This study proposes a low-complexity permittivity estimation for ground penetrating radar applications based on a contrast source inversion (CSI) approach, assuming multilayered ground media. The homogeneity assumption for each background layer is used to address the ill-posed condition while maintaining accuracy for permittivity reconstruction, significantly reducing the number of unknowns. Using an appropriate initial guess for each layer, the post-CSI approach also provides the dielectric profile of a buried object. The finite difference time domain numerical tests show that the proposed approach significantly enhances reconstruction accuracy for buried objects compared with the traditional CSI approach.

A method to reconstruct the surface shape of a scatterer from the relative intensity of the scattered field is proposed. Reconstruction of the scatterer shape has been studied as an inverse problem. An approach that employs boundary-integral equations can determine the scatterer shape with low computation resources and high accuracy. In this method, the reconstruction process is performed so that the error between the measured far field of the sample and the computed far field of the estimated scatterer shape is minimized. The amplitude of the incident wave at the sample is required to compute the scattered field of the estimated shape. However, measurement of the incident wave at the sample (measurement without the sample) is inconvenient, particularly when the output power of the wave source is temporally unstable. In this study, we improve the reconstruction method with boundary-integral equations for practical use and expandability to various types of samples. First, we propose new boundary-integral equations that can reconstruct the sample shape from the relative intensity at a finite distance. The relative intensity is independent from the amplitude of the incident wave, and the reconstruction process can be performed without measuring the incident field. Second, the boundary integral equation for reconstruction is discretized with boundary elements. The boundary elements can flexibly discretize various shapes of samples, and this approach can be applied to various inverse scattering problems. In this paper, we present a few reconstruction processes in numerical simulations. Then, we discuss the reason for slow-convergence conditions and introduce a weighting coefficient to accelerate the convergence. The weighting coefficient depends on the distance between the sample and the observation points. Finally, we derive a formula to obtain an optimum weighting coefficient so that we can reconstruct the surface shape of a scatterer at various distances of the observation points.

Microwave ultra-wideband (UWB) radar systems are advantageous for their high-range resolution and ability to penetrate dielectric objects. Internal imaging of dielectric objects by UWB radar is a promising nondestructive method of testing aging roads and bridges and a noninvasive technique for human body examination. For these applications, we have already developed an accurate internal imaging approach based on the range points migration (RPM) method, combined with a method that efficiently estimates the dielectric constant. Although this approach accurately extracts the internal boundary, it is applicable only to highly conductive targets immersed in homogeneous dielectric media. It is not suitable for multi-layered dielectric structures such as human tissues or concrete objects. To remedy this limitation, we here propose a novel dielectric constant and boundary extraction method for double-layered materials. This new approach, which simply extends the Envelope method to boundary extraction of the inner layer, is evaluated in finite difference time domain (FDTD)-based simulations and laboratory experiments, assuming a double-layered concrete cylinder. These tests demonstrate that our proposed method accurately and simultaneously estimates the dielectric constants of both media and the layer boundaries.

A total-field/scattered-field (TF/SF) boundary for the constrained interpolation profile (CIP) method is proposed for multi-dimensional electromagnetic problems. Incident fields are added to or subtracted from update equations in order to satisfy advection equations into which Maxwell's equations are reduced by means of the directional splitting. Modified incident fields are introduced to take into account electromagnetic fields after advection. The developed TF/SF boundary is examined numerically, and the results show that it operates with good performance. Finally, we apply the proposed TF/SF boundary to a scattering problem, and it can be solved successfully.

An algorithm is formulated for reconstructing a dielectric cylinder with the use of the T-matrix and the singular value decomposition (SVD) and is discussed through numerical examples under noisy conditions. The algorithm consists of two stages. At the first stage the measured data of scattered waves is transformed into the T-matrix. At the second stage we reconstruct the cylinder from the T-matrix. The singular value decomposition is applied in order to separate the radiating and the nonradiating currents, and the radiating current is directly obtained from the T-matrix. The nonradiating current and the object are reconstructed by decreasing a residual error of the current in the least square approximation, where linear equations are solved repeatedly. Some techniques are used in order to reduce the calculation time and to reduce the effects of noise. Numerical examples show us that the presented approach is simple and numerically feasible, and enables us to reconstruct a large object in a short time.

