Movatterモバイル変換


[0]ホーム

URL:


Jump to content
WikipediaThe Free Encyclopedia
Search

Radiance

From Wikipedia, the free encyclopedia
Physical quantity in radiometry
For other uses, seeRadiance (disambiguation).

Inradiometry,radiance is theradiant flux emitted, reflected, transmitted or received by a given surface, per unitsolid angle per unit projected area. Radiance is used to characterize diffuse emission andreflection ofelectromagnetic radiation, and to quantify emission ofneutrinos and other particles. TheSI unit of radiance is thewatt persteradian persquare metre (W·sr−1·m−2). It is adirectional quantity: the radiance of a surface depends on the direction from which it is being observed.

The related quantityspectral radiance is the radiance of a surface per unitfrequency orwavelength, depending on whether thespectrum is taken as a function of frequency or of wavelength.

Historically, radiance was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant inheat transfer,astrophysics andastronomy. "Intensity" has many other meanings inphysics, with the most common beingpower per unit area (so the radiance is the intensity per solid angle in this case).

Description

[edit]
Comparison of photometric and radiometric quantities

Radiance is useful because it indicates how much of the power emitted, reflected, transmitted or received by a surface will be received by an optical system looking at that surface from a specified angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical system'sentrance pupil. Since theeye is an optical system, radiance and its cousinluminance are good indicators of how bright an object will appear. For this reason, radiance and luminance are both sometimes called "brightness". This usage is now discouraged (see the articleBrightness for a discussion). The nonstandard usage of "brightness" for "radiance" persists in some fields, notablylaser physics.

The radiance divided by the index of refraction squared isinvariant ingeometric optics. This means that for an ideal optical system in air, the radiance at the output is the same as the input radiance. This is sometimes calledconservation of radiance. For real, passive, optical systems, the output radiance isat most equal to the input, unless the index of refraction changes. As an example, if you form a demagnified image with a lens, the optical power is concentrated into a smaller area, so theirradiance is higher at the image. The light at the image plane, however, fills a larger solid angle so the radiance comes out to be the same assuming there is no loss at the lens.

Spectral radiance expresses radiance as a function of frequency or wavelength. Radiance is the integral of the spectral radiance over all frequencies or wavelengths. For radiation emitted by the surface of an idealblack body at a given temperature, spectral radiance is governed byPlanck's law, while the integral of its radiance, over the hemisphere into which its surface radiates, is given by theStefan–Boltzmann law. Its surface isLambertian, so that its radiance is uniform with respect to angle of view, and is simply the Stefan–Boltzmann integral divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased byintegration over the cosine of the zenith angle.

Mathematical definitions

[edit]

Radiance

[edit]

Radiance of asurface, denotedLe,Ω ("e" for "energetic", to avoid confusion with photometric quantities, and "Ω" to indicate this is a directional quantity), is defined as[1]

Le,Ω=2ΦeΩ(Acosθ),{\displaystyle L_{\mathrm {e} ,\Omega }={\frac {\partial ^{2}\Phi _{\mathrm {e} }}{\partial \Omega \,\partial (A\cos \theta )}},}

where

In generalLe,Ω is a function of viewing direction, depending onθ through cosθ andazimuth angle through∂Φe/∂Ω. For the special case of aLambertian surface,2Φe/(∂Ω ∂A) is proportional to cosθ, andLe,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]
Main article:Spectral radiance

Spectral radiance in frequency of asurface, denotedLe,Ω,ν, is defined as[1]

Le,Ω,ν=Le,Ων,{\displaystyle L_{\mathrm {e} ,\Omega ,\nu }={\frac {\partial L_{\mathrm {e} ,\Omega }}{\partial \nu }},}

whereν is the frequency.

Spectral radiance in wavelength of asurface, denotedLe,Ω,λ, is defined as[1]

Le,Ω,λ=Le,Ωλ,{\displaystyle L_{\mathrm {e} ,\Omega ,\lambda }={\frac {\partial L_{\mathrm {e} ,\Omega }}{\partial \lambda }},}

whereλ is the wavelength.

