Partially coherent vortex beams of arbitrary radial order and a van Cittert-Zernike theorem for vortices

We theoretically define a complete class of partially coherent vortex beams of any radial and azimuthal order and characterize the behavior of their phase singularities and orbital angular momentum. These beams are shown to exhibit a coherence vortex supplement to the van Cittert-Zernike theorem, in which the vortex structure of the random beam reconstitutes upon propagation. This full characterization of a class of partially coherent Laguerre-Gauss beams of any order may find application in free-space optical communication, among other uses.