Editing Radiance (section)

==Description==
[[File:photometry_radiometry_units.svg|thumb|upright=1.5|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'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 (see the article [[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 or wavelength. Radiance is the integral of the spectral radiance over all frequencies or wavelengths. For radiation emitted by the surface of an ideal [[black body]] at a given temperature, spectral radiance is governed by [[Planck's law]], while the integral of its radiance, over the hemisphere into which its surface radiates, is given by the [[Stefan–Boltzmann law]]. Its surface is [[Lambert's cosine law|Lambertian]], 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 by [[Stefan–Boltzmann law#Integration of intensity derivation|integration over the cosine of the zenith angle]].