Forward and inverse studies for optical image reconstruction

This dissertation is devoted to both forward and inverse studies for optical image reconstruction. This work contain four major contributions.; First, analytical solutions of excitation photon density waves (EPDWs) and fluorescent photon density waves (FPDWs) in a spherically multi-layer turbid medium are investigated. The geometry and dimension chosen are intended to represent multilayer tissue structures such as a breast or a head containing a tumor. The aim of this study is to investigate the potential sensitivity of an optical imaging system to an embedded object, without and with fluorescence.; Secondly, a fast and efficient multigrid finite difference method (MGFD) has been developed to solve the diffusion equation for light propagation in tissue. Simulation results with homogeneous test media show that our multigrid algorithm can obtain very accurate solution (as compared to the analytical solution) for both weak and strong discontinuous media.; Thirdly, a Born iterative method has been developed based on the integral form of the wave equation for photon density waves. The forward solution is obtained with the MGFD method and the inverse solution is obtained by a regularized least squares (RLS) method. Our results show that quite accurate reconstructions can be obtained from full-angle as well as limited angle measurement data. The results are significantly better than one step Born approximation.; Finally, more general Born-type and Rytov-type inverse algorithms have been developed based on the integral form of the diffusion equation. The Born-type iterative method is used to reconstruct "pathologies" embedded in an inhomogeneous test medium simulating a normal female breast. The test medium is constructed by assigning optical coefficients according to a MR derived anatomical map. The finite element method is employed as the forward solver, while a RLS method is used as the inverse solution. This algorithm is computationally practical and can yield qualitatively and quantitatively correct absorption and scattering distributions of embedded objects.