Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Sparsity-based efficient simulation of cluster targets electromagnetic scattering

An efficient and real-time simulation method is proposed for the dynamic electromagnetic characteristics of cluster targets to meet the requirements of engineering practical applications.First,the coordinate transformation method is used to establish a geometric model of the observation scene,which is described by the azimuth angles and elevation angles of the radar in the target reference frame and the attitude angles of the target in the radar reference frame.Then,an approach for dynamic electromagnetic scattering simulation is proposed.Finally,a fast-computing method based on sparsity in the time domain,space domain,and frequency domain is proposed.The method analyzes the sparsity-based dynamic scattering characteristic of the typical cluster targets.The error between the sparsity-based method and the benchmark is small,proving the effectiveness of the proposed method.

EVALUATION OF ELECTROMAGNETIC SCATTERING OF TWO DIMENSIONAL CONDUCTING OBJECTS--TE CASE

A hybrid technique is developed for the evaluation of two dimensional electromagnetic scattering from electrically large conducting bodies with cracks on their surfaces (TE case). The edge based finite element method (FEM) is employed to compute the scattering from the cracks. Physical optics (PO) and physical theory of diffraction (PTD) are utilized to evaluate the scattering from the large bodies with the cracks filled with perfect conductors. These two methods are combined by an efficient coupling scheme. Some of numerical results are presented. It is shown that the hybrid technique has some advantages over other methods in regard to saving computer memory units and CPU time.

Electromagnetic scattering from two parallel 2D targets arbitrarily located in a Gaussian beam

In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a Gaussian beam. However, because of the difficulty in formulating the couple scattering field, it is almost impossible to find an analytical solution for the second-order scattered field if the shapes of 2D targets are not canonical geometries. In order to overcome this problem, in this paper, the second-order solution is derived by using the technique based on the reciprocity theorem and the equivalence principle. Meanwhile, the relation between the secondary scattered field from target #1 and target #2 is obtained. Specifically, the bi- and mono-static scattering of Gaussian beam by two parallel adjacent inhomogeneous plasma-coated conducting circular cylinders is calculated and the dependence of attenuation of the scattering width on the thickness of the coated layer, electron number density, collision frequency and radar frequency is discussed in detail.

Analytical solution for electromagnetic scattering from a sphere of uniaxial left-handed material

Based on the analytical solution of electromagnetic scattering by a uniaxial anisotropic sphere in the spectral domain, an analytical solution to the electromagnetic scattering by a uniaxial left-handed materials (LHMs) sphere is obtained in terms of spherical vector wave functions in a uniaxial anisotropic LHM medium. The expression of the analytical solution contains only some one-dimensional integral which can be calculated easily. Numerical results show that Mie series of plane wave scattering by an isotropic LHM sphere is a special case of the present method. Some numerical results of electromagnetic scattering of a uniaxial anisotropic sphere by a plane wave are given.

A Second-Order Method for the Electromagnetic Scattering from a Large Cavity

In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.

Fast and accurate analysis of electromagnetic scattering from targets situated in dielectric half space

Electromagnetic scattering from targets situated in half space is solved by applying fast inhomogeneous plane wave algorithm combined with a tabulation and interpolation method. The integral equation is set up based on derivation of dyadic Green＇s functions in this environment. The coupling is divided into nearby region and well-separated region by grouping. The Green＇s function can be divided into two parts： primary term and reflected term. In the well-separated region, the two terms are both expressed as Sommerfeld integral, which can be accelerated by deforming integral path and taking interpolation and extrapolation. For the nearby region, the direct Sommerfeld integral makes the filling of impedance matrix time-expensive. A tabulation and interpolation method is applied to speed up this process. This infinite integral is pre-computed in sampling region, and a two-dimensional table is then set up. The impedance elements can then be obtained by interpolation. Numerical results demonstrate the accuracy and efficiency of this algorithm.

Polarization ratio characteristics of electromagnetic scattering fromsea ice inpolar areas

In the global climate system, the polar regions are sensitive indicators of climate change, in which sea ice plays an important role. Satellite remote sensing is a significant tool for monitoring sea ice. The use of synthetic aperture radar(SAR) images to distinguish sea ice from sea water is one of the current research hotspots in this topic. To distinguish sea ice from the open sea, the polarization ratio characteristics of sea ice and sea water are studied for L-band and C-band radars, based on an electromagnetic scattering model of sea ice derived from the integral equation method(IEM) and the radiative transfer(RT) model. Numerical experiments are carried out based on the model and the results are given as follows. For L-band, the polarization ratio for sea water depends only on the incident angle, while the polarization ratio for sea ice is related to the incident angle and the ice thickness. For C-band, the sea water polarization ratio is influenced by the incident angle and the root mean square(RMS) height of the sea surface. For C-band, for small to medium incident angles,the polarization ratio for bare sea ice is mainly determined by the incident angle and ice thickness. When the incident angle increases, the RMS height will also affect the polarization ratio for bare sea ice. If snow covers the sea ice, then the polarization ratio for sea ice decreases and is affected by the RMS height of snow surface, snow thickness, volume fraction and the radius of scatterers. The results show that the sea ice and the open sea can be distinguished by using either L-band or C-band radar according to their polarization ratio difference. However, the ability of L-band to make this differentiation is higher than that of C-band.