Conservation of basic radiance

[edit]

Radiance of a surface is related toétendue by

Le,Ω=n2ΦeG,{\displaystyle L_{\mathrm {e} ,\Omega }=n^{2}{\frac {\partial \Phi _{\mathrm {e} }}{\partial G}},}

where

  • n is therefractive 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[2]

Le,Ω=Le,Ωn2{\displaystyle L_{\mathrm {e} ,\Omega }^{*}={\frac {L_{\mathrm {e} ,\Omega }}{n^{2}}}}

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
QuantityUnitDimensionNotes
NameSymbol[nb 1]NameSymbol
Radiant energyQe[nb 2]jouleJML2T−2Energy of electromagnetic radiation.
Radiant energy densitywejoule per cubic metreJ/m3ML−1T−2Radiant energy per unit volume.
Radiant fluxΦe[nb 2]wattW = J/sML2T−3Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and calledluminosity in astronomy.
Spectral fluxΦe,ν[nb 3]watt perhertzW/HzML2T −2Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1.
Φe,λ[nb 4]watt per metreW/mMLT−3
Radiant intensityIe,Ω[nb 5]watt persteradianW/srML2T−3Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is adirectional quantity.
Spectral intensityIe,Ω,ν[nb 3]watt per steradian per hertzW⋅sr−1⋅Hz−1ML2T−2Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is adirectional quantity.
Ie,Ω,λ[nb 4]watt per steradian per metreW⋅sr−1⋅m−1MLT−3
RadianceLe,Ω[nb 5]watt per steradian per square metreW⋅sr−1⋅m−2MT−3Radiant flux emitted, reflected, transmitted or received by asurface, per unit solid angle per unit projected area. This is adirectional quantity. This is sometimes also confusingly called "intensity".
Spectral radiance
Specific intensity
Le,Ω,ν[nb 3]watt per steradian per square metre per hertzW⋅sr−1⋅m−2⋅Hz−1MT−2Radiance of asurface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is adirectional quantity. This is sometimes also confusingly called "spectral intensity".
Le,Ω,λ[nb 4]watt per steradian per square metre, per metreW⋅sr−1⋅m−3ML−1T−3
Irradiance
Flux density
Ee[nb 2]watt per square metreW/m2MT−3Radiant fluxreceived by asurface per unit area. This is sometimes also confusingly called "intensity".
Spectral irradiance
Spectral flux density
Ee,ν[nb 3]watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Irradiance of asurface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density includejansky (1 Jy =10−26 W⋅m−2⋅Hz−1) andsolar flux unit (1 sfu =10−22 W⋅m−2⋅Hz−1 =104 Jy).
Ee,λ[nb 4]watt per square metre, per metreW/m3ML−1T−3
RadiosityJe[nb 2]watt per square metreW/m2MT−3Radiant fluxleaving (emitted, reflected and transmitted by) asurface per unit area. This is sometimes also confusingly called "intensity".
Spectral radiosityJe,ν[nb 3]watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Radiosity of asurface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity".
Je,λ[nb 4]watt per square metre, per metreW/m3ML−1T−3
Radiant exitanceMe[nb 2]watt per square metreW/m2MT−3Radiant fluxemitted by asurface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity".
Spectral exitanceMe,ν[nb 3]watt per square metre per hertzW⋅m−2⋅Hz−1MT−2Radiant exitance of asurface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity".
Me,λ[nb 4]watt per square metre, per metreW/m3ML−1T−3
Radiant exposureHejoule per square metreJ/m2MT−2Radiant energy received by asurface per unit area, or equivalently irradiance of asurface integrated over time of irradiation. This is sometimes also called "radiant fluence".
Spectral exposureHe,ν[nb 3]joule per square metre per hertzJ⋅m−2⋅Hz−1MT−1Radiant exposure of asurface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence".
He,λ[nb 4]joule per square metre, per metreJ/m3ML−1T−2
See also:
  1. ^Standards organizations recommend that radiometricquantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric orphoton quantities.
  2. ^abcdeAlternative symbols sometimes seen:W orE for radiant energy,P orF for radiant flux,I for irradiance,W for radiant exitance.
  3. ^abcdefgSpectral quantities given per unitfrequency are denoted with suffix "ν" (Greek letternu, not to be confused with a letter "v", indicating a photometric quantity.)
  4. ^abcdefgSpectral quantities given per unitwavelength are denoted with suffix "λ".
  5. ^abDirectional quantities are denoted with suffix "Ω".

See also

[edit]

References

[edit]
  1. ^abc"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions".ISO 9288:1989.ISO catalogue. 1989. Retrieved2015-03-15.
  2. ^William Ross McCluney,Introduction to Radiometry and Photometry, Artech House, Boston, MA, 1994ISBN 978-0890066782

External links

[edit]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Radiance&oldid=1262174022"
Categories:
Hidden categories:

[8]ページ先頭

©2009-2025 Movatter.jp