A Transport Model for Multi-Frequency Acousto-Optic Tomography

TL;DR

This paper develops a transport model for multi-frequency acousto-optic tomography, demonstrating how to recover optical properties of a medium from boundary measurements using the radiative transport equation.

Contribution

It introduces a novel inverse problem framework for acousto-optic tomography based on the RTE, enabling the reconstruction of absorption and scattering coefficients from boundary data.

Findings

Absorption coefficient can be reconstructed from a single boundary measurement.

Scattering coefficients can be reconstructed from a family of boundary measurements.

The model relies on assumptions of regularity and isotropicity of the medium.

Abstract

In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this medium from measurements of the frequency-shifted light, using a radiative transport equation (RTE) model for light propagation. Given some assumptions on the regularity and isotropicity of the coefficients of the RTE, we show that the absorption coefficient can be reconstructed from the boundary measurements of a single well chosen illumination, and that the scattering coefficients can be reconstructed from boundary measurements of a one-parameter family of illuminations.