Efficient Solution to Electromagnetic Scattering Problems of Bodies of Revolution by Compressive Sensing

Under the theory structure of compressive sensing （CS）, an underdetermined equation is deduced for describing the discrete solution of the electromagnetic integral equation of body of revolution （BOR）, which will result in a small-scale impedance matrix. In the new linear equation system, the small-scale impedance matrix can be regarded as the measurement matrix in CS, while the excited vector is the measurement of unknown currents. Instead of solving dense full rank matrix equations by the iterative method, with suitable sparse representation, for unknown currents on the surface of BOR, the entire current can be accurately obtained by reconstructed algorithms in CS for small-scale undetermined equations. Numerical results show that the proposed method can greatly improve the computgtional efficiency and can decrease memory consumed.

Analysis of the Linear Sampling Method for Boundary Reconstruction of Chiral Obstacle in Electromagnetic Scattering Problems

In this paper, we consider the inverse scattering by chiral obstacle in electromagnetic fields, and prove that the linear sampling method is also effective to determine the support of a chiral obstacle from the noisy far field data.

Overview: Electromagnetic Scattering from Ocean Surface

Understanding the sea surface scattering process is very important in the development of models to detect the target above or under the surface. In this paper, both the analytical and the numerical methods applied in sea surface scattering are summarized. Some important problems concerned in this field are discussed. For numerical study, edge effect brings artificial nonrealistic scattering and therefore must be suppressed. Different edge treatment methods are compared in this paper. Scattering of breaking wave surface at very low grazing angle always needs more attentions than other scattering problems. Some numerical results show the existence of the special phenomena at very low grazing angle, for example, the ＂sea spikes＂ and the Doppler splitting.

An angular cutoff composite model for investigation on electromagnetic scattering from two-dimensional rough sea surfaces

Based on the local configuration angle division to select the corresponding method for electromagnetic scattering calculation from rough sea surface, this paper presents an angular cutoff composite model： when the local scattered angle is in the specular region that is given by an approximately 20 degrees cone around the specular direction, the Kirchhoff approximation is applied to evaluate the specular reflection, which dominates the total scattering in this region; the small perturbation method is employed to handle the diffuse reflection which is predominant as the local scattered angle is situated out of the specular region. Numerical results are compared with those of experimental and theoretical models in several configurations as a function of incident angle, wind speed, wind direction. The comparison of numerical results of other experimental and theoretical models in several configurations shows that the new composite model is robust to give accurate numerical evaluations for the sea surface scattering.

Fast SSED-MoM /FEM Analysis for Electromagnetic Scattering of Large-Scale Periodic Dielectric Structures

A hybrid method combining simplified sub-entire domain basis function method of moment with finite element method( SSED-MoM /FEM) is accelerated for electromagnetic( EM) scattering analysis of large-scale periodic structures.The unknowns are reduced sharply with non-uniform mesh in FEM. The computational complexity of the hybrid method is dramatically declined by applying conjugate gradient-fast Fourier transform( CG-FFT) to the integral equations of both electric field and magnetic field. The efficiency is further improved by using OpenMP technique. Numerical results demonstrate that the SSED-MoM /FEM method can be accelerated for more than three thousand times with large-scale periodic structures.

Investigation on electromagnetic scattering from rough soil surface of layered medium using the small perturbation method

Electromagnetic scattering from a rough surface of layered medium is investigated, and the formulae of the scattering coefficients for different polarizations are derived using the small perturbation method. A rough surface with exponential correlation function is presented for describing a rough soil surface of layered medium, the formula of its scattering coefficient is derived by considering the spectrum of the rough surface with exponential correlation function; the curves of the bistatic scattering coefficient of HH polarization with variation of the scattering angle are obtained by numerical calculation. The influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the roughness surface parameters and the frequency of the incident wave on the blstatic scattering coefficient is discussed. Numerical results show that the influence of the permittivity of layered medium, the mean layer thickness of intermediate medium, the rms and the correlation length of the rough surface, and the frequency of the incident wave on the bistatic scattering coefficient is very complex.

