Correlations in scattered perfect optical vortices

We study correlations in the speckle patterns generated by the scattering of perfect optical vortex (POV) beams and use them to produce a new class of coherence functions, namely Bessel coherence functions. Higher (zeroth) order Bessel coherence functions have been realized in cross (auto)-correlation between the speckle patterns generated by the scattering of perfect vortex beams of different orders. We have also studied the propagation of produced Bessel coherence functions and characterized their divergence with respect to the radius of their first ring for different orders m = 0-4. We observe that the divergence varies linearly with the order of the coherence function. We provide the exact analytical expression for the auto-correlation, as well as cross-correlation functions for speckle patterns. Our experimental results are in good agreement with the analytical results.