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.     

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.     

表面功能特性分形分析

表面分形分析已开展多年,虽然在涉及制造过程控制方面时出现过一些争论,但已获得了许多有意义的结果与此同时,用分形来研究表面功能特性所取得的进展有限,其原因之一是,以前分形的重点在于功率谱,而不是对于空间更为敏感的自相关函数．基于此,笔者首次将分形参数引入到基于自相关系数的表面功能参数．进展有限的另一原因是,与表面功能相关的许多确定性实验没有将分形参数包含在参数集中,这主要是由于过去没有能够给出分形参数的表面光洁度仪器,从而失去了确定分形参数价值的可能性．文中提出了一种新的、简单的测量分形特性的方法,它不仅能够利用现有仪器,而且可以从已进行的测量中根据已有的数据快速评定分形特性．     

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.     

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.     

平面电磁波在非均匀等离子体柱上的散射研究

基于微分形式的麦克斯韦方程组,采用严格两点边值方法求解等离子体柱对入射平面波的散射问题.结合柱约束空间径向非均匀等离子体分布特征推导电磁波散射系数的数学模型,计算了不同入射波频率、等离子体频率、等离子体碰撞频率条件下散射场的分布.结果表明:电磁波的散射场由等离子体特征参数、入射波频率及极化方式共同决定;等离子体碰撞频率对平行极化波的散射场分布影响较大.     

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.     

Evanescent Wave Mixing on Nonlinear Surfaces

Abstract

The problem of using evanescent fields in nonlinear optics is discussed by employing results on quantization of evanescent waves. It is shown that the peculiar properties of the momentum of evanescent modes can be used to realize non-critical optical frequency mixing. In the first illustration, the case of surface second-harmonic generation is discussed. It is then shown that, in the case of difference-frequency generation, it is possible to generate a ‘completely evanescent mode’ which is ‘trapped’ by the surface, which becomes a two-dimensional waveguide.     

Investigation of the Heterogeneous Nucleation on Fractal Surfaces

Classical theory of heterogeneous nucleation has been developed with an implied hypothesis of smooth substrate surfaces; however, morphologies of any real substrate surfaces are generally complicated and demonstrate fractal characteristics. In this paper, the wettability between the embryo and the fractal substrate surface was discussed, and heterogeneous nucleation behaviors were theoretically analyzed. The result shows that the roughness factor of a fractal surface varies with the scale of the embryo. As a result, the fractal character of the substrate surface has important effects on heterogeneous nucleation behaviors. It has been shown that the energy barrier for heterogeneous nucleation of a non-wetting phase on a fractal rough surface increases with increasing fractal dimensions, and both the critical nucleus radius and the nucleation energy barrier decrease with increasing fractal dimensions for heterogeneous nucleation of a wetting phase on the fractal rough surface. For a non-wetting system, the critical nucleus radius shows a slight shift with changes of the intrinsic wetting angle, but for a wetting system, the critical nucleus radius shows an obvious change with decreasing intrinsic wetting angle, thus imposes a stronger effect on the heterogeneous nucleation behaviors.     

Fractal Properties of Fracture Surfaces in Steel 1045

In this work a study of the fractal properties of fracture surfaces in steel 1045 tested at different temperatures is performed. It is found that measured values of fractal dimension comply to a normal distribution; nevertheless the self-affine correlation length, _c , as well as other fracture parameters, possess notable variations with test temperature.     

Perimeter-Area Relation and Fractal Dimension of Fracture Surfaces

We have theoretically analysed the perimeter-area relation and simulated its application to measuring the fractal dimension of fracture surfaces. It is proved that the fractal dimension Dobtained by slit island method (SIM) is related to the dependence of measured area A(δ) ofthe slit island on yardstick δ. So in some cases, the dimension D obtained by SIM is dependenton yardstick and in other cases independent on yardstick δ. But in all cases, when δ→0 thedimension D obtained by SIM approaches the real fractal dimension (similar dimension) of coastline' of the island. We analysed some experimental data and found some new and interestingcharacteristics of crack propagation in steels.     

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.     

Wave Scattering from a Slightly Wavy Interface Between two Anisotropic Media

Wave scattcring from a periodic interface separating two anisotropic layers in a thick elastic plate is studied in the two-dimensional case. The problem is solved by replacing the exact boundary conditions, i.e. continuous displacement and traction on the wavy interface, by approximate first order conditions on a flat reference surface. Numerical results are presented for a number of cases and compared to the exact solution obtained by the null field approach. The conclusion is that the approximate method gives reasonably accurate results as long as the slope of the surface is small and the amplitude of the wavy surface is not too large compared to the wavelength of the incident wave.     

Fractal Nature of the Brittle Fracture Surfaces of Metal

We have studied the fracture surfaces of low-alloy low-perlite steel after impact bending tests and of aluminum wire after fatigue failure at different temperatures. We have established that the fracture surfaces after brittle destruction are fractal surfaces. On the basis of the fractal model of a crack and the determined fractal dimensionalities of the boundaries of fracture surfaces, we have evaluated the critical sizes of brittle cracks.__________Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 1, pp. 58 – 62, January – February, 2005.     

Remnant Fractal Structure at Sintered Crack Surfaces in Glass

This is to demonstrate that the Raman spectroscopic analysis allows one to estimate a size of residual ("unhealed") cracks from measurements of the fractal units dimensions in real space. In contrast to the microscopical fractal structure reported for cracks in glass ceramics (Mecholsky, Passoja and Feinberg-Ringel, 1989), we present the observation of fractals at the nanostructural scale.     

一种新的Bush型分形曲面及其维数

在Bush型分形曲线的基础上,首先构造了一种分形曲面,然后研究这种曲面的分形维数及光滑性。得到了曲面的Box维数,Packing维数的计算公式以及Hausdorff维数的下界估计式。     

粉末NBR-PVC共混型热塑性弹性体断裂面的分形维数

本文利用扫描电镜对粉末NBR-PVC共混型热塑性弹性体拉伸断面形貌进行了观察与分析;基于断面小岛周长-面积关系,测定了试样的断口分形维数,考察了NBR含量、拉伸断面分形维数、力学性能(拉伸强度、断裂伸长率、邵氏硬度)之间的关系。结果表明,NBR-PVC弹性体拉伸断面的分形维数随着NBR含量的增加而增加,当NBR含量超过29份后其分形维数呈下降趋势;分形维数与材料的拉伸强度、断裂伸长率和邵氏硬度变化关系一致。     

超细粉末团聚体分形结构的小角散射测量及分维表征

通过小角散射实验对多种超细粉末的团聚体结构进行了研究，发现分形形态是粉末团聚体的普遍特征。提出了用新的团聚参数分维来表征粉末的聚集程度。分析并讨论了分维与团聚状态、工艺条件和粉末性能的相互关系。