IEVref:845-21-049ID:
Language:enStatus: Standard
Term: radiance
Synonym1:
Synonym2:
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Symbol: Le
L
Definition: density of radiant intensity with respect to projected area in a specified direction at a specified point on a real or imaginary surface

L e = d I e dA 1 cosα MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaeyzaaqabaGccqGH9aqpdaWcaaqaaiaabsga caWGjbWaaSbaaSqaaiaabwgaaeqaaaGcbaGaaeizaiaadgeaaaWaaS aaaeaacaaIXaaabaGaci4yaiaac+gacaGGZbGaeqySdegaaaaa@43DC@

where Ie is radiant intensity, A is area, and α is the angle between the normal to the surface at the specified point and the specified direction

Note 1 to entry: In a practical sense, the definition of radiance can be thought of as dividing a real or imaginary surface into an infinite number of infinitesimally small surfaces which can be considered as point sources, each of which has a specific radiant intensity, Ie, in the specified direction. The radiance of the surface is then the integral of these radiance elements over the whole surface.

The equation in the definition can mathematically be interpreted as a derivative (i.e. a rate of change of radiant intensity with projected area) and could alternatively be rewritten in terms of the average radiant intensity, I ¯ e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai qadMeagaqeamaaBaaaleaacaqGLbaabeaaaaa@3914@ , as:

L e = lim A0 I ¯ e A 1 cosα MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaeyzaaqabaGccqGH9aqpdaWfqaqaaiaabYga caqGPbGaaeyBaaWcbaGaamyqaiabgkziUkaabcdaaeqaaOWaaSaaae aaceWGjbGbaebadaWgaaWcbaGaaeyzaaqabaaakeaacaWGbbaaaiaa ykW7daWcaaqaaiaabgdaaeaacaqGJbGaae4BaiaabohacqaHXoqyaa aaaa@4A18@ .

Hence, radiance is often considered as a quotient of averaged quantities; the area, A, should be small enough so that uncertainties due to variations in radiant intensity within that area are negligible; otherwise, the quotient L ¯ e = I ¯ e A 1 cosα MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai qadYeagaqeamaaBaaaleaacaqGLbaabeaakiabg2da9maalaaabaGa bmysayaaraWaaSbaaSqaaiaabwgaaeqaaaGcbaGaamyqaaaacaaMc8 +aaSaaaeaacaqGXaaabaGaae4yaiaab+gacaqGZbGaeqySdegaaaaa @43BD@ gives the average radiance and the specific measurement conditions have to be reported with the result.

Note 2 to entry: For a surface being irradiated, an equivalent formula in terms of irradiance, Ee, and solid angle, Ω, is L e = d E e dΩ 1 cosθ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaeyzaaqabaGccqGH9aqpdaWcaaqaaGqaaiaa =rgacaWGfbWaaSbaaSqaaiaabwgaaeqaaaGcbaGaa8hzaiaadM6aaa GaaGPaVpaalaaabaGaaeymaaqaaiaabogacaqGVbGaae4CaiabeI7a Xbaaaaa@45DE@ , where θ is the angle between the normal to the surface being irradiated and the direction of irradiation. This form is useful when the source has no surface (e.g. the sky, the plasma of a discharge).

Note 3 to entry: An equivalent formula is L e = d Φ e dG MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaeyzaaqabaGccqGH9aqpdaWcaaqaaGqaaiaa =rgacqqHMoGrdaWgaaWcbaGaaeyzaaqabaaakeaacaWFKbGaam4raa aaaaa@3F56@ , where Φe is radiant flux and G is geometric extent.

Note 4 to entry: Radiant flux can be obtained by integrating radiance over projected area, A·cos α, and solid angle, Ω: Φ e = L e cosαdAdΩ .

Note 5 to entry: Since the optical extent, expressed by G·n2, where G is geometric extent and n is refractive index, is invariant, the quantity expressed by Le·n−2 is also invariant along the path of the beam if the losses by absorption, reflection and diffusion are taken as 0. That quantity is called "basic radiance".

Note 6 to entry: The equation in the definition can also be described as a function of radiant flux, Φe. In this case, it is mathematically interpreted as a second partial derivative of the radiant flux at a specified point (xy) in space in a specified direction (ϑ, φ) with respect to projected area, A·cos α, and solid angle, Ω:

L e (x,y,ϑ,φ)= 2 Φ e (x,y,ϑ,φ) A(x,y)cosαΩ( ϑ,φ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdh9vqqj=hEeea0xXdbb a9frFj0=OqFfea0dXdd9vqaq=JfrVkFHe9pgea0dXdar=Jb9hs0dXd bPYxe9vr0=vr0=vqpWqaaeaaciWacmGadaGadeaaeaGaauaaaOqaai aadYeadaWgaaWcbaGaaeyzaaqabaGccaGGOaGaamiEaiaacYcacaWG 5bGaaiilaiabeg9akjaacYcacqaHgpGAcaGGPaGaeyypa0ZaaSaaae aacqGHciITdaahaaWcbeqaaiaaikdaaaGccqqHMoGrdaWgaaWcbaGa aeyzaaqabaGccaGGOaGaamiEaiaacYcacaWG5bGaaiilaiabeg9akj aacYcacqaHgpGAcaGGPaaabaGaeyOaIyRaamyqaiaacIcacaWG4bGa aiilaiaadMhacaGGPaGaeyyXICTaci4yaiaac+gacaGGZbGaeqySde MaeyyXICTaeyOaIyRaamyQdmaabmaabaGaeqy0dOKaaiilaiabeA8a QbGaayjkaiaawMcaaaaacaaMc8oaaa@6998@

where α is the angle between the normal to that area at the specified point and the specified direction.

Note 7 to entry: The corresponding photometric quantity is "luminance". The corresponding quantity for photons is "photon radiance".

Note 8 to entry: The radiance is expressed in watt per square metre per steradian (W·m−2·sr−1).

Note 9 to entry: This entry was numbered 845-01-34 in IEC 60050-845:1987.


Publication date:2020-12
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