Statistics of speckle patterns

TL;DR

This paper introduces a general method for calculating the statistical properties of speckle patterns generated by coherent waves in disordered media, revealing long-range correlations and sensitivities to external parameters.

Contribution

It presents a novel approach similar to Boltzmann-Langevin for speckle statistics, with new results for long-range correlations and parameter sensitivities in specific scattering regimes.

Findings

Correlation function decays as a power law with distance

Speckle patterns exhibit sign-changing long-range correlations

Speckle sensitivity to frequency and angle changes is characterized

Abstract

We develop a general method for calculating statistical properties of the speckle pattern of coherent waves propagating in disordered media. In some aspects this method is similar to the Boltzmann-Langevin approach for the calculation of classical fluctuations. We apply the method to the case where the incident wave experiences many small angle scattering events during propagation, but the total angle change remains small. In many aspects our results for this case are different from results previously known in the literature. The correlation function of the wave intensity at two points separated by a distance $r$, has a long range character. It decays as a power of $r$ and changes sign. We also consider sensitivities of the speckles to changes of external parameters, such as the wave frequency and the incidence angle.