The radiance and phase-space representations of the cross-spectral density operator

Abstract

Hilbert space operators are introduced into classical wave theory, which make it possible to associate a unique operator with the cross-spectral density. By linearly mapping this operator onto an associated phase-space one obtains a wide class of generalized radiance functions, including two well-known ones that were introduced by Walther in a different manner. When the source is quasi-homogeneous and the wavelength is short enough all these functions become identical; and this unique limit is found to have all the properties of the traditional radiance, at least in the source plane.