Frequency Domain Optical Tomography Based on the Equation of Radiative Transfer

Abstract

Optical tomography consists of reconstructing the spatial distribution of absorption and scattering properties of a medium from surface measurements of transmitted light intensities. Mathematically, this problem amounts to parameter identification for the equation of radiative transfer (ERT) with diffusion‐type boundary measurements. Because they are posed in the phase‐space, radiative transfer equations are quite challenging to solve computationally. Most past works have considered the steady‐state ERT or the diffusion approximation of the ERT. In both cases, substantial cross‐talk has been observed in the reconstruction of the absorption and scattering properties of inclusions. In this paper, we present an optical tomographic reconstruction algorithm based on the frequency‐domain ERT. The inverse problem is formulated as a regularized least‐squares minimization problem, in which the mismatch between forward model predictions and measurements is minimized. The ERT is discretized by using a discrete ordinates method for the directional variables and a finite volume method for the spatial variables. A limited‐memory quasi‐Newton algorithm is used to minimize the least‐squares functional. Numerical simulations with synthetic data show that the cross‐talk between the two optical parameters is significantly reduced in reconstructions based on frequency‐domain data as compared to those based on steady‐state data.