Reliable approach for bistatic scattering of three-dimensional targets from underlying rough surface based on parabolic equation

A parabolic equation(PE) based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional(3-D) electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit(ADI) differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation(KA) and moment of method(Mo M). Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.     

Rapid computation of acoustic impulse scattering for rough penetrable surfaces

Chu’s theory for the impulse response of a point source to an isovelocity density contrast wedge [Chu D. Impulse response of density contrast wedge using normal coordinates. J Acoust Soc Am 1989;86:1883-96] enables wedge-assemblage rough surface scattering models to be extended to a broad range of penetrable seafloors, but is computationally intensive since it necessitates finding the multifold roots of a characteristic eigenvalue equation, and summing a power series, for each wedge apex. This present work considers the properties and relationships of the direct, reflected, and diffracted field components of a density contrast wedge. In particular, an analysis of the physical origin and behavior of diffractions associated with specular reflections of the source in the wedge faces leads to a simple extension of the Biot-Tolstoy theory [Biot MA, Tolstoy I. Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction. J Acoust Soc Am 1957;29:381-91] to density contrast wedges with reflectivity ∣R∣ < 1, for wedge angles within the range 150 ? θ_w ? 210°, where the diffractions are predominantly associated with a single reflection in each wedge face. This facilitates rapid time domain calculations of acoustic bottom scattering and penetration for complex multilayered seafloors.     

Field transformational approach to three-dimensional scattering from two-dimensional rough surfaces

In 1985, Tappert and Nghiem-Phu introduced a field-transformation technique for computing rough surface scattering from a parabolic equation model utilizing a split-step Fourier marching algorithm. The approach was based on a two-dimensional parabolic equation with a standard operator approximation that was capable of computing scattering from a one-dimensional rough surface. Although this approach has been used extensively and effectively, extensions of this approach to higher order approximations or three-dimensional propagation have only recently been investigated. In this work, the expressions that incorporate higher-order approximations and three-dimensional scattering from two-dimensional rough surfaces are presented. The implications of some computationally necessary approximations are also provided.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Acoustic scattering from a rough sea surface: the mean field by the integral equation method

Abstract

The scattering of an acoustic signal incident from below at low angles on a rough sea surface is treated by the integral equation method in the parabolic approximation. Equations are obtained allowing the mean scattered field to be calculated even when the surface causes a large phase modulation in the incident wave. Solutions are found using the method of Laplace transforms and some results are presented for a specific type of rough surface.     

Scattering from Alpha-Stable Non-Gaussian Distributed Surfaces

The scattering problem of alpha-stable non-Gaussian distributed rough surfaces is studied. The alpha-stable non-Gaussian distribution is used to describe the surfaces that exhibit sharp and sparse peaks, not usually seen in Gaussian distributed surfaces. Then a magnetic field integral equation is formulated to calculate the scattered field and the scattering coefficient. Numerical simulations show that the magnitude distribution of the scattered field is affected significantly by the probability distribution of the surface when the height of the surface changes in a random way. In addition, simulation results are presented as bistatic scattering coefficient for alpha-stable distributed surfaces.     

Direct Solution of the Inverse Problem for Rough Surface Scattering

We consider the inverse scattering problem for a scalar wave field incident on a perfectly conducting one-dimensional rough surface. The Dirichlet Green function for the upper half-plane is introduced, in place of the free-space Green function, as the fundamental solution to the Helmholtz equation. Based on this half-plane Green function, two reasonable approximate operations are performed, and an integral equation is formulated to approximate the total field in the two-dimensional space, then to determine the profile of the rough surface as a minimum of the total field. Reconstructions of sinusoidal, non-sinusoidal and random rough surface are performed using numerical techniques. Good agreement of these results demonstrates that the inverse scattering method is reliable.     

