Methods in wave propagation and scattering

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Vita.Includes bibliographical references (p. 195-213).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Aspects of wave propagation and scattering with an emphasis on specific applications in engineering and physics are examined. Frequency-domain methods prevail. Both forward and inverse problems are considered. Typical applications of the method of moments to rough surface three-dimensional (3-D) electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave. It is shown how such wave can be constructed as a superposition of plane waves, avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence. The proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a wave that is optimal in a least squared error sense. Issues in the application to 3-D scattering from an object over a rough surface are discussed. Approximate 3-D scalar and vector tapered waves are derived which can be evaluated without resorting to any numerical integrations. Important limitations to the accuracy and applicability of these approximations are pointed out. An analytical solution is presented for the electromagnetic induction problem of magnetic diffusion into and scattering from a permeable, highly but not perfectly conducting prolate spheroid under axial excitation, expressed in terms of an infinite matrix equation. The spheroid is assumed to be embedded in a homogeneous non-conducting medium as appropriate for low-frequency, high-contrast scattering governed by magnetoquasistatics. The solution is based on separation of variables and matching boundary conditions where the prolate spheroidal wavefunctions with complex wavenumber parameter are expanded in terms of spherical harmonics. For small skin depths, an approximate solution is constructed, which avoids any reference to the spheroidal wavefunctions. The problem of long spheroids and long circular cylinders is solved by using an infinite cylinder approximation. In some cases, our ability to evaluate the spheroidal wavefunctions breaks down at intermediate frequencies. To deal with this, a general broadband rational function approximation technique is developed and demonstrated. We treat special cases and provide numerical reference data for the induced magnetic dipole moment or, equivalently, the magnetic polarizability factor. The magnetoquasistatic response of a distribution of an arbitrary number of interacting small conducting and permeable objects is also investigated. Useful formulations are provided for expressing the magnetic dipole moment of conducting and permeable objects of general shape. An alternative to Tikhonov regularization for deblurring and inverse diffraction, based on a local extrapolation scheme, is described, analyzed, and illustrated numerically for the cases of continuation of fields obeying Laplace and Helmholtz equations. At the outset of the development, a special deconvolution problem, where a parameter describes the degree of additive blurring, is considered. No a priori knowledge on the unblurred data is assumed. A standard solution based on an output least squares formulation includes a regularization parameter into a linear, shift-invariant filter. The proposed alternative approach takes advantage of the analyticity of the smoothing process with respect to the blurring parameter. Here a simple local extrapolation scheme is employed. The problem is encountered in applications involving potential theories dealing with magnetostatics, electrostatics, and gravity data. As a generalization to the dynamic case, inverse diffraction of scalar waves is considered. Examples are presented and the two methods compared numerically. The problem of inferring unknown geometry and material parameters of a waveguide model from noisy samples of the associated modal dispersion curves is considered. In a significant reduction of the complexity of a common inversion methodology, the inner of two nested iterations is eliminated: The approach described does not employ explicit fitting of the data to computed dispersion curves. Instead, the unknown parameters are adjusted to minimize a cost function derived directly from the determinant of the boundary condition system matrix. This results in a very efficient inversion scheme that, in the case of noise-free data, yields exact results. Multi-mode data can be simultaneously processed without extra complications. Furthermore, the inversion scheme can accommodate an arbitrary number of unknown parameters, provided that the data have sufficient sensitivity to these parameters. As an important application, the sonic guidance condition for a fluid-filled borehole in an elastic, homogeneous, and isotropic rock formation is considered for numerical forward and inverse dispersion analysis. The parametric inversion with uncertain model parameters and the influence of bandwidth and noise are investigated numerically. The cases of multi-frequency and multi-mode data are examined. Finally, the borehole leaky-wave modes are classified according to the location of the roots of the characteristic equation on a multi-sheeted Riemann surface. A comprehensive set of dipole leaky-wave modal dispersions is computed. In an independent numerical experiment the excitation of some of these modes is demonstrated. The utilization of leaky-wave dispersion data for inversion is discussed.by Henning Braunisch.Ph.D

