Edwin A. Marengo

A New Theory for Analysis and Synthesis of Time-Dependent Scalar and Electromagnetic Sources and Fields

August 26, 1997
1:00 PM
406 Egan

Abstract:

This thesis contains a new frequency domain/time domain theoretical framework to treat direct and inverse problems of interest in acoustics and electromagnetics. We derive and explore {bf 1)} a new theory for analysis and characterization of scalar ultrawideband volume (three-dimensional) sources and the fields they radiate, {bf 2)} a new limited view Radon inversion framework to source inversion (synthesis) of scalar and electromagnetic sources from time domain far field data and {bf 3)} a new multipole expansion of the electromagnetic field in the time domain. The first aspect enumerated above has to do with the analysis problem (e.g., the radiation problem) while the second has to do with the inverse source problem. The third and final aspect provides a new (time domain) multipole expansion of electromagnetic radiation fields of interest in both direct and inverse source problems.

The class of sources considered in {bf (1)} are the time domain analog of time-harmonic three-dimensional phased arrays of isotropic, non-dispersive point radiators. Sources of this class are shown to radiate short duration/high amplitude pulses in the vicinity of the main beam direction and long duration/low amplitude pulses away from the main beam direction. By studying this particular class of sources we provide insight into the role of the space-time structure of a source on its radiation performance (and, in particular, in generating well-collimated radiation when excited by transient signals.)

The second component of the present investigation explores the inverse source problem for deterministic, time-dependent scalar and electromagnetic sources and fields based on full and limited view data of the (far field) time domain radiation pattern generated by the source. We treat the inverse source problem using a limited view Radon inversion framework in space-time domain which leads, in analogy with the limited view computed tomography (CT) reconstruction problem, to a "filtered backprojection"-like solution to the inverse source problem. Our source inversion formulation gives the minimum energy source consistent with time domain far field data provided over a continuum or discrete set of observation directions. The work reported here constitutes the first formulation of the inverse source problem using a limited view Radon inversion framework in space-time domain. The concluding section of Chapter 4 also contains new theorems on radiating and nonradiating sources relevant to both radiation and inverse source problems.

The third portion of this investigation provides a new time domain multipole theory for electromagnetic fields. Potential applications of the new expansion include time domain near field scanning of antennas and scatterers and time domain antenna characterization, among others. This thesis also contains new theorems on monochromatic radiating and nonradiating scalar sources and the fields they generate of interest in both radiation and inverse source problems. The theorems in question give light into the properties of radiating and nonradiating sources and the fields they generate. They are addressed from the points of view of both the direct and the inverse source problem to the inhomogeneous Helmholtz equation, thereby having close connection with other portions of the present investigation.

Thesis Committee:
Prof. Anthony J. Devaney (Advisor)
Prof. Philip Serafin
Prof. Carey Rappaport
Prof. Eric L. Miller