photon radiance

L_p; L

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

where I_p is photon intensity, A is area and α 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 photon 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 photon intensity, I_p, in the specified direction. The photon radiance of the surface is then the integral of these photon 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 photon intensity with projected area) and could alternatively be rewritten in terms of the average photon intensity, , as:

Hence, photon radiance is often considered as a quotient of averaged quantities; the area, A, should be small enough so that uncertainties due to variations in photon intensity within that area are negligible; otherwise, the quotient gives the average photon radiance 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 photon irradiance, E_p, 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_p is photon flux and G is geometric extent.

Note 4 to entry:
Photon flux can be obtained by integrating photon radiance 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_p⋅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 photon radiance".

Note 6 to entry: The equation in the definition can also be described as a function of photon flux, Φ_p. In this case, it is mathematically interpreted as a second partial derivative of the photon 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 photometric quantity is "luminance".

Note 8 to entry: The photon radiance is expressed in second to the power minus one per square metre per steradian (s⁻¹·m⁻²·sr⁻¹).

Note 9 to entry: This entry was numbered 845-01-36 in IEC 60050-845:1987.

Note 10 to entry: This entry was numbered 17-931 in CIE S 017:2011.