Optical vortex behavior in dynamic speckle fields

Abstract

The dynamic behavior of phase singularities, or optical vortices, in the pseudo-phase representation of dynamic speckle patterns is investigated. Sequences of band-limited, dynamic speckle patterns with predetermined Gaussian decorrelation behavior were generated, and the pseudo-phase realizations of the individual speckle patterns were calculated via a two-dimensional Hilbert transform algorithm. Singular points in the pseudo-phase representation are identified by calculating the local topological charge as determined by convolution of the pseudo-phase representations with a series of 2x2 nabla filters. The spatial locations of the phase singularities are tracked over all frames of the speckle sequences, and recorded in three-dimensional space (x,y,f), where f is frame number in the sequence. The behavior of the phase singularities traces 'vortex trails' which are representative of the speckle dynamics. Slowly decorrelating speckle patterns results in long, relatively straight vortex trails, while rapidly decorrelating speckle patterns results in tortuous, relatively short vortex trails. Optical vortex analysis such as described herein can be used as a descriptor of biological activity, flow, and motion.