Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering

First Advisor

Peter J. Collins, PhD


Diffusing photons can be used to detect and localize optical inhomogeneities embedded in turbid media such as clouds, fog, paint and human tissue. This thesis shows that a transfer function derived from an analytic solution of the Helmholtz equation can completely characterize in three dimensions the perturbations in the forward propagation phenomena caused by a spherical defect object in a multiple-scattering medium. Two models of the forward propagation behavior of diffuse photon density waves in homogeneous, infinite, turbid media that contains a spherical inhomogeneity are examined. The first model is an exact analytic solution based on a modal expansion in spherical harmonics. The second model uses Fourier optics theory for wave propagation in a plane through homogeneous turbid media containing a spherical lens. The Fourier optics model is found to be a good approximation to the exact analytic solution when the optical absorptive contrast of the inhomogeneity and the surrounding media is weakly perturbative, and the detector is not near the inhomogeneity. Using linear system theory, a transfer function from the analytic model is derived. This function improves the Fourier optics model by replacing the spherical lens approximation with an exact representation of the system perturbation behavior. The transfer function is shown through simulation to completely characterize the sensitivity of the system to detect and localize in three dimensions inhomogeneities of varying optical contrast with the surrounding media.

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