Two-dimensional microwave imaging by a numerical inverse scatteringsolution

A numerical approach that aims to detect, by means of interrogating microwaves, the locations and the dielectric permittivities of unknown inhomogeneous dielectric cylindrical objects of arbitrary cross sections that might be present inside a fixed area of interest is proposed. An illumination is assumed with the electric field vector polarized along the cylindrical axis. The two-dimensional Lippman-Schwinger integral equation of electromagnetic scattering is transformed into matrix form by the moment method. The system obtained is solved by using a pseudoinversion algorithm to overcome ill-conditioning problems. The first-order Born approximation is also applied when the dielectric inhomogeneities are weakly scattering. Computer simulations have been performed by means of a numerical program. Results show the capabilities and limitations of the proposed approach     

Electromagnetic scattering by multiple three-dimensional scatterersburied under multilayered media. I. Theory

A general procedure is developed for the analysis of electromagnetic (EM) scattering by multiple three-dimensional (3D) dielectric and/or conducting objects buried under one-dimensional (1D) multilayered media. In this first part of a two-part paper, general closed-form formulations for the electric fields excited by an arbitrarily oriented electric dipole under the layered media are first presented, from which electric-field integral equations for the buried dielectric objects, pure conducting objects, and their combinations are then obtained, and the scattered electric fields in the upper space are formulated. Finally, the physical significance of the above formulations is discussed. In the second part, numerical implementations for these integral equations and the scattered fields are investigated     

Genetic algorithms as applied to the numerical computation ofelectromagnetic scattering by weakly nonlinear dielectric cylinders

This paper deals with the application of an optimization procedure based on a genetic algorithm (GA) to the prediction of the electromagnetic fields scattered by weakly nonlinear dielectric objects. Starting by an integral approach and describing the nonlinearities of the constitutive parameters by the Volterra-type integrals, the nonlinear scattering problem is numerically solved by an iterative procedure developed for the minimization of a suitable defined cost function. A GA is applied in order to deal with a large number of unknowns related to the harmonic components of the nonlinear internal electromagnetic field. In a preliminary stage, the behavior of typical parameters of the GA is analyzed; then numerical solutions are carried out and compared with those provided by other methods. Finally, some considerations are made concerning the rate of convergence of the iterative procedure     

Combined field solution for TM scattering from multiple conducting and dielectric cylinders of arbitrary cross section

A simple moment solution is given for the problem of electromagnetic scattering from multiple conducting and dielectric cylinders of arbitrary cross section. The system of conducting and dielectric cylinders is excited by a plane-wave polarized transverse magnetic to the axis of the cylinders. The equivalence principle is used to obtain three coupled integral equations for the induced electric current on the conducting cylinders and the equivalent electric and magnetic currents on the surface of dielectric cylinders. The combined field integral equation (CFIE) formulation is used. Sample numerical results are presented. The agreement with available published data is excellent.     

Electromagnetic radiation and scattering from finite conducting anddielectric structures: surface/surface formulation

An efficient and accurate numerical procedure for the analysis of the electromagnetic scattering and radiation from arbitrarily shaped, composite finite conducting and dielectric bodies is proposed. A set of coupled electric field integral equations involving surface equivalent electric and magnetic currents is used. The coupled integral equations are solved through planar triangular patch modeling and the method of moments. Two separate, mutually orthogonal vector functions for each edge connecting a pair of triangular patches have been developed. Numerical results for disk/cone and cylinder/cone structures are compared with other available data. Limited comparison with experimental data has also been made     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

Redundant electromagnetic data for microwave imaging ofthree-dimensional dielectric objects

The possibilities of reconstructing the dielectric characteristics of unknown three-dimensional dielectric objects located inside a known volume are studied by means of numerical computer simulations. A numerical approach is proposed that is based on the moment method and on the utilization of redundant data (i.e., the values of the components of the scattered electric field measured outside the investigation volume) in order to strictly constrain the solution. In particular, a multi-illumination-angle multiview approach is proposed, which is based on an integrodifferential formulation of the three-dimensional inverse electromagnetic scattering problem. The analytical model is discretized using the moment method, and a regularization procedure is employed to find a solution, in a least-squares sense, to the resulting rectangular ill-conditioned linear system of algebraic equations. Since the heaviest computations can be performed off line, the computer resources required by the approach are entirely independent of the number of views. Numerical simulations have been performed to assess the effectiveness of the approach in dielectric reconstruction, in particular, by evaluating the distortions due to the ill-posedness of the inverse-scattering formulation     

TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape

The theory and equations are developed for the scattering pattern of a dielectric cylinder of infinite length and arbitrary cross-section shape. The harmonic incident wave is assumed to have its electric vector perpendicular to the axis of the cylinder, and the fields are assumed to have no variations along this axis. Although some investigators have approximated the field within the dielectric body by the incident field, a more accurate solution is obtained here by treating the field as an unknown function which is determined by solving a system of linear equations. Scattering patterns obtained by this method are presented for dielectric shells of circular and semicircular cross section, and for a thin plane dielectric slab of finite width. The results for the circular shell agree accurately with the exact classical solution. The effects of surface-wave excitation and mutual interaction among the various portions of the shell are included automatically in this solution.     

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme     

Improving Conditioning of Electromagnetic Surface Integral Equations Using Normalized Field Quantities

When the surface integral equation method is applied to study electromagnetic scattering by dielectric or composite metallic and dielectric objects, the unknowns, i.e., the electric and magnetic surface current densities, and the elements of the system matrix, are often of the very different scales. As a consequence, the system matrix may have a high (singular value) condition number. An efficient method is presented to balance the unknowns and the integral equations, and the elements of the system matrix, too. The method is based on the use of normalized field quantities and unknowns, and carefully chosen scaling factors. In the case of dielectric and composite objects the condition numbers of the SIE matrices can be reduced with several orders of magnitudes by the developed method. In the case of high contrast objects, or if the frequency is very low, the developed method leads also to a clear improvement on the convergence of iterative solutions     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

Scattering by a dielectric cylinder of arbitrary cross section shape

The theory and equations are developed for the scattering pattern of a dielectric cylinder of arbitrary cross section shape. The harmonic incident wave is assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities are assumed to be independent of distance along the axis. Solutions are readily obtained for inhomogeneous cylinders when the permittivity is independent of distance along the cylinder axis. Although other investigators have approximated the field within the dielectric body by the incident field, we treat the total field as an unknown function which is determined by solving a system of linear equations. In the case of the dielectric cylindrical shell of circular cross section, this technique yields results which agree accurately with the exact classical solution. Scattering patterns are also presented in graphical form for a dielectric shell of semicircular cross section, a thin homogeneous plane dielectric sheet of finite width, and an inhomogeneous plane sheet. The effects of surface-wave excitation and mutual interaction among the various portions of the dielectric shell are included automatically in this solutiom     

Electromagnetic scattering from dielectric-coated axisymmetricobjects using the generalized point-matching technique (GPMT)

This paper describes the use of the generalized point-matching technique (GPMT) in analyzing plane electromagnetic (EM) scattering from 3-D bounded objects consisting of (or modeled by) an arbitrarily shaped axisymmetric perfect electrically conducting (PEC) or dielectric obstacle embedded in an arbitrarily shaped dielectric body of revolution and arbitrarily disposed with respect to the propagation direction of an arbitrarily polarized incident electric field vector. The treatment may be validly applied to scatterers whose boundary surfaces must have no sharp corners or edges which will introduce a discontinuity in the direction of the unit vector normal to the core and/or outer coat surfaces. It should be pointed out, however, that when applicable, the method is remarkably robust and capable of providing highly accurate numerical modelling predictions for the full-vector EM wave interactions with a large variety of arbitrarily shaped two-layered structures. Numerical results for a variety of scatterer configurations are provided and compared to exact or otherwise available results to demonstrate the potency and versatility of the suggested GPMT formulation     

Iterative numerical computation of the electromagnetic fieldsinside weakly nonlinear infinite dielectric cylinders of arbitrary crosssections using the distorted-wave Born approximation

The electromagnetic scattering by weakly nonlinear infinite dielectric cylinders is the topic dealt with in this paper. The cylinders are assumed to be isotropic, inhomogeneous, and lossless and to have arbitrarily shaped cross sections. A time-periodic illumination of the transverse magnetic type is considered. The nonlinearity is assumed to be expressed by the dependence of the dielectric permittivity on the internal electric field, under the hypothesis that the operator responsible for the nonlinearity does not modify the scalar nature of the dielectric permittivity and produces a time-periodic output. The electromagnetic scattering is then described by an integral equation formulation, and the electromagnetic field distributions inside and outside a scatterer are approximated by an iterative numerical procedure starting with the application of the distorted-wave Born approximation. In a simplified version of the approach, the classic first-order Born approximation is used. The convergence of the approach is discussed in several examples. In the computer simulations concerning cylinders with different cross-section shapes, the effects of the nonlinearity on the field-component fundamental frequency were evaluated for different values of the nonlinear parameters in the case of a Kerr-like nonlinearity and of a uniform incident plane wave. The generation of higher-order harmonics was also considered     

