Evolution equation for radiance and coherence

If the field of applications of radiometry is restricted to energy calculations of optical systems then the theorem about invariant of the phase radiance (or the reduced radiance) along the light ray takes the form of Liouville's equation. This differential equation is a good basis for the traditional radiometry of Lambertian sources, as well as radiometry of the quasi-homogeneous sources. It is known that the wave analogue of phase radiance is the Wigner definition function. This wave analogy helps to clarify the limits of applicability of the concepts and approximations, e.g. properties of optical media in which the radiation transfer can be described by Liouville's equation.