Radiance

Radiance is the measure 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. Radiance is used in radiometry to characterize diffused emissions and reflection of electromagnetic radiation. It 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^-1m^-2).

Radiance characterizes total emissions or reflection. It 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. The solid angle of interest in this case is the solid angle subtended by the optical system’s entrance pupil. Because the eye is an optical system, radiance and luminance are good indicators of how bright an object will appear. This is the reason radiance and luminance is often called brightness.

The radiance divided by the index of refraction squared is invariant in geometric optics. It is an ideal optical system in air. The radiance at the output is the same as the radiance of the input. This principle is called the conservation of radiance. Most real, passive, optical systems follow the conservation of radiance.

Radiance is

L = (d²φ)/(dAdΩcosϴ)

Where

L is the observed or measured rasiance

d is the differential operator

φ is the total radiant flux

ϴ is the angle between the surface normal and the specified direction

A is the area of the surface

Ω is the solid angle

This approximation will only hold for small A and Ω where cosϴ is approximately constant.

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