"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 Newton'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, Newton'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.
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU