Electromagnetic scattering and induction models for spheroidal geometries

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Vita.Includes bibliographical references (p. 271-280).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Electromagnetic scattering from a medium containing randomly distributed discrete dielectric spheroidal inclusions is studied. Also, the broadband magnetoquasistatic solution for the induced magnetic field from a conducting and permeable spheroid under time harmonic excitation is demonstrated. Analytical electromagnetic solutions for spheroidal geometries are desirable because of their versatility in modeling manmade and natural shapes includ- ing solid and hollow needles, spheres, and disks, while at the same time possessing analytic solutions. Coherent scattering from a collection of small dielectric spheroids populating a dense medium is compared to scattering from a homogeneous sphere. A Method of Moments (MoM) solution is adopted which accounts for spheroid-spheroid interactions directly. Coherent scattering results from these collections are compared to Mie scattering and the effective permittivity of the dense medium is obtained. Results are in good agreement to the classical mixing formula and this lends credibility to both models. In order to reduce memory requirements and computational complexity, the Sparse Matrix/Canonical Grid (SMCG) method is applied to 3-D dense media scattering. By approximating the dyadic Green's function about a canonical rectilinear grid, weak interaction between spheroid far apart may be quickly approximated. Strong interactions between dielectric spheroid in close proximity are still calculated directly. Weak interactions are quickly evaluated using a novel multilevel block-Toeplitz matrix vector multiply based on the Fast Fourier Transform.(cont.) Electromagnetic induction (EMI) models of conducting and permeable spheroids under time harmonic excitation are refined to produce the broadband response with high dependability. A hybrid method is constructed consisting of three different approaches: 1) at low frequencies, the formally exact (but truncated) solution is applied, 2) at moderate frequencies, asymptotic expansions of the spheroidal wave functions (SWFs) are employed, 3) and at high, but still magnetoquasistatic, frequencies, a Small Penetration Approximation is borrowed. The combined EMI response is accurate except near a switchover point where there is typically less than a two percent error. Results are compared to data from a set of 17 steel and aluminum machined spheroids taken by the GEM-3 instrument and found to be in excellent agreement. Asymptotic expressions of the SWFs are found to depend on branch points and associated characteristic eigenvalues of the spheroidal wave equation. These branch points are found using polynomial estimation techniques and a quadruple precision Newton-Rhapson search method. Branch points for (n - m) =/< 100 are found in greater accuracy than previously available and many are tabulated in this thesis. The solution for the induced magnetic field from multiple permeable and conducting spheroidal objects in close proximity under time harmonic excitation is presented. Interactions between spheroids is accounted for by a interspheroidal modal interaction matrix. This multibody solution may provide the basis for a forward model used by inversion routines designed to detect and discriminate UXO. Specifically, this multibody solution may help to isolate non-UXO clutter from actual UXO in the field.by Benjamin Earl Barrowes.Ph.D

Joint Diagonalization Applied to the Detection and Discrimination of Unexploded Ordnance

Efforts to discriminate buried unexploded ordnance from harmless surrounding clutter are often hampered by the uncertainty in the number of buried targets that produce a given detected signal. We present a technique that helps determine that number with no need for data inversion. The procedure is based on the joint diagonalization of a set of multistatic response (MSR) matrices measured at different time gates by a time-domain electromagnetic induction sensor. In particular, we consider the Naval Research Laboratory’s Time-Domain Electromagnetic Multisensor Towed Array Detection System (TEMTADS), which consists of a 5×5 square grid of concentric transmitter/receiver pairs. The diagonalization process itself generalizes one of the standard procedures for extracting the eigenvalues of a single matrix; in terms of execution time, it is comparable to diagonalizing the matrices one by one. We present the method, discuss and illustrate its mathematical basis and physical meaning, and apply it to several actual measurements carried out with TEMTADS at a test stand and in the field at the former Camp Butner in North Carolina. We find that each target in a measurement is associated with a set of nonzero time-dependent MSR eigenvalues (usually three), which enables estimation of the number of targets interrogated. These eigenvalues have a characteristic shape as a function of time that does not change with the location and orientation of the target relative to the sensor. We justify analytically and empirically that symmetric targets have pairs of eigenvalues with constant ratios between them

Radar Cross Section Dependence on Wind Speed and Wave Slope

Abstract-YSCAT was an ultrawideband (2-20 GHz), near constant beam.width scatterometer intended to provide radar cross section (Ole.) measurements at varying radar and environmental parameters. YSCAT was deployed on the CCIW (Canada Centre for Inland Waters) tower on Lake Ontario for a period of six months from June to November, 1994. Using YSCAT data, this paper reports 1) observance of a low wind-speed cutoff\u27\u27, the fall-off of u o which occurs at low wind speeds, and 2) the results of fitting a Rayleigh/2-component lognormal probability distribution to the observed backscattered power measurements at C-band (5 GHz) and Xband (10 GHz). The observed characteristic trends of the fitted pdf model parameters verses wind speed and wave slope are shown. and discussed

The Dependance of Radar Backscatter from Dominant Wavelength Water Waves

Radar backscatter characteristics of sea surfaces depend on many difficult to describe parameters. These parameters include wind speed, incidence angle of the scatterometer, wind direction, frequency used, height of the instrument above the water, footprint size, and the underlying tilt of the waves themselves among others. An ultrawideband scatterometer named YSCAT94 gathered six months of data while deployed at the Canada Center for Inland Waters (CCIW) research platform in Lake Ontario. The backscatter distributions for small footprint scatterometers like YSCAT94 depend on the dominant wavelength of the sea. This paper gives a brief overview of the YSCAT94 instrument and then details the probability model which relates dominant wave slope to backscatter returns. The method used to calculate the dominant wave slope from YSCAT94 data is then presented followed by a conclusion and future directions