Radiative transfer and diffusion limits for wave field correlations in locally shifted random media

TL;DR

This paper develops a mathematical framework for opto-elastography by deriving radiative transfer and diffusion equations for wave field correlations in locally shifted random media, linking speckle decorrelation to these models and validating with simulations.

Contribution

It introduces a novel derivation of radiative transfer and diffusion equations for wave correlations in shifted random media, advancing the theoretical understanding of opto-elastography.

Findings

Derived radiative transfer equation for wave field cross-correlation.

Obtained diffusion approximation in the relevant regime.

Numerical simulations agree with experimental data.

Abstract

The aim of this paper is to develop a mathematical framework for opto-elastography. In opto-elastography, a mechanical perturbation of the medium produces a decorrelation of optical speckle patterns due to the displacements of optical scatterers. To model this, we consider two optically random media, with the second medium obtained by shifting the first medium in some local region. We derive the radiative transfer equation for the cross-correlation of the wave fields in the media. Then we derive its diffusion approximation. In both the radiative transfer and the diffusion regimes, we relate the correlation of speckle patterns to the solutions of the radiative transfer and the diffusion equations. We present numerical simulations based on our model which are in agreement with recent experimental measurements.