Ali Yapar

On the scattering of electromagnetic waves by bodies buried in a half-space with locally rough interface

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Greens function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Greens function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.

Inverse scattering for an impedance cylinder buried in a dielectric cylinder

An inverse scattering problem is considered for arbitrarily shaped cylindrical objects that have inhomogeneous impedance boundaries and are buried in arbitrarily shaped cylindrical dielectrics. Given the shapes of the impedance object and the dielectric, the inverse problem consists of reconstructing the inhomogeneous boundary impedance from a measured far field pattern for an incident time-harmonic plane wave. Extending the approach suggested by Akduman and Kress [Direct and inverse scattering problems for inhomogeneous impedance cylinders of arbitrary shape. Radio Sci. 38 (2003), pp. 1055–1064] for an impedance cylinder in an homogeneous background medium, both the direct and the inverse scattering problem are solved via boundary integral equations. For the inverse problem, representing the scattered field as a potential leads to severely ill-posed linear integral equations of the first kind for the densities. For their stable numerical solution Tikhonov regularization is employed. Knowing the scattered field, the boundary impedance function can be obtained from the boundary condition either by direct evaluation or by a least squares approach. We provide a mathematical foundation of the inverse method and illustrate its feasibility by numerical examples.

Detecting and Locating Dielectric Objects Buried Under a Rough Interface

We present a method to detect and locate dielectric objects buried under a rough surface. The method is based on the determination of appearing surface impedance of the half-space, where the dielectric objects are located. The equivalent surface impedance is obtained directly from the impedance boundary condition, which requires the knowledge of the electric field and its normal derivative on the surface. These field values are obtained by measuring the far-field data and using single-layer-potential representation of the scattered field. Using the equivalent surface impedance, one can detect and locate the buried objects. The efficiency and efficacy of the method are tested via numerical simulations

Iterative reconstruction of dielectric rough surface profiles at fixed frequency

A new, simple and fast method is presented for determining the location and the shape of a one-dimensional rough interface between two lossy dielectric half-spaces. The reconstruction is obtained from a set of reflected field measurements for a single illumination by a plane wave at a fixed frequency. Through a special representation of the scattered field in the half-spaces above and below the interface in terms of a Fourier transform and a Taylor expansion the problem is first reduced to the solution of a system of two nonlinear operator equations. Then this system is solved iteratively by alternating between a linear equation for a spectral coefficient of the scattered wave and a linearization of a nonlinear equation for the surface profile. The numerical simulations show that the method yields satisfactory reconstructions for slightly rough surface profiles.

3-D Imaging of Inhomogeneous Materials Loaded in a Rectangular Waveguide

A Newton-type method for the reconstruction of inhomogeneous 3-D complex permittivity variation of arbitrary shaped materials loaded in a rectangular waveguide is presented. The problem is first formulated as a system of integral equations consist of the well-known data and object equations, which contain the dyadic Greens function of an empty rectangular waveguide. Two unknowns of this system are solved in an iterative fashion by linearizing one of them, i.e., the data equation in the sense of the Newton method, which corresponds to a first-order Taylor expansion of the related integral operator. Since the problem is severely ill posed by nature, a regularization in the sense of Tikhonov is applied to the data equation. A detailed numerical implementation of the method, together with some numerical examples are also given to show the capabilities and validation limits of the method.

A Nonlinear Microwave Breast Cancer Imaging Approach Through Realistic Body–Breast Modeling

A nonlinear microwave tomography approach which suggests monitoring of differences inside the breast with respect to a reference breast model that adequately represents the healthy breast is presented. This approach simplifies the breast cancer imaging problem through realistic modeling of the body-breast configuration and does not require the imaging of the entire breast tissues. The tumor is considered as a buried object inside the breast which is assumed to be located on the interface of two-half spaces media composed of air or a coupling liquid and the chest wall or the base of the bed on which patient lies in a prone position. Then, the tumor, as well as the deviations of the actual breast from the breast model, is imaged by using the contrast source inversion method at a single frequency. The Greens function of the inhomogeneous background required in the application of the inversion algorithm is obtained through the buried object approach and accelerated by an adaptation of the discrete complex images method. Through the simulations it has been shown that, the proposed modeling and nonlinear inversion algorithm is capable of reconstructing tumors as small as 4 mm in radius for 3-D scenarios.

One-dimensional profile inversion of a cylindrical Layer with inhomogeneous impedance boundary: a Newton-type iterative solution

A method to reconstruct the one-dimensional profile of a cylindrical layer with an inhomogeneous impedance boundary is proposed. Through the finite Fourier transformation of the field expressions the problem is first reduced to the solutions of a two-coupled system of operator equations which is solved iteratively starting from an initial estimate of the profile. The reconstruction of the profile is achieved by linearizing one of the equations in the Newton sense. The method is tested by considering several numerical examples and yields satisfactory reconstructions. As is typical for Newton-type methods, the convergence of the iteration depends on the initial guess.

Higher Order Inhomogeneous Impedance Boundary Conditions for Perfectly Conducting Objects

A new, simple, and fast method for the solution of electromagnetic scattering problems for perfectly conducting objects of arbitrary shape is presented. The method is based on an equivalent representation of the conducting object in terms of a circular one having a higher order impedance boundary condition on its surface. As a first result, a new universal relation between the higher order surface impedances and the shape of the object is obtained. Then, by taking advantage of this relationship, the scattering problem related to a conducting object is recast as the solution of a matrix equation whose coefficients are determined from the higher order impedances. Numerical simulations show that the method yields to accurate results, and that, it is computationally effective

A Newton method for the reconstruction of perfectly conducting slightly rough surface profiles

A new method for the reconstruction of a one-dimensional profile of a perfectly conducting rough surface illuminated by a plane wave at a fixed frequency is addressed. By a special representation of the scattered electric field, the total field in the half-space over the surface is obtained from the measured data, which leads to a nonlinear equation with a surface function as unknown. The nonlinear equation is solved iteratively via the Newton method and a regularization in the least square sense. Numerical simulations show that the method yields satisfactory reconstructions for slightly rough surface profiles.

Electromagnetic Scattering by Radially Inhomogeneous Dielectric Spheres

A method to determine the electric field scattered by a dielectric sphere with a permittivity and conductivity varying only in the radial direction is presented. In order to take advantage of the spherically symmetrical geometry, the interior electric field is expanded in terms of vector spherical harmonics which are orthogonal over a spherical surface. Using the orthogonality of those functions with the vector wave functions in the expanded form of the free space dyadic Greens function, one can reduce the three-dimensional (3-D) electric field integral equation into a system of one-dimensional (1-D) integral equations. The scalar coefficients of the series expansion for the interior electric field are then obtained by solving this system of equations. For the medium outside the sphere, the scattered field is evaluated through the same procedure. Comparisons with alternative methods for specific cases demonstrate that the method is reliable in determining the interior field and the scattered field, for spherical objects with layered or continuously varying radial profile.