Methods in wave propagation and scattering

Supervised by Jin A. Kong.Also issued as Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 195-213).by Henning Braunisch

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

Understanding the magnetic polarizability tensor

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects

Electromagnetic wave scattering by discrete random media with remote sensing applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (p. 171-182).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The scattering of electromagnetic waves in medium with randomly distributed discrete scatterers is studied. Analytical and numerical solutions to several problems with implications for the active and passive remote sensing of the Earth environment are obtained. The quasi-magnetostatic (QMS) solution for a conducting and permeable spheroid under arbitrary excitation is presented. The spheroid is surrounded by a weakly conducting background medium. The magnetic field inside the spheroid satisfies the vector wave equation, while the magnetic field outside can be expressed as the gradient of the Laplace solution. We solve this problem exactly using the separation of variables method in spheroidal coordinates by expanding the internal field in terms of vector spheroidal wavefunctions. The exact formulation works well for low to moderate frequencies; however, the solution breaks down at high frequency due to numerical difficulty in computing the spheroidal wavefunctions. To circumvent this difficulty, an approximate theory known as the small penetration-depth approximation (SPA) is developed. The SPA relates the internal field in terms of the external field by making use of the fact that at high frequency, the external field can only penetrate slightly into a thin skin layer below the surface of the spheroid. For spheroids with general permeability, the SPA works well at high frequency and complements the exact formulation. However, for high permeability, the SPA is found to give accurate broadband results. By neglecting mutual interactions, the QMS frequency response from a collection of conducting and permeable spheroids is also studied.(cont.) In a dense medium, the failure to properly take into account of multiple scattering effects could lead to significant errors. This has been demonstrated in the past from extensive theoretical, numerical, and experimental studies of electromagnetic wave scattering by densely packed dielectric spheres. Here, electromagnetic wave scattering by dense packed dielectric spheroids is studied both numerically through Monte Carlo simulations and analytically through the quasi-crystalline approximation (QCA) and QCA with coherent potential (QCA-CP). We assume that the spheroids are electrically small so that single-particle scattering is simple. In the numerical simulations, the Metropolis shuffling method is used to generate realizations of configurations for non-interpenetrable spheroids. The multiple scattering problem is formulated with the volume integral equation and solved using the method of moments with electrostatic basis functions. General expressions for the self-interaction elements are obtained using the low-frequency expansion of the dyadic Green's function, and radiative correction terms are included. Results of scattering coefficient, absorption coefficient, and scattering matrix for spheroids in random and aligned orientation configurations are presented. It is shown that independent scattering approximation can give grossly incorrect results when the fractional volume of the spheroids is appreciable.(cont.) In the analytical approach, only spheroids in the aligned configuration are solved. Low-frequency QCA and QCA-CP solutions are obtained for the average Green's function and the effective permittivity tensor. For QCA-CP, the low-frequency expansion of the uniaxial dyadic Green's function is required. The real parts of the effective permittivities from QCA and QCA-CP are compared with the Maxwell-Garnett mixing formula. ...by Chi On Ao.Ph.D

An Explicit Formula for the Magnetic Polarizability Tensor for Object Characterization

The magnetic polarizability tensor (MPT) has attracted considerable interest due to the possibility it offers for characterizing conducting objects and assisting with the identification and location of hidden targets in metal detection. An explicit formula for its calculation for arbitrary-shaped objects is missing in the electrical engineering literature. Furthermore, the circumstances for the validity of the magnetic dipole approximation of the perturbed field, induced by the presence of the object, are not fully understood. On the other hand, in the applied mathematics community, an asymptotic expansion of the perturbed magnetic field has been derived for small objects and a rigorous formula for the calculation of the MPT has been obtained. The purpose of this paper is to relate the results of the two communities, to provide a rigorous justification for the MPT, and to explain the situations in which the approximation is valid

