Radiometry and wide-angle wave fields II Coherent fields in three dimensions

The wave-based generalized radiance definitions presented in a previous manuscript [J. Opt. Soc. A18, 902 (2001)] for two-dimensional coherent monochromatic fields in free space are extended here to the three-dimensional case. These new definitions preserve all the properties of their two-dimensional analogs. Notably, they are exactly conserved along rays and well suited for the description of fields traveling in all directions. The different members of this set of functions are seen to correspond to weighted radial projections in momentum of the Wigner function of the field.