radiance

_{e};

density of radiant intensity with respect to projected area in a specified direction at a specified point on a real or imaginary surface

where _{e} is radiant intensity,

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, _{e}, 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, , as:

Hence, radiance is often considered as a quotient of averaged quantities; the area,

Note 2 to entry: For a surface being irradiated, an equivalent formula in terms of irradiance, _{e}, and solid angle,

Note 3 to entry: An equivalent formula is , where _{e} is radiant flux and

Note 4 to entry:

Radiant flux can be obtained by integrating radiance over projected area,

Note 5 to entry: Since the optical extent, expressed by ^{2}, where _{e}⋅^{−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, _{e}. In this case, it is mathematically interpreted as a second partial derivative of the radiant flux at a specified point (

where

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.

Note 10 to entry: This entry was numbered 17-1012 in CIE S 017:2011.