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.     

Imaging and Reconstruction for Rough Surface Scattering in the Kirchhoff Approximation by Confocal Microscopy

Abstract

Imaging of rough surfaces in confocal microscopy can be described using the concept of the three-dimensional (3D) coherent transfer function (CTF), which is developed on the basis of the Kirchhoff approximation. The 3D CTF is presented using a scalar but high-angle theory. Methods for reconstruction of surface profiles are considered.     

Light Scattering by Composite Rough Surfaces

Abstract

Light scattering from a dielectric surface with composite roughness is considered, where the surface irregularities are modelled as a superposition of two roughness types of different length scales. Geometrical optics and the Rayleigh-Rice expansion, respectively, are employed in describing the scattering from the two roughness structures. Contrary to previous work, we concentrate on bistatic cross-sections, which are calculated analytically for scattering in the plane of incidence, and resulting plots for various parameter values are shown, especially for small-scale correlation lengths of the order of the wavelength of the incident light. The main effects of the small-scale roughness are an overall decrease of the coherent reflectance and a depolarization of the scattered light, which in the plane of incidence is not present for scattering from a surface with a single scale of roughness. It is, however, concluded that scattering at the surface and volume scattering have to be taken into account in order to explain the experimentally found degrees of depolarization.     

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.     

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.     

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.     

Thermal Image Approximation Using B-Spline Surfaces

This article presents a method of filtering thermal images by means of approximation using cubic B-spline patch surfaces. Approximation uses chord length parameterization with non-uniform distribution of knots, depending on the change rate of pixel values in rows and columns of the image. Advantages of approximation with such parameterization are compared with popular uniform parameterization. Presented method is very versatile and can be used for example in 3D surface topography of objects tested with stereoscopic microscopes, in resolution change of arbitrary images or modeling processes depending on two parameters. Filtering results are presented using plugin for the Soft4Image program, which was designed to unify different digital signal processing algorithms.     

Scattering from Gamma-distributed Surfaces

Abstract

We present a theoretical and experimental study of the scattering of light from diffusers with gamma-distributed surface height profiles. The theory is developed using a thin-phase screen model: it is shown that, following a steepest-descent method, the mean scattered intensity as a function of the scattering angle follows a modified Bessel K-function. The theory is compared with experimental data in the two extreme cases of the gamma distribution, namely the negative exponential and Gaussian cases. The surfaces used were made by exposing photoresist-coated plates with laser speckle patterns. For the case of a negative-exponential surface it is shown that it is not possible, in practice at least, to extinguish the specular component.     

Delta Function Boundary Operator Method for the Rigorous Solution of the Problem of Scattering from Rough Surfaces

Abstract

A rigorous method for computing the field scattered by a two-dimensional, perfectly conducting rough surface is introduced. This method leads to the calculation of a ψ-distribution which is the integral representation of the impedance operator. This calculation is completed by solving a DBO (delta boundary operator) problem using an integral equation. The ψ-distribution allows one to achieve the solution of a large class of scattering problems by a simple integration, whatever the incident field. Numerical results are shown to be very accurate and it will be seen that the method appears to be very capable of generalization to three-dimensional problems of scattering.     

Wave Scattering from Fractal Surfaces

Abstract

In this paper, a normalized band-limited Weierstrass function is presented for modelling 2D fractal rough surfaces. Some conventional statistical parameters, namely the root mean square and the correlation length of rough surfaces, are used to assess between fractal parameters and the roughness of surfaces. An analytic solution of the scattered light field from these fractal surfaces is derived based on Kirchhoff theory. Three statistical parameters, namely the average scattering coefficient, the average intensity of scattered field, and the root mean square of scattered field, are introduced to study the influence of various fractal parameters on the scattered field by theoretical analysis and numerical calculations.     

Second- and Higher-order Scattering of Electromagnetic Waves by a Rough Metal Surface

The scattering of a plane monochromatic wave by a rough metal surface with imperfections comparable with the wavelength is evaluated by an iterative method.     

Scattering from infinitely sloped surfaces by use of the Kirchhoff approximation

A simple reformulation of the double-scatter Kirchhoff approximation is presented to extend the use of this calculation method to infinitely sloped surfaces. Examples are presented for square grooves and lines on perfectly conducting surfaces. The results presented show the accuracy of the method and the errors produced by not including higher-order scattering in the calculations.     

The Possibility of Using Rail-Gun Arcs for Cleaning Metal Surfaces

Results are given of theoretical and experimental investigations of the physical characteristics of a free electric arc moving in a self-magnetic field along metal surfaces of different shapes contaminated by dielectric deposits. Similarly to welding, a direct-action arc is used, when the material being cleaned is one of the electrodes stabilizing the electric arc. Compared to plasmotrons, a facility using rail-gun arcs may exhibit a higher specific heat flux. This enables one to attain higher efficiency and capacity by reducing the loss of heat for heating the plate to be cleaned. Experiments are performed with steel samples contaminated by paraffin films. Data are obtained on the rate of arc propagation and its geometric characteristics, on the heat flux to the electrode being cleaned, on the cleaning capacity at different amplitudes of current, and on the thickness of paraffin coating. The basic possibility of removing dielectric deposits from metal surfaces with the aid of electric-arc treatment is demonstrated.     

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.     

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。     

The Eikonal Approximation to Near-forward Light Scattering from Homogeneous Spheres

The eikonal approximation and modified eikonal approximation are considered for near-forward light scattering from transparent homogeneous spheres of diameter 0·2-5·0 μm. Numerical comparisons with the exact theory are presented for values of relative refractive indices of less than 1·15. The implications of these results for sizing spherical particles are briefly discussed.     

随机结构粗糙表面的湿润性研究

依据荷叶表面具有的不规则自相似微纳双重结构,引入分形几何学构造类似荷叶的随机分形结构,建立相应的Cassie、Wenzel模型接触角方程,分析随机分形结构的分形维数和结构参数对其润湿性的影响。结果表明:分形结构表面的分形维数越大,结构越致密,接触角越大;分形结构中微/纳尺度参数之比越大,接触角也越大。然而,随机结构即使分形维数趋于最大的3.0,Wenzel模型表观接触角也不能达到超疏水的150°,Cassie模型最大表现接触角大于150°;更适合用于制备超疏水表面。     

广义近似空间与粗糙分类代数

提出了广义近似空间、粗近似公理、干扰集公理、粗糙集的分类原则、粗选原则、不确定偶集原则、精选原则、对策分类、量子逻辑分类、bit量子对称分类、不可比集、bit空间集、协议关系、粗糙集函数、粗糙分类代数和粗糙单代数等基本概念，并提出了一个猜想；展示了一些新观点；基于协议关系构造了粗糙商代数和粗糙子代数，给出了回避-归并算法及算例。