Bistatic electromagnetic scattering from a three-dimensional perfect electric conducting object above a Gaussian rough surface based on the Kirchhoff–Helmholtz and electric field integral equation

A hybrid integral equation is developed to solve the problem of electromagnetic (EM) scattering from a three-dimensional (3D) perfect electric conducting (PEC) object above a two-dimensional (2D) PEC or dielectric Gaussian rough surface. Firstly, the Kirchhoff–Helmholtz (KH) equation is adopted to describe the wave reflection on the rough surface; only one integral operation on the rough surface is needed, and the scattering from the object can be described by solving the electric field integral equation (EFIE) on the surface of the object. Moreover, according to scattering theory, the KH equation and the EFIE are coupled together (KH-EFIE) to describe wave propagation between the object and the rough surface. Then method of moments (MoM) is adopted to solve the KH-EFIE, and the current is obtained to calculate the scattering field. Finally, compared with other methods, the accuracy of the proposed approach is validated, and its efficiency is proved to be much higher than numerical solutions. Furthermore, by calculating the statistic composite radar cross-section (RCS) of the object/surface and the difference radar cross-section (DRCS) of the object, the influence of the rough surface root mean square (rms) height, the correlation length, the medium permittivity, the shape of the object, and the altitude of the object on the scattering characteristic is investigated.     

Investigation on global positioning system signal scattering and propagation over the rough sea surface

This paper is devoted to the study of polarization properties, scattering properties and propagation properties of global positioning system (GPS) scattering signal over the rough sea surface. To investigate the polarization and the scattering properties, the scattering field and the bistatic scattering coefficient of modified Kirchhoff approximation with using the tapered incident wave is derived in detail. In modeling the propagation properties of the GPS scattering signal in the evaporation duct, the initial field of parabolic equation traditionally computed by the antenna pattern with using fast Fourier transform (FFT) is replaced by the GPS scattering field. And the propagation properties of GPS scattering signal in the evaporation duct with different evaporation duct heights and elevation angles of GPS are discussed by the improved discrete mixed Fourier transform with taking into account the sea surface roughness.     

Fractal Characteristics Investigation on Light Scattering from Two Dimensional Rough Surface

A normalized two dimensional band-limited Weierstrass fractal function is used for modeling the rough surface. Based on Kirchhoff theory, an analytic solution of the average scattering field and the variance of scattering intensity are derived with emphasis on examining the relation of fractal dimension with the scattering pattern. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated to a slope of linear equation.     

Non-relativistic expansion of single-nucleon Dirac equation:Comparison between Foldy-Wouthuysen transformation and similarity renormalization group

By following the Foldy-Wouthuysen(FW) transformation of the Dirac equation,we derive the exact analytic expression up to the 1/M~4 order for general cases in the covariant density functional theory.The results are compared with the corresponding ones derived from another novel non-relativistic expansion method,the similarity renormalization group(SRG).Based on this comparison,the origin of the difference between the results obtained with the FW transformation and the SRG method is explored.     

Study of MPI based on parallel MOM on PC clusters for EM-beam scattering by 2-D PEC rough surfaces

This paper firstly applies the finite impulse response filter (FIR) theory combined with the fast Fourier transform (FFT) method to generate two-dimensional Gaussian rough surface. Using the electric field integral equation (EFIE), it introduces the method of moment (MOM) with RWG vector basis function and Galerkin's method to investigate the electromagnetic beam scattering by a two-dimensional PEC Gaussian rough surface on personal computer (PC) clusters. The details of the parallel conjugate gradient method (CGM) for solving the matrix equation are also presented and the numerical simulations are obtained through the message passing interface (MPI) platform on the PC clusters. It finds significantly that the parallel MOM supplies a novel technique for solving a two-dimensional rough surface electromagnetic-scattering problem. The influences of the root-mean-square height, the correlation length and the polarization on the beam scattering characteristics by two-dimensional PEC Gaussian rough surfaces are finally discussed.     

大尺度分层介质粗糙面电磁散射的特性研究

首先建立大尺度分层介质粗糙面散射的物理模型, 基于Stratton-Chu积分方程和Kirchhoff近似导出了粗糙面散射场的计算公式. 采用高斯随机粗糙面来模拟实际的分层介质粗糙面, 通过数值计算得到了正下视单站雷达接收到的后向散射回波. 理论推导了散射场强度与表面粗糙度之间的定量关系, 并从数值仿真的角度分析了表面和次表面的粗糙度对散射回波的影响, 给出了散射场随粗糙度变化的曲线. 最后考察了分层介质的电特性参数(介电常数和电导率)对分层粗糙面散射场的影响, 并对计算结果做出了分析.     

