Radiometry and wide-angle wave fields III: partial coherence

The analogs of the generalized radiances introduced in two previous manuscripts [J. Opt. Soc. Am. A 18, 902 (2001) and J. Opt. Soc. Am. A 18, 910 (2001)] for fully coherent fields in two- and three-dimensional free space are given here for the case of partial coherence. These functions are exactly conserved along rays and are suitable for the description of fields with components propagating in any direction. Also defined here is a global measure of coherence, which can be expressed in terms of the new functions. The cases of radiation in a blackbody cavity and partially coherent focused waves are considered as examples.