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'''Radiance''' and '''spectral radiance''' are measures of the quantity of [[radiation]] that passes through or is emitted from a surface and falls within a given [[solid angle]] in a specified direction. They are used in [[radiometry]] to characterize diffuse emission and [[diffuse reflection|reflection]] of [[electromagnetic radiation]]. In [[astrophysics]], radiance is also used to quantify emission of [[neutrino]]s and other particles. The [[SI]] unit of radiance is [[watt]]s per [[steradian]] per [[square metre]] (W·sr<sup>−1</sup>·m<sup>−2</sup>), while that of [[Electromagnetic spectrum|spectral]] radiance is {{nobreak|W·sr<sup>−1</sup>·m<sup>−2</sup>·Hz<sup>−1</sup>}} or {{nobreak|W·sr<sup>−1</sup>·m<sup>−3</sup>}} depending on whether the spectrum is a function of [[frequency]] or of [[wavelength]].


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==Description==
Radiance characterizes total emission or reflection. Radiance is useful because it indicates how much of the power emitted by an emitting or reflecting surface will be received by an optical system looking at the surface from some angle of view. In this case, the [[solid angle]] of interest is the solid angle subtended by the optical system's [[entrance pupil]]. Since the [[human eye|eye]] is an optical system, radiance and its cousin [[luminance]] 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&nbsp;– see [[Brightness]] for a discussion. The nonstandard usage of "brightness" for "radiance" persists in some fields, notably [[laser physics]].
 
The radiance divided by the index of refraction squared is [[Invariant (physics)|invariant]] in [[geometric 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 called '''conservation of radiance'''. For real, passive, optical systems, the output radiance is ''at 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 the [[irradiance]] 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 (Hz) with SI units {{nobreak|W·sr<sup>−1</sup>·m<sup>−2</sup>·Hz<sup>−1</sup>}} or wavelength (nm) with units of {{nobreak|W·sr<sup>−1</sup>·m<sup>−2</sup>·nm<sup>−1</sup>}} (more common than {{nobreak|W·sr<sup>−1</sup>·m<sup>-3<!--YES THIS IS CORRECT. ONE LENGTH DIMENSION FOR WAVELENGTH--></sup>}}). In some fields spectral radiance is also measured in [[microflick]]s.<ref>{{cite web|last=Palmer|first=James M.|title=The SI system and SI units for Radiometry and photometry|url=http://www.optics.arizona.edu/palmer/opti400/suppdocs/bkappndx.pdf}}</ref><ref>{{cite web|last=Rowlett|first=Russ|title=How Many? A Dictionary of Units of Measurement|url=http://www.unc.edu/~rowlett/units/dictF.html#flick|accessdate=10 August 2012}}</ref>  Radiance is the integral of the spectral radiance over all wavelengths or frequencies.
 
For radiation emitted by an ideal [[black body]] at temperature ''T'', spectral radiance is governed by [[Planck's law]], while the integral of radiance over the hemisphere into which it radiates, in W/m<sup>2</sup>, is governed by the [[Stefan-Boltzmann law]].  There is no need for a separate law for radiance normal to the surface of a black body, in W/m<sup>2</sup>/sr, since this is simply the Stefan-Boltzmann law divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased by [[Stefan%E2%80%93Boltzmann_law#Integration_of_intensity_derivation|integration over the cosine of the zenith angle]]. More generally the radiance at an angle ''θ'' to the normal (the zenith angle) is given by the Stefan-Boltzmann law times cos(''θ'')/π.
 
==Definition==
Radiance is defined by
:<math>L = \frac{\mathrm{d}^2 \Phi}{\mathrm{d}A\,\mathrm{d}{\Omega} \cos \theta} \approx \frac{\Phi}{\Omega A \cos \theta}</math>
 
where
:''L'' is the observed or measured radiance ({{nobreak|[[Watt|W]]·[[square metre|m<sup>&minus;2</sup>]]·[[steradian|sr<sup>&minus;1</sup>]]}}), in the direction ''θ'',
:d is the [[differential operator]],
:''Φ'' is the total [[radiant flux]] or power ([[Watt|W]]) emitted
:''θ'' is the [[angle]] between the [[surface normal]] and the specified direction,
:''A'' is the [[area]] of the surface ([[square metre|m<sup>2</sup>]]), and
:<math>{\Omega}</math> is the [[solid angle]] ([[Steradian|sr]]) subtended by the observation or measurement.
:The approximation only holds for small ''A'' and ''Ω'' where cos&nbsp;''θ'' is approximately constant.
 
