High-frequency analysis of EM scattering from a conducting spherecoated with a composite material

The asymptotic high-frequency solution for the scattered field produced by a plane wave incident on a perfectly conducting sphere coated with a thin composite material is considered. In the shadow region, the high-frequency scattered field is entirely associated with the usual creeping-wave diffraction. In the lit region, the scattered field can be expressed as a sum of geometrical optics (GO) and creeping-wave diffraction terms. The field in the caustic regions, where the ray solution fails, is excluded. The appropriate formula for each term is derived, and the result is presented in a form suitable for computation. Numerical results for the bistatic scattering patterns of the coated sphere show excellent agreement with the rigorous eigenfunction solutions     

Scattering from a sphere of small radius embedded into a dielectricone

In this paper, the scattering of a plane electromagnetic wave from a metallic or dielectric sphere of electrically small radius, embedded into a dielectric one, is considered. The classical method of separation of variables is used, combined with translational addition theorems for spherical vector wave functions. Analytical expressions are obtained for the scattered field and the various scattering cross-sections, in the case of an inner sphere with electrically small radius. Numerical results are given for various values of the parameters and for metallic and dielectric inner sphere. Some remarks are made about the possibility of detection or identification of inhomogeneities or nonsymmetries     

手征涂覆球对高斯波束的散射

在广义米理论的基础上,通过把入射高斯波束、散射场和内部场用适当的球矢量波函数展开,给出了一种求解手征涂覆球对高斯波束散射的解析方法。待定的展开系数可由从边界条件得到的线性方程组求出。对于波束的区域近似模型,给出了微分散射截面的数值结果。结果表明：与介质涂覆的情况相比,手征涂覆对微分散射截面和散色场的极化特性都产生了较大的影响。     

An analytical solution to the diffraction problem of diagnosing the position and size of a sphere

A method for determining the position and dimensions of a body from the scattered field is described. The body (a metal solid sphere) is situated in the near-field zone of a transmitting antenna, and the receiving antenna is situated in the near zone of the body. The parameters of the body are calculated from the measured wave amplitudes in the dielectric waveguide of the receiving antenna. For calibration of the antenna, the body is replaced by a metal mirror.     

平面上方小球的光散射计算

本文基于扩展的Mie理论方法求解平面上方小球的散射问题。通过建立小球和平面的模型,解决小球和平面的边界条件问题,并利用矢量波函数展开的方法求得了散射场。强调了小球与表面的相互作用。散射总场是小球本身的散射场,平面反射场,和小球与平面之间的相互作用场三者的叠加。结论给出了均匀介质小球的微分散射截面图并进行了详细讨论。     

Radar cross sections of dielectric or plasma coated conducting spheres and circular cylinders

Radar cross sections for a variety of spherical and cylindrical scatterers having homogeneous dielectric or plasma shells are obtained by using both the exact boundary value solutions and approximate, semi-empirical methods based on physical principles. The plasma is assumed to have the macroscopic properties of a lossless dielectric with a permittivity less than that of free space. A superposition approximation for the radar cross section of a dielectric coated conducting body is obtained by considering the scattered field to be the phasor sum of two principal components, the field scattered by the air-dielectric interface and the field scattered by an equivalent conducting body which differs from the actual body because of the lens action of the shell. This approximation yields very good agreement with the exact solutions for both spherical and cylindrical dielectric clad scatterers with radii in the Rayleigh region and in the resonant region, and for bistatic scattering as well as for backscatter. The echo area of a conducting sphere with nonconcentric spherical dielectric shell calculated by means of the superposition approximation is in excellent agreement with experimental measurements, thus demonstrating the validity of this method in a case for which the exact solution cannot be obtained.     

Microwave imaging using the finite-element method and a sensitivity analysis approach

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.     