Validation of Advanced EM Models for UXO Discrimination

The work reported here details basic validation of our advanced physics-based EMI forward and inverse models against data collected by the NRL TEMTADS system. The data was collected under laboratory-type conditions using both artificial spheroidal targets and real UXO. The artificial target models are essentially exact, and enable detailed comparison of theory and data in support of measurement platform characterization and target identification. Real UXO targets cannot be treated exactly, but it is demonstrated that quantitative comparisons of the data with the spheroid models nevertheless aids in extracting key target discrimination information, such as target geometry and hollow target shell thickness.Comment: 15 pages, 16 figure

Classification, identification, and modeling of unexploded ordnance in realistic environments

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 205-218).Recovery of buried unexploded ordnance (UXO) is very slow and expensive due to the high false alarm rate created by clutter. Electromagnetic induction (EMI) has been shown to be a promising technique for UXO detection and discrimination. This thesis uses the EMI response of buried targets to identify or classify them. To perform such discrimination, accurate forward models of buried UXO are needed. This thesis provides a survey of existing target models: the dipole model, the spheroid model, and the fundamental mode model. Then the implementation of a new model, the spheroidal mode model, is described and validated against measurements of a UXO. Furthermore, an in-depth study of the effects of permeable soil, modeled as a permeable half space, is presented. This study concludes that the discontinuity created by the air to permeable soil interface produces minimal effect in the response of a buried object. The change is limited to a magnitude shift of the real portion of the EMI response and can be reproduced by superposition of a permeable half space response on the response of the same object in frees pace. Accurate soil modeling also allows one to invert for soil permeability values from measured data if such data are in known units. However, the EMI sensor used in this study provides measurements in consistent but unknown units. Furthermore, the instrument is from a third party and is proprietary. Therefore, this thesis describes the development of a non-invasive method to model and calibrate non-adaptive instruments so that all measurements can be converted into units consistent with modeled data. This conversion factor is shown to be a constant value across various conditions, thus demonstrating its validity.(cont.) Given that now a more complete model of the measurable response of a buried UXO is implemented, this study proceeds to demonstrate that EMI responses from UXO and clutter objects can be used to identify the objects through the application of Differential Evolution (DE), a type of Genetic Algorithm. DE is used to optimize the parameters of the UXO fundamental mode model to produce a match between the modeled response and the measured response of an unknown object. When this optimization procedure is applied across a library of models for possible UXO, the correct identity of the unknown object can be ascertained because the corresponding library member will produce the closest match. Furthermore, responses from clutter objects are shown to produce very poor matches to library objects, thus providing a method to discriminate UXO from clutter. These optimization experiments are conducted on measurements of UXO in air, UXO in air but obscured by clutter fragments, buried UXO, and buried UXO obscured by clutter fragments. It is shown that the optimization procedure is successful for shallow buried objects obscured by light clutter contributing to roughly 20 dB SNR, but is limited in applicability towards very deeply buried UXO or those in dense clutter environments. The DE algorithm implemented in this study is parallelized and the optimization results are computed with a multi-processor supercomputer. Thus, the computational requirement of DE is a considerable drawback, and the method cannot be used for real time, on-site inversion of measured UXO data. To address this concern, a different approach to inversion is also implemented in this study. Rather than identifying particular UXO, one may do a discrimination between general UXO and general clutter items. Previous work has shown that the expansion coefficients of EMI responses in the spheroidal coordinate system can uniquely characterize the corresponding targets.(cont.) Therefore, these coefficients readily lend themselves for use as features by which objects can be classified as likely to be UXO or unlikely to be UXO. To do such classification, the relationship between these coefficients and the physical properties of UXO and clutter, such as differences in size or body-of-revolution properties or material heterogeneity properties, must be found. This thesis shows that such relationships are complex and require the use of the automated pattern recognition capability of machine learning. Two machine learning algorithms, Support Vector Machines and Neural Networks, are used to identify whether objects are likely to be UXO. Furthermore, the effects of small diffuse clutter fragments and uncertainty about the target position are investigated. This discrimination procedure is applied on both synthetic data from models and measurements of UXO and clutter. It is found that good discrimination is possible for up to 20 dB SNR. But the discrimination is sensitive to inaccurate estimations of a target's depth. It is found that the accuracy must be within a 10 cm deviation of an object's true depth. The general conclusion forwarded by this work is that while increasingly accurate discrimination capabilities can be produced through more detailed forward modeling and application of robust optimization and learning algorithms, the presence of noise and clutter is still of great concern. Minimization or filtering of such noise is necessary before field deployable discrimination techniques can be realized.by Beijia Zhang.Ph.D

