Random matrix description of dynamically backscattered coherent waves propagating in a wide-field-illuminated random medium

TL;DR

This paper uses random matrix theory to analyze backscattered coherent waves in random media, enabling separation of single and multiple scattering components for improved imaging applications.

Contribution

It introduces a novel approach applying RMT to distinguish scattering components in dynamic speckle patterns, with practical applications demonstrated through simulations and experiments.

Findings

Marcenko-Pastur law describes multiple scattering eigenvalues

Low-rank characteristic of single scattering component

Effective estimation strategy for scattering moments

Abstract

The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each propagation trajectory and form dynamic speckle patterns in the backscattered direction. In this study, we applied the random matrix theory (RMT) to investigate the eigenvalue density of the backscattered intensity matrix. We find that the dynamic speckle patterns can be utilized to decouple the singly and multiply backscattered components. The Wishart random matrix of multiple scattering component is well described by the Marcenko-Pastur law, while the single scattering part has low-rank characteristic. We therefore propose a strategy for estimating the first and the second order moments of single and multiple scattering components, respectively, based on the Marcenko-Pastur law and trace analysis. Electric field Monte Carlo simulation and in-vivo experiments demonstrate its potential applications in hidden absorbing object detection and in-vivo blood flow imaging. Our method can be applied to other coherent domain elastic scattering phenomenon for wide-filed propagation of microwave, ultrasound and etc.