E-P-AMCBFM分析介质与PEC混合体的电磁散射

使用基于表面积分方程的矩量法来分析介质与理想导体混合体的电磁散射是计算电磁学的一大热点。对理想导体目标体表面建立电场积分方程,在介质目标体表面建立PMCHW方程组,与基于矩阵分块技术的自适应修正特征基函数法结合,对介质涂敷理想导体目标体的电磁散射进行分析,将其称之为EFIE-PMCHW-AMCBFM(E-P-AMCBFM)。并讨论不同参数如基函数阶数,矩阵块间重叠区域等对计算效率的影响,数值结果表明E-P-AMCBFM对于处理介质-理想导体混合体的电磁散射问题具有较高的精度和效率。     

Electromagnetic scattering and radiation by surfaces of arbitraryshape in layered media. I. Theory

An accurate and general procedure for the analysis of electromagnetic radiation and scattering by perfectly conducting objects of arbitrary shape embedded in a medium consisting of an arbitrary number of planar dielectric layers is developed. The key step in this procedure is a formulation of the so-called mixed-potential electric field integral equation (MPIE) that is amenable to an existing advanced solution technique developed for objects in free space and that employs the method of moments in conjunction with a triangular-patch model of the arbitrary surface. Hence, the goal is to immediately increase analysis capabilities in electromagnetics, yet remain compatible with the large existing base of knowledge concerning the solution of surface integral equations. Three alternative forms of the MPIE in plane-stratified media are developed, and their properties are discussed. One of the developed MPIEs is used to analyze scatterers and antennas of arbitrary shape that penetrate the interface between contiguous dielectric half-spaces     

Different formulations for numerical solution of single or multibodies of revolution with mixed boundary conditions

A numerical method for determining the electromagnetic field in the presence of one or several bodies of revolution is presented. The objects can be made of conductors, dielectrics or their combinations. The excitation is assumed to be due to a plane wave or infinitesimal electric dipoles located within or outside the dielectric. Several formulation types are considered and used to investigate the scattering by different objects. It is found that for moderate values of the dielectric constant, all formulation types give satisfactory results. However, for small or large relative permittivities the solution accuracies depend on the formulation type. As an application of the method to practical problems, two special cases of dielectric rod and microstrip antennas are considered. These antennas have widespread applications and the proposed method can be used to investigate their performance accurately.     

基于BP神经网络的介质圆柱体逆散射方法研究

将人工智能技术应用于介质圆柱体电磁逆散射问题研究,通过BP神经网络将原逆散射问题转化为一个回归估计问题,重构了目标的几何与电磁参数。在TM波的照射下,设置多个目标散射场的观测点,以散射场的幅值作为BP网络的输入,相应的几何与电磁参数作为输出,经过适当的训练,建立了介质圆柱体逆散射模型,并以此模型重构了已知探测范围内的介质圆柱体的半径、相对介电常数及电导率。比较结果显示了该方法的有效性和准确性,为目标的实时逆散射研究提供了一种有效方法。     

Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects

The recent development and extension of the method of moments technique for analyzing electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects is presented based on the combined field integral equations. The surfaces of the homogeneous three-dimensional arbitrary geometrical shapes are modeled using surface triangular patches, similar to the case of arbitrary shaped conducting objects. Further, the development and extensions required to treat efficiently three-dimensional lossy dielectric objects are reported. Numerical results and their comparisons are also presented for two canonical dielectric scatterers-a sphere and a finite circular cylinder.     

Scattering of electromagnetic waves by a system of two dielectricspheroids of arbitrary orientation

By means of modal series expansion of the incident, scattered, and transmitted electric and magnetic fields in terms of appropriate vector spheroidal eigenfunctions an exact solution is obtained to the problem of electromagnetic scattering by two dielectric spheroids of arbitrary orientation is obtained. The incident wave is considered to be a monochromatic uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. To impose the boundary conditions at the surface of one spheroid, the electromagnetic field scattered by the other spheroids is expressed as an incoming field to the first one, in terms of the spheroidal coordinates attached to it, using rotational-translational addition theorems for vector spheroidal wave functions. The solution of the associated set of algebraic equations gives the unknown expansion coefficients. Numerical results are presented in the form of plots for the bistatic and backscattering cross sections of two lossless prolate spheroids having various axial ratios, center-to-center separations, and orientations