A Rigorous Theory for Problems of Scattering: The Delta Boundary Operator Method

Abstract

A rigorous approach for solving a large class of scattering problems is presented and implemented for the classical problem of scattering by a perfectly conducting circular cylinder. This method is characterized by the preliminary calculations of a ψ distribution, deduced from a new kind of boundary value problem. This ψ distribution allows us to express the surface current density in the form of the integral of a known function, valid for any kind of incident wave. Numerical comparisons with the classical method are performed. A numerical study of ψ allows us to deal with cylinders having diameters larger than 100 wavelengths on a HP 1000 F minicomputer.     

A New Electromagnetic Theory for Scattering from Shallow Rough Surfaces

A new approximate theory for scattering from arbitrary rough surfaces is presented. It is shown that this theory gives the exact result, to the first order, when the depth of the asperities tends to zero. On the other hand, we prove that this is not the case for formulae relying upon the Kirchhoff approximation, even in cases for which many authors have claimed their validity. Many applications can be envisaged, in particular to direct or inverse scattering from random rough surfaces.     

Multiple Scattering from Random Rough Surfaces Using the Kirchhoff Approximation

Abstract

Numerical results for scattering of electromagnetic waves from a rough surface are presented and compared with experimental results. The method uses the Kirchhoff or physical optics approximation to separate the single and double scatter terms in the total scatter pattern. It is shown that enhanced backscatter occurs in the double scatter term as predicted by a simple ray picture of the scattering process.     

Large-Angle in-Plane Light Scattering from Rough Surfaces: Comment

A recent paper by Karabacak et al. [Appl. Opt. 39, 4658 (2000)], which discussed the scattering from rough surfaces in directions out of the plane of incidence, exhibited an error in the derivation of a polarization factor. An asymmetry in the scattering function for directions out of the plane of incidence and for circularly polarized incident light is predicted by the correct derivation of this factor and can be observed in their data.     

Multiple Scattering from Rough Dielectric and Metal Surfaces Using the Kirchhoff Approximation

Abstract

The Kirchhoff double-scatter method for calculating the intensity distribution scattered from a rough surface is extended to dielectric and metal surface materials. The material properties are contained in the Fresnel reflection coefficients only. It is shown that the results agree well with calculations using the exact method for a surface of Gaussian statistics with standard deviation of height σ = 1·93λ and 1/e correlation length τ = 5·02λ.     

A Detailed Study of the Scattering of Scalar Waves from Random Rough Surfaces

A multiple scattering theory of scalar waves from random rough surfaces is presented. By using the Ewald-Oseen extinction theorem the scattering integral equation is solved by means of an expansion in σ powers (σ being the standard deviation of the corrugation). Values of the mean scattered intensity until the fourth order of σ are given. The quick convergence of this series for low σ permits us to deal with those situations of small roughness in which the Kirchhoff approximation given by Beckmann and Spizzichino [2] fails. These are the cases in which σ ? T and λ ? T (λ being the wavelength and T the surface correlation length). Thus this theory can give the intensity for white noise surfaces, and yields the conditions under which the single scattering Kirchhoff approximation works, as well as its percentage of error. As such it is shown that Beckmann's theory gives good results in all cases in which σ /T < 0·05 and, thus, the reason why it is valid for interpreting laser speckle measurements is given. All the analysis is done for normal statistics and a gaussian correlation function of the corrugation.     

一种粗糙面双站散射非定常迭代算法

发展了一种残差光滑平方化共轭梯度(RSCGS)方法.通过残差光滑技术和平方化共轭梯度法的结合,使该方法既有收敛迅速的特点,同时又保持良好的收敛性质.在电磁离散矩阵方程求解计算中,该方法能加速迭代收敛和改善迭代收敛性质.最后利用该方法计算了当TE、TIM高斯波束入射在高斯粗糙导体表面和复合粗糙导体表面的双站散射系数,计算结果表明了该方法的有效性.     

A Numerical Method for the Solution of the Second Boundary Value Problem of Elasticity for Solids with Cracks

A series of experiments detecting electromagnetic radiation (EMR) emitted during percussion drilling were carried out. The electromagnetic signals obtained could be classified into four groups. Three groups are similar to former pulse types observed during conventional uniaxial and triaxial compression experiments, while the fourth is a new one possibly emanating from conical fracturing or fragmentation of chips.     

Two-dimensional Glitter Function in the Study of Rough Surfaces Via Remote Sensing

Abstract

The van Cittert-Zernike theorem is used to obtain in a rigorous way the bidimensional glitter function used in the problem of retrieving spatial information of surface heights from aerial images. The results show that the glitter function can be described by a circular function where the radius is a function of the angular extent and the position of the source and the viewing direction. This result comes from considering the source as a circular one that is projected on the detector or camera after reflection, taken into consideration the slopes of the surface and the geometrical optics.     

