The simulation of light transport in highly scattering media under realistic conditions is a prerequisite for solving the inverse problem in optical tomography. In this contribution we study both theoretically and experimentally the transport of photons in highly scattering media following the injection of ultrashort laser pulses. The diffusion equation has been integrated by a two-dimensional Finite Element Method (FEM). For comparison with FEM results, time-resolved transmittance was measured in a way to effectively simulate a two-dimensional geometry. For the reconstruction of the interior structure an iterative method based on the FEM forward model will be introduced. Using the full information contained in the time-resolved measurements, the number of sources and detectors necessary for reconstructing inhomogeneities in optical properties can be considerably reduced. The effectiveness of the algorithm will be demonstrated by some instructive examples.

As mathematical model for the light propagation in highly scattering media the diffusion equation for the photon density is used. The solution of the forward problem obtained by the Finite Element Method (FEM) is compared with the analytical solution in a rectangle homogeneous domain. The application of a numerical method as the FEM allows to take into account different geometries and various embedded objects. For the inverse imaging problem two reconstruction methods are introduced acting as iterative algorithms based on the FEM forward model. As cost function the 12-norm of output flux differences for a selected combination of times, detector and source positions is used. The effectiveness of the image reconstruction method is demonstrated by some instructive examples.

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