An inverse scattering problem of estimating the reflection coefficient and the surface impedance from two sets of absolute values of the near field with periodic change is investigated. The problem is formulated in terms of a nonlinear simultaneous equations which is derived from the relation between the two sets of absolute values and the field defined by a finite summation of the modal functions by applying the Fourier analysis. The reflection coefficient is estimated by solving the equations by Newton's method through the successive algorithm with the increment of the number of truncation in the summation one after another. Numerical examples are given and the accuracy of the estimation is discussed.

In this paper, we propose a new technique for the scattering problems of multilayered inhomogeneous columnar dielectric gratings loaded rectangular dielectric constant both TM and TE waves using the combination of improved Fourier series expansion method, the multilayer method, and the eigenvalue matrix method. Numerical results are given for the power transmission coefficients in the parameters ε 3 /ε 0 , c/p, and b/d of rectangular cylinders to obtain the basic characteristic of the power transmission coefficients and reflection coefficients switching or frequency selective devices for both TM and TE waves. The influence of the incident angle and frequency of the transmitted power are also discussed in the connection with the propagation constant β in the free mode.

An inverse scattering problem of estimating the surface impedance for an inhomogeneous half-space is investigated. By virtue of the fact that the far field representation contains the spectral function of the scattered field, complex values of the function are estimated from a set of absolute values of the far field. An approximate function for the spectral function is reconstructed from the estimated complex values by the least-squares sense. The surface impedance is estimated through calculating the field on the surface of the half-space expressed by the inverse Fourier transform. Numerical examples are given and the accuracy of the estimation is discussed.

In this paper, a new method based on the mode-matching method in the sense of least squares is presented for analyzing the two dimensional scattering problem of TE plane wave incidence to the infinite plane surface with an arbitrary imperfection of finite extent. The semi-infinite upper and lower regions of that surface are a vacuum and a perfect conductor, respectively. Therefore the discussion of this paper is developed about the Dirichlet boundary value problem. In this method, the approximate scattered wave is represented by the integral transform with band-limited spectrum of plane waves. The boundary values of those scattered waves are described by only abscissa z and Fourier spectra are obtained by applying the ordinary Fourier transform. Moreover, new approximate functions are made by inverse Fourier transform of band-limited those spectra. Consequently, the integral equations of Fredholm type of second kind for spectra of approximate scattered wave functions are derived by matching those new functions to exact boundary value in the sense of least squares. Then it is shown analytically and numerically that the sequence of boundary values of approximate wave functions converges to the exact boundary value, namely, the boundary value of the exact scattered wave in the sense of least squares when the profile of imperfection part is described by continuous and piecewise smooth function at least. Moreover, it is shown that this sequence uniformly converges to exact boundary value in arbitrary finite region of the boundary and the sequence of approximate wave functions uniformly converges to the exact scattered field in arbitrary subdomain in the upper vacuum domain of the boundary in wider sense when the uniqueness of the solution of the Helmholtz equation is satisfied with regard to the profile of the imperfection parts of the boundary.

A novel formulation for the Scalar-field approach of Integral Equation formulation of the Measured Equation of Invariance (SIE-MEI) is derived from the scalar reciprocity relation to solve the scalar Helmholtz equation. The basics of this formulation are similar to IE-MEI method for the electromagnetic (EM) problem. The surface integral equation is derived from reciprocity relation and on-surface MEI postulates are used. As a result it generates a sparse linear system with the same number of unknowns as of Boundary Element Method (BEM) and keeps the merits in minimum storage memory requirements and CPU time consumption for computing the final matrix. IE-MEI method has been proposed for two-dimensional (2D) electromagnetic problem, but three-dimensional (3D) problem is very difficult to be extend. This scalar-field approach of IE-MEI method is identical to electromagnetic in 2D, but easily extended to the 3D scalar-field scattering problem contrary to EM problem. The numerical results of sphere and cube are verified with some rigorous or numerical solutions, which give excellent agreement.

The diffraction of a plane electromagnetic wave by an impedance wedge whose boundary is described in terms of the skew coordinate systems is treated by using the Wiener-Hopf technique. The problem is formulated in terms of the simultaneous Wiener-Hopf equations, which are then solved by using a factorization and decomposition procedure and introducing appropriate functions to satisfy the edge condition. The exact solution is expressed through the Maliuzhinets functions. By deforming the integration path of the Fourier inverse transform, which expresses the scattered field, the expressions of the reflected field, diffracted field and the surface wave are obtained. The numerical examples for these fields are given and the characteristics of the surface wave are discussed.

