  The notion of brightness is efficiently conveyed in geometric optics as
density of rays in phase space. Wigner has introduced his famous distribution
in quantum mechanics as a quasi-probability density of a quantum system in
phase space. Naturally, the same formalism can be used to represent light
including all the wave phenomena. It provides a natural framework for radiation
propagation and optics matching by transferring the familiar `baggage' of
accelerator physics (beta-function, emittance, phase space transforms, etc.) to
synchrotron radiation. This paper details many of the properties of the Wigner
distribution and provides examples of how its use enables physically insightful
description of partially coherent synchrotron radiation in phase space.
