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The existence of a spatial correlation singularity or a ring dislocation in the spatial coherence function when a vortex is present has been demonstrated recently. Here, we investigate how the spatial correlation singularity is affected by both the radial and azimuthal mode indices (p, ') in a partially coherent light field. Theoretically, we find that the spatial correlation singularity may exist even in a non-vortex beam (' = 0) due to the radial index. Numerical simulations show the number of ring dislocations in the far-field cross correlation function is equal to 2p+|'| for the low coherence cases. This is confirmed by our experimental results. This phenomenon may occur in any partially coherent vortex wave.

Effect of the radial and azimuthal mode indices of a partially coherent vortex field upon a spatial correlation singularity