Low-energy Compton scattering by a proton: Comparison of effective hamiltonians with relativistic corrections

We discuss low-energy Compton scattering by a proton using two different methods of obtaining “effective 2 × 2 hamiltonians” of the electromagnetic interaction which include relativistic corrections. One is the standard Foldy-Wouthuysen transformation which we compare with the hamiltonian obtained from a direct reduction of the matrix element of the interaction hamiltonian between positive-energy solutions of the free Dirac equation. It is found that the Foldy-Wouthuysen hamiltonian yields the same result as a covariant calculation. However, an identification of the Z-diagrams of the usual Dirac representation with the contact graphs of the Foldy-Wouthuysen representation is incorrect beyond the order of the low-energy theorem. The direct-reduction method will, in general, lead to incorrect results. Although part of the problem may be cured by restoring the gauge invariance property of the hamiltonian, gauge invariance alone is not sufficient to reproduce the correct result.     

Acoustic scattering of a high-order Bessel beam by an elastic sphere

The exact analytical solution for the scattering of a generalized (or “hollow”) acoustic Bessel beam in water by an elastic sphere centered on the beam is presented. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis and the half-conical angle of the wave vector components of the generalized Bessel beam. The sphere is assumed to have isotropic elastic material properties so that the nth partial wave amplitude for plane wave scattering is proportional to a known partial-wave coefficient. The transverse acoustic scattering field is investigated versus the dimensionless parameter ka(k is the wave vector, a radius of the sphere) as well as the polar angle θ for a specific dimensionless frequency and half-cone angle β. For higher-order generalized beams, the acoustic scattering vanishes in the backward (θ = π) and forward (θ = 0) directions along the beam axis. Moreover it is possible to suppress the excitation of certain resonances of an elastic sphere by appropriate selection of the generalized Bessel beam parameters.     

The motion of particle spin in a nonuniform electromagnetic field

We have applied the Foldy-Wouthuysen transformation to spin-1 particles interacting with a nonuniform electromagnetic field. This allowed us to simultaneously confirm that the Pomeransky-Khriplovich-Sen’kov theory is valid and that the interaction of spin 1-particles with a weak field is properly described by the Corben-Schwinger equation. We analyzed the possibilities for experimentally testing theoretical conclusions by observing spin oscillations for the planar channeling of particles or nuclei in straight crystals. By carrying out such experiments, we can also detect the spin oscillations produced by electromagnetic interaction and measure the quadrupole moments of short-lived nuclei.     

微粗糙面上方球形粒子的光散射及其散射截面的计算

基于互易定理研究了光波入射时微粗糙面与其上方球形粒子复合模型的光散射。根据粗糙表面电流积分方程并利用表面微扰展开，得到了微粗糙面表面极化电流的迭代解，给出了耦合电场的计算方法。结合散射耦合场散射矩阵和已有的微粗糙面及球形粒子的散射矩阵，给出了复合模型散射截面的计算公式，数值计算了复合模型的后向散射截面并进行了详细讨论。     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.     

时域混合算法在一维海面与舰船目标复合电磁散射中的应用

采用时域积分方程(TDIE)与时域基尔霍夫近似(TDKA)的混合算法研究粗糙海面与舰船目标的复合瞬态电磁散射.该方法将舰船目标及其近邻海面划分为TDIE区域,用TDIE方法精确求解;将剩余电大尺寸的粗糙海面划分为TDKA区域,采用高效的TDKA电流近似求解.通过混合算法和传统TDIE算法结果的对比,表明TDIE-TDKA混合算法能保证计算的精度,同时具有较高的计算效率.最后,讨论了海面上方有无目标、海面上方风速、电磁脉冲入射角、舰船目标尺寸、吃水深度对后向散射磁场的影响.