Diffuse correlation tomography in the transport regime: a theoretical study of the sensitivity to Brownian motion

Abstract

Numerous methods consider the temporal field autocorrelation function in order to study the dynamical properties of a medium, e.g. diffuse correlation tomography (DCT) [1] and speckle contrast optical tomography (SCOT) [5]. In this paper, we calculate the field correlation function in the transport regime as the solution to the correlation transport equation (CTE) introduced in [1]. We show how perturbation theory can be applied to the CTE in order to calculate the sensitivity kernel relating the variation of the local Brownian motion of particles to the typical data. The Green’s function of the standard radiative transport equation (RTE) can be used to construct the sensitivity kernel in the first Born approximation where the correlation time is considered to be the small parameter. We stress that the sensitivity kernel is defined for every point within the scattering medium. The sensitivity kernel is then the Jacobian matrix required in DCT or SCOT in order to perform the image reconstruction [5]. Eventually, we demonstrate how the use of the CTE, instead of the correlation diffusion approximation, is increasing the resolution of reconstructed images of dynamical parts of a scattering medium.