Radiance - Description

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 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. Radiance is the integral of the spectral radiance over all wavelengths.

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.