In general, ''L'' is a function of viewing angle through the cos&nbsp;''θ'' term in the denominator as well as the ''θ'', and potentially azimuth angle, dependence of <math>{\mathrm{d} \Phi}/{\mathrm{d}{\Omega}}</math>.  For the special case of a [[Lambertian reflectance|Lambertian]] source, ''L'' is constant such that <math>\mathrm{d}^2 \Phi \over \mathrm{d}A\ \mathrm{d}{\Omega}</math> is proportional to cos&nbsp;''θ''.
 
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 at 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.
 
The spectral radiance (radiance per unit wavelength) is written ''L''<sub>λ</sub> and the radiance per unit frequency is written ''L''<sub>ν</sub>.
 
==Intensity==
{{See also|Intensity (disambiguation)|Intensity (heat transfer)}}
Radiance is often, confusingly, called ''intensity'' in other areas of study, especially [[heat transfer]], [[astrophysics]] and [[astronomy]].  ''Intensity'' has many other meanings in [[physics]], with the most common being [[intensity (physics)|power per unit area]].  The distinction lies in the area rather than the subtended angle of the observer, and relative area of the source.
 
==See also==
*[[Etendue]]
*[[Light field]]
*[[Sakuma–Hattori equation]]
*[[Wien displacement law]]
 
==References==
{{Reflist}}
 
== External links ==
* [http://ncr101.montana.edu/Light1994Conf/4_2_Sliney/Sliney%20Text.htm International Lighting in Controlled Environments Workshop]
 
{{SI radiometry units}}
 
[[Category:Physical quantities]]
[[Category:Radiometry]]
[[Category:Heat transfer]]

Revision as of 17:58, 1 February 2014

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my site; wellness [continue reading this..] Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emitted from a surface and falls within a given solid angle in a specified direction. They are used in radiometry to characterize diffuse emission and reflection of electromagnetic radiation. In astrophysics, radiance is also used to quantify emission of neutrinos and other particles. The SI unit of radiance is watts per steradian per square metre (W·sr−1·m−2), while that of spectral radiance is Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park. or Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park. depending on whether the spectrum is a function of frequency or of wavelength.

Description

Radiance characterizes total emission or reflection. Radiance is useful because it indicates how much of the power emitted by an emitting or reflecting surface will be received by an optical system looking at the surface from some angle of view. In this case, the solid angle of interest is the solid angle subtended by the optical system's entrance pupil. Since the eye is an optical system, radiance and its cousin luminance 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 Brightness for a discussion. The nonstandard usage of "brightness" for "radiance" persists in some fields, notably laser physics.

The radiance divided by the index of refraction squared is invariant in geometric 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 called conservation of radiance. For real, passive, optical systems, the output radiance is at 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 the irradiance 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 (Hz) with SI units Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park. or wavelength (nm) with units of Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park. (more common than Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park.). In some fields spectral radiance is also measured in microflicks.[1][2] Radiance is the integral of the spectral radiance over all wavelengths or frequencies.

For radiation emitted by an ideal black body at temperature T, spectral radiance is governed by Planck's law, while the integral of radiance over the hemisphere into which it radiates, in W/m2, is governed by the Stefan-Boltzmann law. There is no need for a separate law for radiance normal to the surface of a black body, in W/m2/sr, since this is simply the Stefan-Boltzmann law divided by π. This factor is obtained from the solid angle 2π steradians of a hemisphere decreased by integration over the cosine of the zenith angle. More generally the radiance at an angle θ to the normal (the zenith angle) is given by the Stefan-Boltzmann law times cos(θ)/π.

Definition

Radiance is defined by

L=d2ΦdAdΩcosθΦΩAcosθ

where

L is the observed or measured radiance (Analyst Programmer Alfonzo Crosser from Newcastle, usually spends time with interests which include frisbee golf - frolf, property developers properties for sale in singapore singapore and collecting music albums. Ended up in recent past visiting Puerto-Princesa Subterranean River National Park.), in the direction θ,
d is the differential operator,
Φ is the total radiant flux or power (W) emitted
θ is the angle between the surface normal and the specified direction,
A is the area of the surface (m2), and
Ω is the solid angle (sr) subtended by the observation or measurement.
The approximation only holds for small A and Ω where cos θ is approximately constant.

In general, L is a function of viewing angle through the cos θ term in the denominator as well as the θ, and potentially azimuth angle, dependence of dΦ/dΩ. For the special case of a Lambertian source, L is constant such that d2ΦdAdΩ is proportional to cos θ.

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 at 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.

The spectral radiance (radiance per unit wavelength) is written Lλ and the radiance per unit frequency is written Lν.

Intensity

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See also

References

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External links

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