Numerical methods for electromagnetic wave propagation and scattering in complex media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Vita.Includes bibliographical references (p. 227-242).Numerical methods are developed to study various applications in electromagnetic wave propagation and scattering. Analytical methods are used where possible to enhance the efficiency, accuracy, and applicability of the numerical methods. Electromagnetic induction (EMI) sensing is a popular technique to detect and discriminate buried unexploded ordnance (UXO). Time domain EMI sensing uses a transient primary magnetic field to induce currents within the UXO. These currents induce a secondary field that is measured and used to determine characteristics of the UXO. It is shown that the EMI response is difficult to calculate in early time when the skin depth is small. A new numerical method is developed to obtain an accurate and fast solution of the early time EMI response. The method is combined with the finite element method to provide the entire time domain response. The results are compared with analytical solutions and experimental data, and excellent agreement is obtained. A fast Method of Moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces. To facilitate the solution, the Forward Backward method with Spectral Acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. First, the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. Second, the accuracy, efficiency, and convergence of the method are studied for various rough surfaces and layer permittivities. The Finite Difference Time Domain (FDTD) method is used to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands.(cont.) The structure under study is the well-known periodic arrangement of rods and split-ring resonators, previously used in experimental setups. For the first time, the numerical results of this work show that fields propagating inside the metamaterial with a forward power direction exhibit a backward phase velocity and negative index of refraction. A new metamaterial design is presented that is less lossy than previous designs. The effects of numerical dispersion in the FDTD method are investigated for layered, anisotropic media. The numerical dispersion relation is derived for diagonally anisotropic media. The analysis is applied to minimize the numerical dispersion error of Huygens' plane wave sources in layered, uniaxial media. For usual discretization sizes, a typical reduction of the scattered field error on the order of 30 dB is demonstrated. The new FDTD method is then used to study the Angular Correlation Function (ACF) of the scattered fields from continuous random media with and without a target object present. The ACF is shown to be as much as 10 dB greater when a target object is present for situations where the target is undetectable by examination of the radar cross section only.by Christopher D. Moss.Ph.D

Identification of metallic objects using spectral magnetic polarizability tensor signatures: Object characterisation and invariants

The early detection of terrorist threat objects, such as guns and knives, through improved metal detection, has the potential to reduce the number of attacks and improve public safety and security. To achieve this, there is considerable potential to use the fields applied and measured by a metal detector to discriminate between different shapes and different metals since, hidden within the field perturbation, is object characterisation information. The magnetic polarizability tensor (MPT) offers an economical characterisation of metallic objects that can be computed for different threat and non-threat objects and has an established theoretical background, which shows that the induced voltage is a function of the hidden object's MPT coefficients. In this article, we describe the additional characterisation information that measurements of the induced voltage over a range of frequencies offer compared with measurements at a single frequency. We call such object characterisations its MPT spectral signature. Then, we present a series of alternative rotational invariants for the purpose of classifying hidden objects using MPT spectral signatures. Finally, we include examples of computed MPT spectral signature characterisations of realistic threat and non-threat objects that can be used to train machine learning algorithms for classification purposes