Energy transport in optical systems with partially coherent light

The propagation of a generalized radiance through optical systems is considered under the customary assumptions of physical optics (paraxial propagation in a uniform medium and amplitude transmission functions associated with optical elements). It is shown that in specular optical systems that consist of homogeneous media separated by spherical surfaces, the generalized radiance remains invariant along each paraxial ray regardless of the state of coherence of the wavefield. It is further demonstrated that with nonspecular optical systems it is more convenient to use, in place of the generalized radiance, a closely related physical-optics quantity known as the Wigner (distribution) function. As an application, we analyze the energy transport through an optical device that has been employed to produce highly directional, partially coherent beams.