Optical memory in random fields generated by perfect vortex beams

We introduce what we believe to be a novel method to quantify the discrete spatial correlation between random fields originating from volumetric scattering media illuminated by perfect vortex beams with different topological charges. The degree of correlation is parametrized as the space-dependent maximum magnitude of the cross correlation function between the two different intensity distributions. We present a theoretical framework that elucidates the relationship between this new metric and the properties of complex media including surface and volume scattering and free-space propagation. Systematic experiments demonstrate the validity of our procedure in a variety of practical situations involving scattering media with varying optical density. We demonstrate that the decay of the cross correlation magnitude with increasing the difference between topological charges provides robust means to characterize optical densities and depolarization processes over a broad range of scattering regimes. The results are relevant for active sensing procedures involving stochastic propagation.