radiance (in a given direction, at a given point of a real or imaginary surface) [Le]
quantity defined by the equation:
dΦe is the radiant flux transmitted by an elementary beam passing through the given point and propagating in the solid angle, dΩ, containing the given direction;
dA is the area of a section of that beam containing the given point;
Θ is the angle between the normal to that section and the direction of the beam
NOTE 1 The above equation does not represent a derivative (i.e. a rate of change of flux with solid angle or area) but rather the quotient of an element of flux by an element of solid angle and an element of area. In strict mathematical terms the definition could be written:
In practical measurements, A and Ω should be small enough that variations in Φv do not affect the result. Otherwise, the ratio gives the average radiance and the exact measurement conditions must be specified.
NOTE 3 For an area, dA, of the surface of a source, since the intensity, dI, of dA in the given direction is , then an equivalent formula is , a form mostly used in illuminating engineering.
NOTE 4 For an area, dA, of a surface receiving the beam, since the irradiance or illuminance, dE, produced by the beam on dA is , then an equivalent formula is , a form useful when the source has no surface (e.g. the sky, the plasma of a discharge).
NOTE 5 Making use of the geometric extent, dG, of the elementary beam, since dG = dA cosΘ dΩ, then an equivalent formula is .
NOTE 6 Since the optical extent, Gn2, (see NOTE to “geometric extent”) is invariant, then the quantity Ln-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 7 The relation between dΦ and L given in the formulae above is sometimes called the “basic law of radiometry and photometry”:
with the notation given here and at “geometric extent”.