Analysis of electromagnetic scattering from dielectrically coatedconducting cylinders using a multifilament current model

A method of moments solution is presented for the problem of transverse magnetic scattering from dielectrically coated conducting cylinders. The solution uses fictitious filamentary electric sources of yet unknown currents to simulate both the field scattered by the cylinder and the field inside the dielectric coating. The simulated fields obey the boundary conditions, namely, the continuity of the tangential components of the electric and magnetic fields across the air-dielectric interface and the vanishing of the tangential component of the electric field at the perfect conductor, at selected sets of points on these respective surfaces. The result is a matrix equation that is readily solved for the unknown current. The currents can be used to determine approximate values for the fields and field-related parameters of interest. The procedure is simple to implement and is general in that cylinders of smooth but otherwise arbitrary shape and coating of arbitrary complex permittivity can be handled. Illustrative examples are considered and compared with available data, demonstrating the efficiency of the solution     

Scattering of TM excitation by coupled and partially buried cylinders at the interface between two media

An analysis of scattering from coupled conducting cylinders near the planar interface between two semi-infinite, homogeneous halfspaces of different electromagnetic properties and from partially buried conducting cylinders is presented. The perfectly conducting cylinders of general cross sections are of infinite extent and the excitation is transverse magnetic to the cylinder axes. Coupled integral equations for the unknown current induced on the cylinders are derived and a numerical method for solving them is described. In addition, a simple technique is employed to determine the far-zone scattered field from knowledge of the cylinder current. Data displaying the distribution of the induced current and the scattered field patterns for cylinders of interest are presented and discussed.     

A simple and accurate resonance expansion for the electromagnetic field scattered by a Lossy Dielectric Sphere

A simple and accurate resonance expansion for the space-frequency representation of the electromagnetic field scattered by a homogeneous dielectric sphere with loss is discussed. Results are presented which establish the accuracy of the resonance expansion by comparing with the corresponding Mie series.     

Analysis of Electromagnetic Scattering from an Eccentric Multilayered Sphere

An exact analytic solution of a plane electromagnetic (EM) wave scattered by an eccentric multilayered sphere (EMS) is obtained. It is assumed that the layers are perfect dielectrics and that the innermost core is a perfectly conducting sphere. Each center of a layer is translated along the incident axis. All fields are expanded in terms of the spherical vector wave functions with unknown expansion coefficients. The addition theorem for spherical wave functions is used prior to applying the boundary conditions. The unknown coefficients are determined by solving a system of linear equations derived from the boundary conditions. Numerical results of the scattering cross sections are presented on the plane of φ=0 degrees and φ=90 degrees. The convergence of modal solutions and the characteristics of patterns are examined with various geometries and permittivity distributions     

Three-dimensional electromagnetic scattering from inhomogeneousobjects by the hybrid moment and finite element method

The hybrid moment and finite element methods are used to obtain 3-D scattering and/or absorption from inhomogeneous, arbitrarily shaped objects. The surface of the object is approximated by triangles and the volume of the object is approximated by tetrahedrons. The electrical parameters are assumed constant in each tetrahedron. The Galerkin testing procedure is used. To avoid contaminations of spurious mode, a divergenceless vector basis function is used in finite elements. The calculated internal field and scattered field for a homogeneous sphere, a layered sphere, and a lossy prolate spheroid are compared with Mie series solutions and other numerical techniques. The accuracy and rate of convergence of the solution are discussed     

Three-Dimensional Through-Wall Imaging Under Ambiguous Wall Parameters

A through-wall imaging problem for a 3-D geometry is considered. Scatterers are located beyond a wall represented by a dielectric slab whose features are unknown or known with some degree of uncertainty. A two-step imaging procedure is presented. First, the thickness and the dielectric permittivity of the wall are estimated by a simple procedure which takes into account that actual measurements concern the total scattered field (i.e., the field reflected by the wall plus the one scattered by the obscured scatterers). Then, the problem is cast as a linear inverse scattering problem and solved by means of a truncated-singular value decomposition algorithm. In particular, a 2-D sliced approach is employed to obtain the 3-D scene. Numerical examples are shown to assess the effectiveness of the reconstruction procedure.     