An inverse scattering problem in three dimensional two layered media is investigated. The shape and the location of the acoustic scatterer buried in one half-space are determined. With some a priori information, it becomes possible to solve this problem in three dimensions. Using the moment method, the scattered field is obtained for the estimated scatterer. An iterative procedure based on the Newton's method for the nonlinear least square problem is able to solve the inverse scattering problem. Some numerical results are presented.

In this paper, we analyze the inverse scattering problem by a new deterministic method called "Source and Radiation Field Solution," which has the merit that both the source and the radiation field can be treated at the same time, the effect of which has already shown in ordinary scattering problems.

A method is presented for reconstructing the surface profile of a two dimensional rough surface boundary from the scattered far field data. The proposed inversion algorithm is based on the Kirchhoff approximation and in order to determine the surface profile, the numerical results illustrating the method are presented.

For the expansion of using the integral equation methods on wave-field analysis, a new method called "Source and Radiation Field Solution" is suggested. This solution uses a couple of integral equations. One of them is the traditional integral expression giving the scattered field from the wave source, another is newly proposed one which expresses the wave source from both of the source and the scattered field, by using the conjugate Green function expression. Therefore this method can derive both of the source and the scattered field at the same time by coupled two equations. For showing the effect of this method, we analyze scattering problems for dielectrics in this paper.

The Yasuura method is effective for calculating scattering problems by bodies of revolution. However dealing with 3-D scattering problems, we need to solve bigger size dense matrix equations. One of the methods to solve 3-D scattering is to use multipole expansion which accelerate the convergence rate of solutions on the Yasuura method. We introduce arrays of multipoles and obtain rapidly converging solutions. Therefore we can calculate scattering properties over a relatively wide frequency range and clarify scattering properties such as frequency dependence, shape dependence, and polarization dependence of 3-D scattering from perfectly conducting scatterer. In these numerical results, we keep at least 2 significant figures.

The two-dimensional scattering problem of electromagnetic waves by a perfectly conducting wedge is analyzed by means of the Wiener-Hopf technique together with the formulation using the partition of scatterers. The Wiener-Hopf equations are derived on two complex planes. Investigating the mapping between these complex planes and introducing the appropriate functions which satisfy the edge condition of the wedge, the solutions of these equations are obtained by the decomposition procedure of functions. By deforming the integration path of the Fourier inverse transform, it is found that the representation of the scattered wave is in agreement with the integral representation using the Sommerfeld contours.

A method is presented for reconstructing the surface profile of a perfectly conducting rough surface boundary from the measurements of the scattered far-field. The proposed inversion algorithm is based on the use of the Kirchhoff approximation and in order to determine the surface profile, the Fletcher-Powell optimization procedure is applied. A number of numerical results illustrating the method are presented.

Reflection mode diffraction tomography is expected to reconstruct a higher resolution image than transmission mode. Its image reconstruction problem, however, in the many cases of practical uses becomes ill-posed one. In this paper, a new reconstruction method of limited angle reflection mode diffraction tomography using maximum entropy method is proposed. Results of simulation showed that the method was able to reconstruct the better quality images than IR method poposed by Kak, et al.

The problem of two-dimensional scattering of electromagnetic waves by a grating with several strips arbitrarily oriented in one period is analyzed by means of the Wiener-Hopf technique together with the formulation using the concept of the mutual field. A formulation for the analysis of multiple scattering from the grating is based on the representation of the scattered field by a grating composed of one strip in one period. The Wiener-Hopf equations and a representation of the scattered wave are obtained. The characteristic of the sampling function is used to expand the unknown function associated with the field on the strip into a series, and then the Wiener-Hopf equations are reduced to a set of simultaneous equations. For evaluation of the convergence and the errors in the numerical results, the relative error with respect to the extrapolated value and the square error for satisfaction of the boundary condition are computed. From numerical comparison of the present method with other various methods, it is found that the present method provides us accurate results. Some numerical examples of the reflection coefficients are presented for the reflection grating and transmission gratings.