Features of the Solution of Direct and Inverse Scattering Problems for Inhomogeneities with a Small Wave Size

Doklady Physics - An acoustic field scattered by a single inhomogeneity consists of components of different orders of multipolarity. For symmetric or weak-contrast inhomogeneities of a small wave...     

One-Dimensional Inverse Scattering Problem in Acoustics

We are concerned with the inverse scattering problem (ISP) in acoustics within the Marchenko inversion scheme. The quantum ISP is first discussed and applied in order to exhibit certain characteristics and application prospects of the method which could be useful in extending it to classical systems. We then consider the ISP in acoustics by assuming plane waves propagating in an elastic, isotropic, and linear medium. The wave equation is first transformed into a Schrödinger-like equation which can be brought into the Marchenko integral equation for the associated nonlocal kernel the solution of which provides us the full information of the underlying reflective profile. We apply the method in several model problems where the reflection coefficient of the multi-layer reflective medium is used as input to the ISP and in all cases we obtain excellent reproduction of the original structure of the scatterer. We then applied the inverse scattering scheme to construct profiles with certain predetermined reflection and transmission characteristics.     

Method of Fundamental Solution for Composite Electromagnetic Scattering from Two-Dimensional Object Located on a Rough Surface

Numerical modeling on the composite electromagnetic （EM） scattering from a two-dimensional （2-D） object located on a rough surface is presented by using the efficient method of fundamental solution （MFS）. The proposed special choice of the MFS is an interesting alternative to the onerous mesh generation in the traditional numerical methods, particularly for the method of moment （MoM）. There is no mesh scheme and singularity analysis, the field to be solved can be obtained directly in terms of the fundamental solutions of the appropriate wave equations. The numerical results are obtained and compared with the traditional MoM results, to demonstrate the accuracy and effectiveness of this technique.     

Inverse Scattering Problem for a Two Dimensional Random Potential

We study an inverse problem for the two-dimensional random Schrödinger equation (Δ + q + k ²)u = 0. The potential q(x) is assumed to be a Gaussian random function whose covariance operator is a classical pseudodifferential operator. We show that the backscattered field, obtained from a single realization of the random potential q, determines uniquely the principal symbol of the covariance operator of q. The analysis is carried out by combining harmonic and microlocal analysis with stochastic methods.     

An Inverse Scattering Problem with Part of the Fixed-Energy Phase Shifts

Assume that q(r) is a real-valued, compactly supported potential, q(r)=0 for , . Let be an arbitrary fixed subset of non-negative integers such that , and be fixed-energy phase shifts corresponding to q(r). The main result is: Theorem. The data determine q(r) uniquely. Received: 3 March 1999 / Accepted: 27 April 1999     

Study of the Electromagnetic Scattering from the Very Rough Fractal Sea Surface

In this paper, based on the fundamental formulae of the first-order and second-order Kirchhoff approx-imation and with consideration of the shadowing effect, the backscattering enhancement of the one-dimensional veryrough fractal sea surface with Pierson-Moskowitz spectrum is studied under the second-order Kirchhoff approximationat microwave frequency. The numerical results are compared with those of the first-order Kirchhoff approximation andintegral equation method. The dependencies of the bistatic scattering cross section and the backscattering enhancementon the incident angle, fractal dimension, and windspeed over the sea surface are analyzed in detail.     

二维粗糙海面的光散射及其红外成像

首先根据JONSWAP海面功率谱模型数值模拟出二维粗糙海面，采用几何光学近拟与基尔霍夫（Kirchhoff）标量近似计算了二维海面的光散射，计算中将每一面元看成一具有微粗糙度的粗糙面而不是近似地当作平面，并利用投影法与射线追踪法数值计算了一定入射角和散射角下的遮挡函数，有效地提高了海面光散射计算的精确性。最后利用太阳光的光谱辐照度数值模拟了海面的3μm-5μm红外散射图像，对于红外探测器抑制海面反射太阳光造成的亮带干扰具有一定的参考价值。     

一维粗糙面散射的射线追踪法研究

在考虑遮蔽效应的情况下,应用射线追踪法对一维导体和介质的高斯粗糙面的散射系数进行了研究,并分别计算了考虑一次反射和二次反射的散射系数。同时,利用蒙特卡罗法生成一维高斯粗糙面,计算了考虑一次、二次反射和遮蔽时不同均方根斜率粗糙面的平均散射系数。     

Time-Domain Scattering Modelling of Two-Dimensional Cylinder Located on a Rough Surface

Numerical modelling on the transient electromagnetic scattering by a two-dimensional （21）） cylinder located on a time-evolving rough surface is presented by using time-domain integral equations. The proposed special choice of a tapered Gauss pulse incident wave removes the truncation error from the rough surface. Additionally, a two-level averaging technique is utilized to overcome the instability from the time marching procedure of solving integral equations. Excellent correspondences between the surface current distributions, as well as the far-zone fields, computed by the proposed method and that obtained by the traditional method of moments associated with the inverse discrete Fourier transformation scheme demonstrate the accuracy of the modelling.     

Modification of Classical SPM for Slightly Rough Surface Scattering with Low Grazing Angle Incidence

Based on the impedance/admittance rough boundaries, the reflection coefficients and the scattering cross section with low grazing angle incidence are obtained for both VV and HH polarizations. The error of the classical perturbation method at grazing angle is overcome for the vertical polarization at a rough Neumann boundary of infinite extent. The derivation of the formulae and the numerical results show that the backscattering cross section depends on the grazing angle to the fourth power for both Neumann and Dirichlet boundary conditions with low grazing angle incidence. Our results can reduce to that of the classical small perturbation method by neglecting the Neumann and Dirichlet boundary conditions.     

A Hybrid Method of Solving the Electromagnetic Inverse Scattering Problem in Lossy Medium

A hybrid method of solving the electromagnetic inverse scattering problem in a lossy medium is proposed. The gradient search method is first used to determine the spatial distribution of the target, then the Monte Carlo method is selected to calculate the conductivity and permittivity of the scatterer. The results of numerical experiments verify that the hybrid method of combining the two ways is high-precision, efficient, and suited to global optimization.     

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.     

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。     

On Recent Analytical Results for Solution of the Scattering Problem for the Sharply Screened Coulomb Potential

Exact representations for the wave function and for the Green function of the Hamiltonian with the sharply screened Coulomb potential are given. The representations are obtained by summing up the partial wave series. The final form of the wave function and the Green function in the region of the coordinate space where the potential is not zero are given in terms of the Coulomb wave function and the Coulomb Green function, respectively. The exact representation has been obtained for the transition operator in the configuration space.     

Intensity Correlation Function of Light Scattering from a Weakly One-Dimensional Random Rough Surface

Based on the Kirchhoff approximation and Gaussian moment theorem, we present a general expression of the intensity correlation scattered from a weakly one-dimensional rough surface, which is applicable to the cases by either two different wavelengths or two different angles of incidence. By using a Gaussian surface model, we give the numerical results for the intensity correlation function with two different wavelengths specially. The results show that with the increasing surface roughness and the decreasing surface correlation length, the correlation function decreases in specular direction and increases in other directions, which indicates that the study of the correlation of the intensities is helpful when investigating the statistical parameters of rough objects. Also the results show that the increase of rms roughness can result in the narrower correlation bandwidth.