Electromagnetic scattering by buried objects of low contrast

The Born approximation is used to derive the plane-wave scattering matrix for objects of low dielectric contrast. For general shapes a numerical integration over the volume of the scatterer is required, but analytical expressions are derived for a sphere, a circular cylinder and a rectangular box (parallelepiped). The plane-wave scattering-matrix theory is used to account for the air-Earth interface. Numerical results are presented for the scattered field and far field for plane-wave excitation. The scattered field are weak for low-contrast objects, but the near-field results have application to electromagnetic detection of buried objects     

Electromagnetic scattering from two adjacent objects

In the paper, the problem of electromagnetic scattering from two adjacent particles is considered and an iterative solution that accounts for multiple scattering up to second-order is proposed. The first-order solution can easily be obtained by calculating the scattered field of isolated particles when illuminated by a plane-wave. To get the second-order solution, the scattered field from one of the particles, with nonuniform phase, amplitude, and polarization, is considered as the illuminating wave for the other particle and vice versa. In the work, the second-order scattered field is derived analytically using a novel technique based on the reciprocity theorem. In specific, the analytical solution for bistatic specular scattering from a cylinder and sphere pair is discussed and the results are compared with numerical computations based on the method of moments     

Synthesis of the fields of a transverse feed for a spherical reflector

The problem of designing a transverse feed for a spherical reflector is considered and a method is presented for synthesizing the fields on a surface of a sphere enclosing a feed that will produce a specified reflected field at the surface of a spherical reflector. The method identifies the reflector and a spherical surface enclosing the feed as a boundary value problem and uses a finite set of spherical waves to approximate the boundary conditions. A feed designed to excite this field will in turn produce the desired reflected field at the surface of the reflector, under the condition that that portion of the reflected field which is scattered by the feed may be neglected. It is shown that the feed need produce only a small part of the synthesized field to obtain an antenna efficiency of more than 70 percent. Some typical field distributions will be shown so as to indicate a method for designing a feed and to point out the correlation between the polarization of the synthesized field and the polarization of the reflected field at the surface of the reflector.     

On the Use of Surface Impedance in the Detection and Location of Buried Objects

A method to detect and locate the cylindrical objects buried in a half-space is presented. The method is based on the reconstruction of the appearing surface impedance of the half-space through remote field measurements of scattered field for a single plane wave illumination. The existence of the objects causes surface impedance to be a function of location. The inhomogeneous surface impedance is determined from the boundary condition itself which requires to know the scattered field and its derivative on the boundary. These values are calculated by analytically continuing the measured data to the boundary of the half-space. The method yields satisfactory results if (i) adjacent cylinders are not very close to each other, (ii) the cylinders are not deeply buried and (iii) the half-space of burial is not highly attenuative.     

Optimization techniques and inverse problems: Reconstruction of conductivity profiles in the time domain

The iterative probing of an inhomogeneous lossy dielectric slab, whose conductivity is unknown, is discussed. The probing is done in the time domain from the measurements of the field on the interface when this slab is illuminated by a known field. An exact integral formulation is used. Minimization of a cost function, characteristic of the discrepancy between the measured field and the field which would be scattered by a known slab, is specified by the optimization theory. The notion of the adjoint state of the field is introduced. The influence of some parameters of this minimization is studied. Great importance is given to the sensitivity of the probing as function of the amplitude of errors in the data. Such an iterative probing appears fast, accurate, and efficient, even in the case of large errors.     

Incremental length diffraction coefficients for the shadow boundaryof a convex cylinder

Incremental length diffraction coefficients (ILDCs) are obtained for the shadow boundaries of perfectly electrically conducting (PEC) convex cylinders of general cross section. A two-step procedure is used. First, the nonuniform (NU) current in the vicinity of the shadow boundary is approximated using Fock (1965) functions. The product of the approximated current and the free-space Green's function is then integrated on a differential strip of the cylinder surface transverse to the shadow boundary to obtain the ILDCs. This integration is performed in closed form by employing quadratic polynomial approximations for the amplitude and unwrapped phase of the integrand. Examples are given of both the current approximations and the integration procedure. Finally, as an example, the scattered far field of a PEC sphere is obtained by adding the integral of the NU ILDCs of a circular cylinder along the shadow boundary of the sphere to the physical optics (PO) far field of the sphere. This correction to the PO field is shown to significantly improve upon the accuracy of the PO far-field approximation to the total scattered field of the sphere