阻尼边界条件的声波散射问题的三种数值求解方法

利用位势理论将阻尼边界条件的声波散射问题转换为一个第二类边界积分方程,在二维情形下给出了Nystrom方法,Garlerkin方法和配置法这三种数值方法并通过对具体的数值例子的分析比较表明Nystrom方法在处理该问题时是最好的。     

利用线性抽样方法重建Dirichlet边界条件声波散射区域

线性抽样方法是考虑一个第一类线性积分方程中的参数从区域内部趋近散射区域边界时,该方程的解趋近于无穷大。本文在此基础上就Dirichlet边界条件的声波反散射问题,利用积分方程理论严格证明了线性抽样方法对其的可用性,具体数值例子表明该方法是有效的。     

Reconstruction of Two-Dimensional Randomly Rough Surfaces Based on Bidirectional Reflectance Distribution Function

This article presents an inverse method for reconstructing two-dimensional randomly rough surfaces based on the available (experimental or given) data of the bidirectional reflectance distribution function (BRDF). The Maxwell’s equations of electromagnetic waves are applied to describe the light scattering process of rough surfaces by accounting for the near-field effect. Such a forward problem is numerically solved with the finite-difference time-domain algorithm. The inverse scattering problem of reconstructing the surface profile is handled by means of an optimization technique—the particle swarm optimizer algorithm. As an example, reconstruction of a Gaussian rough surface is conducted based on the experimental data of BRDFs. The retrieved results of the surface profile are compared with those measured by atomic force microscopy from the samples, which shows that the reconstruction algorithm can provide the credible prediction of surface profiles. The reconstruction approach studied in this study can make reliable predictions of the actual or required surface profiles.     

Solution of Inverse Boundary Optimization Problem by Trefftz Method and Exponentially Convergent Scalar Homotopy Algorithm

The inverse boundary optimization problem, governed by the Helmholtz equation, is analyzed by the Trefftz method (TM) and the exponentially convergent scalar homotopy algorithm (ECSHA). In the inverse boundary optimization problem, the position for part of boundary with given boundary condition is unknown, and the position for the rest of boundary with additionally specified boundary conditions is given. Therefore, it is very difficult to handle the boundary optimization problem by any numerical scheme. In order to stably solve the boundary optimization problem, the TM, one kind of boundary-type meshless methods, is adopted in this study, since it can avoid the generation of mesh grid and numerical integration. In the boundary optimization problem governed by the Helmholtz equation, the numerical solution of TM is expressed as linear combination of the T-complete functions. When this problem is considered by TM, a system of nonlinear algebraic equations will be formed and solved by ECSHA which will converge exponentially. The evolutionary process of ECSHA can acquire the unknown coefficients in TM and the spatial position of the unknown boundary simultaneously. Some numerical examples will be provided to demonstrate the ability and accuracy of the proposed scheme. Besides, the stability of the proposed meshless method will be validated by adding some noise into the boundary conditions.     

The Solution to the Inverse Scattering Problem,Based on Fast Zero Location from Two Measurements

The present paper presents a simple and fast method for solving the phase problem in scattering determinations. After defining the problem in the introduction, the paper outlines, in § 2, the main conventional approaches to solving the phase problem, which is due to the presence of complex zeros of the scattered field in the space of measurement. If N such zeros are present, the ambiguity in solving the inverse scattering problem in 2 ^N . Section 3 offers the mathematical foundations of the proposed new method. It discusses the properties of the distributions of zeros and in particular the way in which they encode the information in the object space. Using these properties as a basis, § 4 puts forward a method for zero location, which involves two conventional scattering measurements, without a priori information. The main advantage of the procedure consists of reducing the number of computations required for determining possible solutions from 2 ^N to 2N, by using an iterative procedure.     

半线性两点边值问题有限元强超收敛性

通过单元正交展开的余项中添加若干待定的低次项,得到所需的超接近于有限元解的逼近函数,由此导出了一类非线性两点边值问题的强超收敛性。最后给出了一个数例验证了这一结论。     

Ray Method of Solution of the Ablation Problem

Consideration is given to a threedimensional problem of heating of a halfspace by the Gaussian energy flux with allowance made for the heatflux inertia. It is assumed that the ablation front is formed at the points at which the temperature is equal to the melting temperature and the Stefan condition is satisfied. The mechanism of removal of mass is not considered. Using the ray method and taking into account three expansion terms, an ablationsurface equation and temperature have been obtained. Account for the inertia of the heat flux leads to the fact that the ablationfront velocity at the initial instant of time is finite. The condition for the onset of ablation of the material at the initial instant of time has been obtained. The solutions for the fronts of ablation and temperature are illustrated by the graphs.     

动态光散射检测的互信息函数分析方法

互信息函数反映的是系统中的非线性关联,是将线性的关联函数对非线性系统的一种推广,动态光散射领域目前未见到用计算互信息函数进行分析的报道.本文中通过计算互信息函数,对动态光散射检测电机转速的时间序列进行分析,研究表明,互信息函数法能准确地测出电机转速.同时,由于互信息函数自身的优点--能实际地反映出数据之间的相互关联,因此,与自相关函数法比较,互信息函数法反映出了更多的动力学信息.目前正在把互信息函数分析法用于检测颗粒粒径的实验当中.希望利用互信息函数分析的方法,在动态光散射检测颗粒粒径的实验当中得到更多的动力学信息.并进一步应用于纳米颗粒粒径的动态光散射检测中.     

粗糙表面散射基模高斯光束的散射特性实验研究

本文介绍良导体二维粗糙表面对红外激光束的散射分布;讨论不同偏振方式入射时散射光的分布特点,以及中等粗糙表面和弱粗糙表面散射能量在不同入射角下的变化趋势;分析表面参数对分布的影响。文章对观察到的弱粗糙表面散射在镜反射方向附近的边凸现象作了简述;这一现象由散射光的相干叠加而引起,有深入研究的价值。     

三阶p-Laplacian方程三点奇异边值问题正解的存在性

本文应用不动点指数理论,讨论了一类三阶p-Laplacian方程三点奇异边值问题正解的存在性,分别得到了这类边值问题至少存在一个和两个正解的充分条件.