν = ∂ L e , Ω ∂ ν , displaystyle L_ mathrm e ,
where ν is the frequency. Spectral radiance in wavelength of a surface, denoted Le,Ω,λ, is defined as[3] L e , Ω , λ = ∂ L e , Ω ∂ λ , displaystyle L_ mathrm e ,
where λ is the wavelength.
Conservation of basic radiance[edit]
L e , Ω = n 2 ∂ Φ e ∂ G , displaystyle L_ mathrm e ,
where n is the refractive index in which that surface is immersed; G is the étendue of the light beam. As the light travels through an ideal optical system, both the étendue and the radiant flux are conserved. Therefore, basic radiance defined by[4] L e , Ω ∗ = L e , Ω n 2 displaystyle L_ mathrm e ,
is also conserved. In real systems, the étendue may increase (for example due to scattering) or the radiant flux may decrease (for example due to absorption) and, therefore, basic radiance may decrease. However, étendue may not decrease and radiant flux may not increase and, therefore, basic radiance may not increase. SI radiometry units[edit] SI radiometry units v t e Quantity Unit Dimension Notes Name Symbol[nb 1] Name Symbol Symbol Radiant energy Qe[nb 2] joule J M⋅L2⋅T−2 Energy of electromagnetic radiation.
Radiant flux
Φe[nb 2]
watt
W = J/s
M⋅L2⋅T−3
Spectral flux
Φe,ν[nb 3]
or
Φe,λ[nb 4]
watt per hertz
or
watt per metre
W/Hz
or
W/m
M⋅L2⋅T−2
or
M⋅L⋅T−3
Radiant intensity
Ie,Ω[nb 5]
watt per steradian
W/sr
M⋅L2⋅T−3
Spectral intensity
Ie,Ω,ν[nb 3]
or
Ie,Ω,λ[nb 4]
watt per steradian per hertz
or
watt per steradian per metre
W⋅sr−1⋅Hz−1
or
W⋅sr−1⋅m−1
M⋅L2⋅T−2
or
M⋅L⋅T−3
Radiance
Le,Ω[nb 5]
watt per steradian per square metre
W⋅sr−1⋅m−2
M⋅T−3
Spectral radiance
Le,Ω,ν[nb 3]
or
Le,Ω,λ[nb 4]
watt per steradian per square metre per hertz
or
watt per steradian per square metre, per metre
W⋅sr−1⋅m−2⋅Hz−1
or
W⋅sr−1⋅m−3
M⋅T−2
or
M⋅L−1⋅T−3
Irradiance
Flux density
Ee[nb 2]
watt per square metre
W/m2
M⋅T−3
Spectral irradiance
Spectral flux density
Ee,ν[nb 3]
or
Ee,λ[nb 4]
watt per square metre per hertz
or
watt per square metre, per metre
W⋅m−2⋅Hz−1
or
W/m3
M⋅T−2
or
M⋅L−1⋅T−3
Radiosity
Je[nb 2]
watt per square metre
W/m2
M⋅T−3
Spectral radiosity Je,ν[nb 3] or Je,λ[nb 4] watt per square metre per hertz or watt per square metre, per metre W⋅m−2⋅Hz−1 or W/m3 M⋅T−2 or M⋅L−1⋅T−3 Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity". Radiant exitance
Me[nb 2]
watt per square metre
W/m2
M⋅T−3
Spectral exitance
Me,ν[nb 3]
or
Me,λ[nb 4]
watt per square metre per hertz
or
watt per square metre, per metre
W⋅m−2⋅Hz−1
or
W/m3
M⋅T−2
or
M⋅L−1⋅T−3
Radiant exposure
He
joule per square metre
J/m2
M⋅T−2
Spectral exposure
He,ν[nb 3]
or
He,λ[nb 4]
joule per square metre per hertz
or
joule per square metre, per metre
J⋅m−2⋅Hz−1
or
J/m3
M⋅T−1
or
M⋅L−1⋅T−2
Hemispherical emissivity ε 1
Spectral hemispherical emissivity εν or ελ 1 Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. Directional emissivity εΩ 1
Spectral directional emissivity εΩ,ν or εΩ,λ 1 Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. Hemispherical absorptance A 1
Spectral hemispherical absorptance Aν or Aλ 1 Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". Directional absorptance AΩ 1
Spectral directional absorptance AΩ,ν or AΩ,λ 1 Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance". Hemispherical reflectance R 1
Spectral hemispherical reflectance Rν or Rλ 1 Spectral flux reflected by a surface, divided by that received by that surface. Directional reflectance RΩ 1
Spectral directional reflectance RΩ,ν or RΩ,λ 1 Spectral radiance reflected by a surface, divided by that received by that surface. Hemispherical transmittance T 1
Spectral hemispherical transmittance Tν or Tλ 1 Spectral flux transmitted by a surface, divided by that received by that surface. Directional transmittance TΩ 1
Spectral directional transmittance TΩ,ν or TΩ,λ 1 Spectral radiance transmitted by a surface, divided by that received by that surface. Hemispherical attenuation coefficient
μ
reciprocal metre
m−1
L−1
Spectral hemispherical attenuation coefficient μν or μλ reciprocal metre m−1 L−1 Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. Directional attenuation coefficient
μΩ
reciprocal metre
m−1
L−1
Spectral directional attenuation coefficient μΩ,ν or μΩ,λ reciprocal metre m−1 L−1 Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. See also: SI · Radiometry · Photometry ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities. ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance. ^ a b c d e f g Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity. ^ a b c d e f g Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek). ^ a b Directional quantities are denoted with suffix "Ω" (Greek). See also[edit] Étendue Light field Sakuma–Hattori equation Wien displacement law References[edit] ^ Palmer, James M. "The SI system and SI units for
External links[edit] International Lighting in Controlled Environme |