luminance

L_v; L

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

where I_v is luminous intensity, A is area and α is the angle between the normal to the surface at the specified point and the specified direction

Note 1 to entry: In a practical sense, the definition of luminance 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 luminous intensity, I_v, in the specified direction. The luminance of the surface is then the integral of these luminance elements over the whole surface.
The equation in the definition can mathematically be interpreted as a derivative (i.e. a rate of change of luminous intensity with projected area) and could alternatively be rewritten in terms of the average luminous intensity, , as:
_.
Hence, luminance is often considered as a quotient of averaged quantities; the area, A, should be small enough so that uncertainties due to variations in luminous intensity within that area are negligible; otherwise, the quotient gives the average luminance and the specific measurement conditions have to be reported with the result.

Note 2 to entry: For a surface being irradiated, an equivalent formula in terms of illuminance, E_v, and solid angle, Ω, is , where θ is the angle between the normal to the surface being irradiated and the direction of irradiation. This form is useful when the source has no surface (e.g. the sky, the plasma of a discharge).

Note 3 to entry: An equivalent formula is , where Φ_v is luminous flux and G is geometric extent.

Note 4 to entry:
Luminous flux can be obtained by integrating luminance over projected area, A⋅cos α, and solid angle, Ω: .

Note 5 to entry: Since the optical extent, expressed by G⋅n², where G is geometric extent and n is refractive index, is invariant, the quantity expressed by L_v⋅n⁻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 luminance".

Note 6 to entry: The equation in the definition can also be described as a function of luminous flux, Φ_v. In this case, it is mathematically interpreted as a second partial derivative of the luminous flux at a specified point (x, y) in space in a specified direction (ϑ, φ) with respect to projected area, A⋅cos α, and solid angle, Ω,

where α is the angle between the normal to that area at the specified point and the specified direction.

Note 7 to entry: The corresponding radiometric quantity is "radiance". The corresponding quantity for photons is "photon radiance".

Note 8 to entry: The luminance is expressed in candela per square metre (cd·m⁻² = lm·m⁻²·sr⁻¹).

Note 9 to entry: This entry was numbered 845-01-35 in IEC 60050-845:1987.

Note 10 to entry: This entry was numbered 17-711 in CIE S 017:2011.