Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions.

By analysis of the far-field cross-correlation function (CCF) of partially coherent optical beams, we demonstrate an implicit rule that the number of ring dislocations (dark zones) of the far-field CCF is equal to the original topological charge of an optical vortex rendered partially coherent. This novel link between an optical vortex and its correlation singularity may offer an efficient method for measuring the orbital angular momentum of partially coherent optical vortices in fields such as astrophysics and astronomy, as well as atmospheric laser communication.