Title:  Numerical Methods for Computing the Modal Decomposition of the Magnetic Polarizability of Conducting Objects

Committee:

Dr. Waymond Scott, ECE, Chair , Advisor

Dr. Andrew Peterson, ECE

Dr. Gregory Durgin, ECE

Dr. Morris Cohen, ECE

Dr. Michael Lacey, Math

Abstract:

This thesis presents numerical methods for characterizing the wideband responses of conducting objects to excitation by electromagnetic induction (EMI) sensors. These sensors operate by exciting eddy currents in conducting media, and detecting the scattered fields that the eddy currents induce. EMI sensors can be used to measure the magnetic polarizability tensor (MPT) of conducting targets, which encapsulates the entire scattering interaction between target and sensor. Wideband characterization of the magnetic polarizability tensor (MPT) can be achieved by expanding the frequency response in pole-expansion form. The pole-expansion coefficients can be used as a signature, which can then be used for subsurface detection. These coefficients are valuable for target detection because they do not depend on the positioning of the target relative to the sensor, or on the specific measurement frequencies, and can be trivially scaled to represent a larger family of targets. In this work, both integral and differential methods are developed for modeling different types of targets, including rotationally symmetric targets and thin conducting sheets. The interaction between sensor and target is modeled as a linear system, which can then be set up as a generalized eigenvalue problem. The eigenvalues of the system correspond to the pole locations of the pole expansion. The remaining coefficients can be derived from the eigenvectors of the system, which correspond to the eddy current modes that are excited by the sensor.