Radiance


 * For the renderer, see Radiance (software).

Radiance and spectral radiance are radiometric measures that describe the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle in a specified direction. They are used to characterize both emission from diffuse sources and reflection from diffuse surfaces. The SI unit of radiance is watts per steradian per square metre (W&middot;sr-1&middot;m-2).

Radiance characterizes total emission or reflection, while spectral radiance characterizes the light at a single wavelength or frequency. The radiance is equal to the sum (or integral) of all the spectral radiances from a surface. Spectral radiance has SI units W&middot;sr-1&middot;m-3 when measured per unit wavelength, and W&middot;sr-1&middot;m-2&middot;Hz-1 when measured per unit frequency interval.

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 aperture. Since the eye is an optical system, radiance and its cousin luminance are good indicators of how bright an object will appear.

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.

Definition
Radiance is defined by
 * $$L = \frac{d^2 \Phi}{dA\,d{\Omega} \cos \theta} \simeq \frac{\Phi}{\Omega A \cos \theta}$$

where
 * the approximation holds for small A and &Omega;,
 * L is the radiance (W&middot;m-2&middot;sr-1),
 * &Phi; is the radiant flux or power (W),
 * &theta; is the angle between the surface normal and the specified direction,
 * A is the area of the source (m2), and
 * $${\Omega}$$ is the solid angle (sr).

The spectral radiance (radiance per unit wavelength) is written L&lambda; and the radiance per unit frequency is written L&nu;.