Partially coherent spherical sources with spherical harmonic modes

A class of partially coherent spherical sources is introduced whose cross-spectral density across the surface has a modal expansion made up of spherical harmonics. For such sources, the solution of the propagation problem in all the outer spaces can be written through a series of the propagated modes, which maintains the spherical harmonic structure. The main features of this class of cross-spectral densities are derived illustrating their coherence properties with examples. Attention is paid to the properties of radial coherence. In particular, it is clearly shown that sources with perfect radial coherence exist with angular coherence that is only partial.