Non-invasive imaging through random media

TL;DR

This paper provides a mathematical analysis of speckle imaging through strongly scattering media, explaining how useful information can be extracted from seemingly random wave patterns in a specific scaling regime.

Contribution

It introduces a detailed mathematical framework for speckle imaging in the white-noise paraxial regime, clarifying the limits and stability of information extraction.

Findings

Identifies the white-noise paraxial regime as optimal for speckle imaging

Characterizes the resolution and stability of information extraction

Provides a detailed model explaining physical experimental results

Abstract

When waves propagate through a strongly scattering medium the energy is transferred to the incoherent wave part by scattering. The wave intensity then forms a random speckle pattern seemingly without much useful information. However, a number of recent physical experiments show how one can extract useful information from this speckle pattern. Here we present the mathematical analysis that explains the quite stunning performance of such a scheme for speckle imaging. Our analysis identifies a scaling regime where the scheme works well. This regime is the white-noise paraxial regime, which leads to the Ito-Schrodinger model for the wave amplitude. The results presented in this paper conform with the sophisticated physical intuition that has motivated these schemes, but give a more detailed characterization of the performance. The analysis gives a description of (i) the information that can be extracted and with what resolution (ii) the statistical stability or signal-to-noise ratio with which the information can be extracted.