N. Fredette, “Imaging Heterogeneous Objects Using Transport Theory and Newton’s Method”, M.S. Thesis, Nuclear Engineering, Texas A&M University, College Station, TX (2012).
This thesis explores the inverse problem of optical tomography applied to two-dimensional heterogeneous domains. The neutral particle transport equation was used as the forward model to simulate how neutral particles stream through and interact within these heterogeneous domains. A constrained optimization technique that uses Newton1″s method served as the basis of the inverse problem. The capabilities and limitations of the presented method were explored through various two-dimensional domains. The major factors that influenced the ability of the optimization method to reconstruct the cross sections of these domains included the locations of the sources used to illuminate the domains, the number of separate experiments used in the reconstruction, the locations where measurements were collected, the optical thickness of the domain, the amount of signal noise and signal bias applied to the measurements, and the initial guess for the cross section distribution. All of these factors were explored for problems with and without scattering. Increasing the number of sources, measurements and experiments used in the reconstruction generally produced more successful reconstructions with less error. Using more sources, experiments and measurements also allowed for optically thicker domains to be reconstructed. The maximum optical thickness that could be reconstructed with this method was ten mean free paths for pure absorber domains and two mean free paths for domains with scattering. Applying signal noise and signal bias to the measured fluxes produced more error in the reconstructed image. Generally, Newton1″s method was more successful at reconstructing domains from an initial guess for the cross sections that was greater in magnitude than their true values than from an initial guess that was lower in magnitude.