Radiance
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Radiance For other uses, see Radiance (disambiguation). Radiance and spectral radiance are measures of the quantity of radiation that passes through or is emit- ted 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 W·sr −1 ·m −2 ·Hz −1 or W·sr −1 ·m −3 (commonly W·sr −1 ·m −2 ·nm −1 ) depending on whether the spectrum is a function of frequency or of wavelength. 1 Description Radiance characterizes total emission or reflection. Radi- ance is useful because it indicates how much of the power emitted by an emitting or reflecting surface will be re- ceived by an optical system looking at the surface from some angle of view. In this case, the solid angle of in- terest is the solid angle subtended by the optical system’s entrance pupil. Since the eye is an optical system, radi- ance 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 discus- sion. The nonstandard usage of “brightness” for “radi- ance” 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 conserva- tion 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 con- centrated 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 fre- quency (Hz) with SI units W·sr −1 ·m −2 ·Hz −1 or wavelength (nm) with units of W·sr −1 ·m −2 ·nm −1 (more common than W·sr −1 ·m -3 ). 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 temper- ature T, spectral radiance is governed by Planck’s law, while the integral of radiance over the hemisphere into which it radiates, in W/m 2 , is governed by the Stefan- Boltzmann law. There is no need for a separate law for ra- diance normal to the surface of a black body, in W/m 2 /sr, since this is simply the Stefan-Boltzmann law divided by π. This factor is obtained from the solid angle 2π stera- dians 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. 2 Definition Radiance is defined by L = d 2 Φ dA dΩ cos θ ≈ Φ ΩA cos θ where L is the observed or measured radiance (W·m −2 ·sr −1 ), 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 (m 2 ), and Ω is the solid angle (sr) subtended by the ob- servation 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 d 2 Φ dA dΩ 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 cal- culating radiance at a detector, A refers to an area on the surface of the detector and Ω to the solid angle subtended 1
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Transcript of Radiance
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Radiance
For other uses, see Radiance (disambiguation).
Radiance and spectral radiance are measures of thequantity of radiation that passes through or is emit-ted from a surface and falls within a given solidangle in a specied direction. They are used inradiometry to characterize diuse emission and reectionof electromagnetic radiation. In astrophysics, radianceis also used to quantify emission of neutrinos and otherparticles. The SI unit of radiance is watts per steradianper square metre (Wsr1m2), while that of spectralradiance is Wsr1m2Hz1 or Wsr1m3 (commonlyWsr1m2nm1) depending on whether the spectrum isa function of frequency or of wavelength.
1 Description
Radiance characterizes total emission or reection. Radi-ance is useful because it indicates howmuch of the poweremitted by an emitting or reecting surface will be re-ceived by an optical system looking at the surface fromsome angle of view. In this case, the solid angle of in-terest is the solid angle subtended by the optical systemsentrance pupil. Since the eye is an optical system, radi-ance and its cousin luminance are good indicators of howbright an object will appear. For this reason, radiance andluminance are both sometimes called brightness. Thisusage is now discouraged see Brightness for a discus-sion. The nonstandard usage of brightness for radi-ance persists in some elds, notably laser physics.The radiance divided by the index of refraction squared isinvariant in geometric optics. This means that for an idealoptical system in air, the radiance at the output is the sameas the input radiance. This is sometimes called conserva-tion of radiance. For real, passive, optical systems, theoutput radiance is at most equal to the input, unless theindex of refraction changes. As an example, if you forma demagnied image with a lens, the optical power is con-centrated into a smaller area, so the irradiance is higherat the image. The light at the image plane, however, llsa larger solid angle so the radiance comes out to be thesame assuming there is no loss at the lens.Spectral radiance expresses radiance as a function of fre-quency (Hz) with SI unitsWsr1m2Hz1 or wavelength(nm) with units of Wsr1m2nm1 (more common thanWsr1m3). In some elds spectral radiance is alsomeasured in microicks.[1][2] Radiance is the integral of
the spectral radiance over all wavelengths or frequencies.For radiation emitted by an ideal black body at temper-ature T, spectral radiance is governed by Plancks law,while the integral of radiance over the hemisphere intowhich it radiates, in W/m2, is governed by the Stefan-Boltzmann law. There is no need for a separate law for ra-diance normal to the surface of a black body, inW/m2/sr,since this is simply the Stefan-Boltzmann law divided by. This factor is obtained from the solid angle 2 stera-dians of a hemisphere decreased by integration over thecosine of the zenith angle. More generally the radianceat an angle to the normal (the zenith angle) is given bythe Stefan-Boltzmann law times cos()/.
2 DenitionRadiance is dened by
L =d2
dA d cos
A cos where
L is the observed or measured radiance(Wm2sr1), in the direction ,d is the dierential operator, is the total radiant ux or power (W) emitted is the angle between the surface normal andthe specied direction,A is the area of the surface (m2), and
is the solid angle (sr) subtended by the ob-servation or measurement.The approximation only holds for small A and where cos is approximately constant.
In general, L is a function of viewing angle through the cos term in the denominator as well as the , and potentiallyazimuth angle, dependence of d/d . For the specialcase of a Lambertian source, L is constant such that d2dA d
is proportional to cos .When calculating the radiance emitted by a source, Arefers to an area on the surface of the source, and tothe solid angle into which the light is emitted. When cal-culating radiance at a detector, A refers to an area on thesurface of the detector and to the solid angle subtended
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by the source as viewed from that detector. When radi-ance is conserved, as discussed above, the radiance emit-ted by a source is the same as that received by a detectorobserving it.The spectral radiance (radiance per unit wavelength) iswritten L and the radiance per unit frequency is writtenL.
3 NomenclatureSee also: Intensity (disambiguation) and Intensity (heattransfer)
Historically, radiance is called intensity and spectral ra-diance is called specic intensity. Many elds still usethis nomenclature. It is especially dominant in heat trans-fer, astrophysics and astronomy. Intensity has many othermeanings in physics, with the most common being powerper unit area.
4 See also Etendue
Light eld
SakumaHattori equation
Wien displacement law
5 References[1] Palmer, James M. The SI system and SI units for Ra-
diometry and photometry. Archived from the originalon August 2, 2012.
[2] Rowlett, Russ. How Many? A Dictionary of Units ofMeasurement. Retrieved 10 August 2012.
6 External links International Lighting in Controlled EnvironmentsWorkshop
[1] Standards organizations recommend that radiometricquantities should be denoted with a sux e (for en-ergetic) to avoid confusion with photometric or photonquantities.
[2] Alternative symbols sometimes seen: W or E for radiantenergy, P or F for radiant ux, I for irradiance, W forradiant emittance.
[3] Spectral quantities given per unit wavelength are denotedwith sux "" (Greek) to indicate a spectral concentra-tion. Spectral functions of wavelength are indicated by"()" in parentheses instead, for example in spectral trans-mittance, reectance and responsivity.
[4] Spectral quantities given per unit frequency are denotedwith sux "" (Greek)not to be confused with the suxv (for visual) indicating a photometric quantity.
[5] NOAA / SpaceWeather Prediction Center includes a def-inition of the solar ux unit (SFU).
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