We use diffuse optical tomography to quantitatively reconstruct images of complex phantoms with millimeter sized features located centimeters deep within a highly-scattering medium. A non-contact instrument was employed to collect large data sets consisting of greater than 10 7 source-detector pairs. Images were reconstructed using a fast image reconstruction algorithm based on an analytic solution to the inverse scattering problem for diffuse light.

A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(ŝ,ŝ ′ ) with the constraint that it depends only on the angle between the angular variablesŝ andŝ ′ . This corresponds to spherically symmetric (on average) random medium constituents. Boundary conditions are considered in the slab and half-space geometries. The approach developed in this paper is spectral. It allows for the expansion of the solution to the RTE in terms of analytical functions of angular and spatial variables to relatively high orders. The coefficients of this expansion must be computed numerically. However, the computational complexity of this task is much smaller than in the standard method of spherical harmonics. The solutions obtained are especially convenient for solving inverse problems associated with radiative transfer.

The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined from the boundary conditions, must also be computed. The Green's function for the radiative transport equation is computed and the results are compared with diffusion approximation and Monte Carlo simulations. We find that the diffusion approximation is not quite correct inside the slab, even when the light emitted from the slab is well described by the diffusion approximation. The solutions we obtain are especially convenient for solving inverse problems associated with radiative transport.

We report the first experimental test of an analytic image reconstruction algorithm for optical tomography with large data sets. Using a continuous-wave optical tomography system with 10 8 source-detector pairs, we demonstrate the reconstruction of an absorption image of a phantom consisting of a highly-scattering medium with absorbing inhomogeneities.Optical tomography (OT) is a biomedical imaging modality that utilizes diffuse light as a probe of tissue structure and function [1]. Clinical applications include imaging of breast disease and functional neuroimaging. The physical problem that is considered is to reconstruct the optical properties of an inhomogenous medium from measurements taken on its surface. In a typical experiment, optical fibers are used for illumination and detection of the transmitted light [2,3,4]. The number of measurements (source-detector pairs) which can be obtained, in practice, varies between 10 2 − 10 4 . A recently proposed alternative to fiber-based experiments is to employ a narrow incident beam for illumination. The beam can be scanned over the surface of the medium while a lens-coupled CCD detects the transmitted light. Using such a "noncontact" method, it is possible to avoid many of the technical difficulties which arise due to fiber-sample interactions [5,6,7,8]. In addition, extremely large data sets of approximately 10 8 − 10 10 measurements can readily be obtained. Data sets of this size have the potential to vastly improve the quality of reconstructed images in OT.The reconstruction of images from large data sets is an extremely challenging problem due to the high computational complexity of numerical approaches to the inverse problem in OT. To address this challenge, we have developed analytic methods to solve the inverse problem [9,11,12]. These methods lead to a dramatic reduction in computational complexity and have been applied in numerical simulations to data sets as large as 10 10 measurements [11]. In this Letter, we report the first experimental test of an analytic image reconstruction method. By employing a noncontact OT system with 10 8 sourcedetector pairs, we reconstruct the optical absorption of a highly-scattering medium. The results demonstrate the feasibility of image reconstruction for OT with large data sets.We begin by considering the propagation of diffuse light. The density of electromagnetic energy u(r) in an absorbing medium obeys the diffusion equationwhere α(r) is the absorption coefficient, S(r) is the power density of a continuous wave source, and D is the diffusion constant. The energy density also obeys the boundary condition u + ℓn · ∇u = 0 on the surface bounding the medium, wheren is the unit outward normal and ℓ is the extrapolation length [10]. The relative intensity measured by a point detector at r 2 due to a point source at r 1 is given, within the accuracy of the first Rytov approximation, by the integral equationwhere the source and detector are oriented in the inward and outward normal directions, respectively [12].Here δα(r) = α...

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large, but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the STM tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.