Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.Comment: 61 pages, 5 figure

Retrieval of equivalent currents by the use of an integral representation and the extinction theorem --- radome applications

The aim of this thesis is to solve an inverse source problem. The approach is based on an integral representation together with the extinction theorem. Both a scalar and a full-wave integral representation are implemented and solved by a Method of Moment procedure. The body of revolution enables usage of a Fourier transform to reduce the dimensions of the problem. A singular value decomposition is utilized to suppress singular values in the inversion process. A nose-cone radome is diagnosed by recreating the equivalent surface currents on its surface from measured near fields. It is shown how the radome interacts with the field, creating beam deflection, pattern distortion, etc. The phase shift of the field due to the transmission through the radome, i.e., the insertion phase delay, is visualized. Disturbances due to defects, not detectable in the measured near field, are correctly localized by the equivalent surface currents. The alteration of side and flash lobes, together with the introduction of scattering due to the defects, are also visualized. Verification is made by comparison between the calculated and measured far field

Regularization Methods in Banach Spaces applied to Inverse Medium Scattering Problems

This work handles inverse scattering problems for both acoustic and electromagnetic waves. That is to reconstruct the irradiated media from measurements of the scattered felds by regularization methods. As a particular feature, the contrasts of the scattering objects are assumed to be supported within a small region, hence called sparse. To apply sparsity regularization schemes it becomes crucial to model the problems in Banach spaces. Traditionally, they are given in a Hilbert space setting, such that reformulation in an L p-sense becomes a key point. Contrasts are linked to the data by forward operators, basing on beforehand stated solution operators and their continuity properties. Thereby, appropriate regularization techniques providing sparsity are given. As the case of scalar-valued contrast functions is already covered in the literature, mainly inverse scattering problems for anisotropic media are shown. In the case where electromagnetic waves are considered, a distinction is made between magnetic and non-magnetic media, since the latter is less complex. Finally, the case of inverse acoustic backscattering is handled, which is rarely seen in literature

Two- Dimensional Inverse Scattering Problems of PEC and Mixed Boundary Scatterers

Ph.DDOCTOR OF PHILOSOPH

Recent Topics in Electromagnetic Compatibility

Recent Topics in Electromagnetic Compatability discusses several topics in electromagnetic compatibility (EMC) and electromagnetic interference (EMI), including measurements, shielding, emission, interference, biomedical devices, and numerical modeling. Over five sections, chapters address the electromagnetic spectrum of corona discharge, life cycle assessment of flexible electromagnetic shields, EMC requirements for implantable medical devices, analysis and design of absorbers for EMC applications, artificial surfaces, and media for EMC and EMI shielding, and much more

Super-resolution in recovering embedded electromagnetic sources in high contrast media

The purpose of this work is to provide a rigorous mathematical analysis of the expected super-resolution phenomenon in the time-reversal imaging of electromagnetic (EM) radiating sources embedded in a high contrast medium. It is known that the resolution limit is essentially determined by the sharpness of the imaginary part of the EM Green's tensor for the associated background. We first establish the close connection between the resolution and the material parameters and the resolvent of the electric integral operator, via the Lippmann-Schwinger representation formula. We then present an insightful characterization of the spectral structure of the integral operator for a general bounded domain and derive the pole-pencil decomposition of its resolvent in the high contrast regime. For the special case of a spherical domain, we provide some quantitative asymptotic behavior of the eigenvalues and eigenfunctions. These mathematical findings shall enable us to provide a concise and rigorous illustration of the super-resolution in the EM source reconstruction in high contrast media. Some numerical examples are also presented to verify our main theoretical results.Comment: 31 pages, 6 figure

Unique Determination of the Shape of a Scattering Screen from a Passive Measurement

We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely, the obstacle is restricted to a two-dimensional plane and interacting with an arbitrary incident wave, it scatters acoustic waves to three-dimensional space. The model is particularly relevant in the study and design of reflecting sonars and antennas, cases where one cannot assume that the incident wave is a plane wave. Our main result is that given the plane where the screen is located, the far-field pattern produced by any single arbitrary incident wave determines the exact shape of the screen, as long as it is not antisymmetric with respect to the plane. This holds even for screens whose shape is an arbitrary simply connected smooth domain. This is in contrast to earlier work where the incident wave had to be a plane wave, or more recent work where only polygonal scatterers are determined.Peer reviewe

Image and conductivity reconstruction of a variable conducting cylinder in a half-space

[[abstract]]In this paper we address an inverse scattering problem whose aim is to determine the geometrical and the physical properties of a variable conducting cylindrical body buried in a half-space. The variable conductivity boundary leads to a mathematically ill-posed nonlinear equation. To overcome this difficulty, the attained system of nonlinear integral equations is reformulated into an optimization problem and solved by using the genetic algorithm. The genetic algorithm is employed to search the global extreme of the object function, such that the shape and the variable conductivity of the scatterer can be reconstructed. Even when the initial guess is far away from the exact one, the genetic algorithm can avoid the local extreme and attain to a global extreme solution sucessfully. In such a case, the gradient-based methods often get stuck in a local extreme. It is found that multiple incident waves from different directions permit good reconstruction of the shape and, to a lesser extent, the conductivity in the presence of noise for the measured data. Numerical results are given to show the effectiveness of the genetic algorithm.[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]紙