Numerical study of electromagnetic scattering from one-dimensional nonlinear fractal sea surface

In recent years, linear fractal sea surface models have been developed for the sea surface in order to establish an electromagnetic backscattering model. Unfortunately, the sea surface is always nonlinear, particularly at high sea states. We present a nonlinear fractal sea surface model and derive an electromagnetic backscattering model. Using this model, we numerically calculate the normalized radar cross section （NRCS） of a nonlinear sea surface. Comparing the averaged NRCS between linear and nonlinear fractal models, we show that the NRCS of a linear fractal sea surface underestimates the NRCS of the real sea surface, especially for sea states with high fractal dimensions, and for dominant ocean surface gravity waves that are either very short or extremely long.

Application of Multi-Grid Method to the Computation of Electromagnetic Scattering Problems

The multi-grid method has been known as an efficient iterative method for the linear systems and nonlinear systems that arise from finite difference approximations for partial differential equations. In this paper, the multigrid method is extended to the application of solving integral equations which appear in electromagnetic scattering problems. The diakoptic theory is used for this purpose. Compared with other methods, the numerical results show that the multigrid method is powerful to solve electromagnetic scattering problems and can be used to compute electromagnetic scattering problems with electrically large bodies and complex structures.

A STUDY OF ELECTROMAGNETIC SCATTERING FROM A DIELECTRIC-COATED CONDUCTING CYLINDER

In order to solve the problem of electromagnetic scattering by a dielectric-coated conducting circular cylinder, the total field excited by an electric and amagnetic dipoles exterior to the cylinder is derived in terms of dyadic Green's function (DGF) technique. Then, the scattering problem can be solved on basis of the relation between the total and the scattered. field. The solution of the scattered field can be obtained directly from the general formula of the scattered field as the cylinder is illuminated by a spherical wave. For a plane wave of arbitrary polarization incident to the cylinder from the direction (theta-0, phi-0), the scattered field can be given by the solution of the scattered field with a spherical wave incident as the center of the spherical wave moves to infinity. For an astigmatic wave incident to the cylinder, the scattered field can be derived by superposing or integrating of the scattered field with the special spherical wave incident.

Electromagnetic Scattering of a High-Order Bessel Trigonometric Beam by Typical Particles

The scattering of an electromagnetic high-order Bessel trigonometric beam by several typical homogeneous dielec- tric particles is investigated. The incident beam is represented by the vector expressions in Cartesian coordinates. The scattering problems involving homogeneous dielectric particles are formulated with the surface integral equation method. As an example, the effects of the beam＇s parameters on the differential scattering cross section for a sphere are analyzed in detail. Then the numerical results for the scattering of a high-order Bessel trigonometric beam by three typical nonspherieal particles, including a spheroid, a cylinder, and a cube, are presented.

Numerical Modeling of Electromagnetic Scattering from Sea Surface Covered by Oil

The aim of this work is to study the impacts of the oil spills on the electromagnetic scattering of the ocean surfaces in bistatic and monostatic configurations. Therefore, in this paper, we will study the influence of the pollutants (oil spills) on the physical and geometrical properties of sea surface. In recent literature, the study of the electromagnetic scattering from contaminated sea surface (sea surface covered by oil spill) was limited in monostatic case. In this paper, we will study this effect in bistatic configuration, which is interested in presence of pollution in sea surface. Indeed, we will start the numerical analysis of the bistatic scattering coefficients of a clean sea surface. Then, we will study the electromagnetic signature from sea surface covered by oil spills in bistatic case using the numerical Forward-Backward Method (FBM). The obtained numerical simulation of bistatic scattering coefficients of clean and contaminated sea surface is studied as a function of various parameters (frequency, incident angle, sea state, type of pollutant…). And the obtained results are also compared with those published in the literature, including those using asymptotic methods.

Electromagnetic scattering from two-layered rough interfaces with a PEC object:vertical polarization

Electromagnetic （EM） scattering from a stack of two rough interfaces separating a homogeneous medium with a perfectly electric conducting （PEC） object has been calculated through the method of moments for vertical polarization. Theoretical formulations of EM scattering from multi-layered rough interfaces with a PEC object have been derived in detail and the total fields and their normal derivatives on the rough interfaces are solved. The two-layered model is a special case. In this work, a Gaussian rough surface was applied to simulate the rough interface. A cylinder was located above, between or below the two-layered rough interfaces. Through numerical simulations, the validity of this work is demonstrated by comparing it with existing scattering models, which are special cases that include a PEC object located above/below a single-layered rough interface and two-layered rough interfaces without an object. Subsequently, the influences of characteristic parameters, such as the relative permittivity of the medium, as well as the average height between the two rough surfaces, on the bistatic scattering coefficient are discussed.