Ibrahim Akduman

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.

Electrostatic imaging via conformal mapping

We present the solution of an inverse boundary value problem for harmonic functions arising in electrostatic imaging through conformal mapping techniques. The numerical method consists of two parts. In a first step, by successive approximations a nonlinear equation is solved to determine the boundary values of a holomorphic function on the outer boundary circle of an annulus. Then in a second step an ill-posed Cauchy problem is solved to determine the holomorphic function in the annulus. The method extends and modifies an earlier analysis of Idemen and Akduman (Idemen M and Akduman I 1988 SIAM J. Appl. Math. 48 703–18). We establish a convergence result for the iteration procedure and through numerical examples we illustrate the feasibility of the method.

An Efficient Nonlinear Imaging Approach for Dielectric Objects Buried Under a Rough Surface

A nonlinear tomographic approach for microwave imaging of dielectrics buried under a rough surface is presented. It has been made possible to efficiently apply the contrast-source-inversion method, which is proven to be one of the most successful nonlinear inversion techniques when the Greens function of the background medium is available, to the given imaging problem. This has been achieved through the application of the buried object approach (BOA) which enables the calculation of the Greens function of layered media with rough interfaces by considering the roughness as a series of objects located alternately on both sides of a planar interface between two half spaces. Furthermore, the calculation of the Greens function of the two-layered medium with a planar interface required in the BOA has been accelerated through an adaptation of the two-level discrete complex image method. By making use of the strength of nonlinear inversion and fast and accurate computation of the Greens function of the layered media with rough interface, superior results have been achieved in a feasible computational time for dielectrics having constitutive parameters in a considerably wide range even if they are inhomogeneous or buried under substantially large rough surfaces.

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.

MODIFIED DIRECTIONAL WIDE BAND PRINTED MONOPOLE ANTENNA FOR USE IN RADAR AND MICROWAVE IMAGING APPLICATIONS

This paper presents a modifled design of directional monopole antenna with parabolic-shaped ground plane. To increase the directivity, axis of parabola in the ground plane is rotated 45 degrees (in comparison with the previous antenna) to extend throughout the direction of the substrates diagonal. Consequently, vertex of the parabola is placed at the optimum point in the corner of the substrate. The aim of this attempt is to design an extended and symmetrical ground plane around the patch, with more clarity, to maximize its capability as a re∞ector. Directivity is further improved by inserting parabolic-shaped slots at the corners of the ground plane. Simulation and measurements show that the proposed antenna has stable directional radiation pattern and higher gain compared to the previous directional monopole antennas. Impedance bandwidth of the antenna covers the frequency range of 4{9GHz. Measured HPBW is among the degrees 54{22 between 4 and 9GHz. Gain and HPBW of the antenna are improved 1.3{3.1dB and 5{15 degrees, respectively among the bandwidth in comparison with previous antenna. Results conflrm the good characteristics of the antenna for use in microwave imaging, where high resolution is required.

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.

Qualitative Microwave Imaging With Scattering Parameters Measurements

Microwave imaging (MWI) systems extensively employ vector network analyzers for microwave measurements due to their high availability and accuracy. This is in contrast to theoretical models, which are naturally formulated in terms of scattered electric field vectors. Accordingly, experimental verification of MWI methods requires an intermediate step where measured scattering parameters are converted to scattered electric fields. In parallel to recent research, which formulates the Born iterative method in terms of scattering parameters, we develop formulations of two closely related qualitative inverse scattering methods-the linear sampling method and the factorization method-directly in terms of scattering parameters to avoid the intermediate conversion step. To this aim, we introduce vector S-parameters and we extend the vector Greens function for S-parameters to the dyadic case. There are certain advantages of these formulations over their electric field counterparts. First of all, the resulting formulations inherently incorporate the antenna radiation characteristics. Moreover, they reduce the measurement time since they do not require any pre- or post-measurement process. We experimentally verified the presented novel formulations against multi-frequency measurements performed inside an anechoic chamber. Obtained results show that the proposed methodologies can accurately reconstruct the shape of the targets by directly exploiting multifrequency measurements in the imaging process.