Second-order perturbation theory for scattering from heterogeneous rough surfaces

We propose a model to calculate scattering from inhomogeneous three-dimensional, rough surfaces on top of a stratified medium. The roughness is made up of an ensemble of deposits with various shapes and permittivities whose heights remain small with respect to the wavelength of the incident light. This geometry is encountered in the remote sensing of soil surfaces, or in optics wherever there are contaminated planar components. Starting from a volume-integral equation involving the Green's tensor of the stratified medium, we derive a height-perturbative expansion up to second-order. Our formulation, which depends explicitly on the profiles of each deposit and on the Fresnel coefficients of the layered substrate, accounts for double-scattering events and permits an evaluation of depolarization in the plane of incidence. Comparisons with rigorous calculations in the simplified case of two-dimensional geometries are presented. It is shown that the second-order scattering term can be much more important for heterogeneous surfaces than for their homogeneous counterparts.     

Hyperhydrophilic rough surfaces and imaginary contact angles

The complete wetting of rough surfaces is only poorly understood, since the underlying phenomena can neither be described by the Cassie‐Baxter nor the Wenzel equation. An experimental accessiblility by the sessile drop method is also very limited. The term “superhydrophilicity” was an attempt to understand the wetting of rough surfaces, but a clear definition is still forthcoming, mainly because non‐superhydrophilic surfaces can also display a contact angle of zero. Since the Wilhelmy balance is based on force measurements, it offers a technology for obtaining signals during the whole wetting process. We have obtained evidence that additional forces occur during the complete wetting of rough surfaces and that mathematically contact angles for a hydrophilicity beyond the contact angle of zero can be defined by imaginary numbers. A hydrophilized TPS‐surface obtained by chemical wettability switching from a superhydrophobic surface has been previously characterized by dynamic imaginary contact angles of 20i°–21i° and near‐zero hysteresis. Here an extremely high wetting rate is demonstrated reaching a virtual imaginary contact angle of Θ_V,Adv > 3.5i° in less than 210 ms. For a rough surface displaying imaginary contact angles and extremely high wetting rates we suggest the term hyperhydrophilicity. Although, as will be shown, the physical basis of imaginary contact angles is still unclear, they significantly expand our methodology, the range of wettability measurements and the tools for analyzing rough hydrophilic surfaces. They may also form the basis for a new generation of rationally constructed medicinal surfaces.     

Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces

A recursive solution of the small-perturbation method for rough surface scattering is presented. These results permit fourth- and higher-order corrections to rough surface scattering coefficients to be determined in a form that explicitly separates surface and electromagnetic properties. Sample results are presented for the fourth-order correction to the specular reflection coefficient of a rough surface and the sixth-order correction to incoherent scattering cross sections.     

Scattering-reduction effect with overcoated rough surfaces: theory and experiment.

We show that a scattering-reduction effect is obtained by coating a rough surface with an antireflection layer. This research is a generalization of Amra's [J. Opt. Soc. Am. A 10, 365-374 (1993)] study of smooth surfaces conducted with a first-order theory to the case of rough surfaces. We show that the differential method with the R matrix algorithm can be used to study scattering from multilayered rough surfaces. A comparison between numerical and experimental results is given.     

A direct differentiation formulation of electromechanical sensitivity analysis for rough surfaces in contact

In this article, the electromechanical sensitivity analysis of a rough surface contact law with respect to its governing parameters is developed using the direct differentiation method. The numerical accuracy of the method is assessed in two numerical examples. Finally, the identifiability of surface roughness parameters using an inverse method based on numerical optimization is investigated using pseudo-experimental input data.     

粗糙表面可见光散射特性的实验研究

为了获得目标材料表面的散射参数,设计了一种测量粗糙表面散射特性的实验装置,并对几种材料进行了测量.激光器发出的激光经样品反射散射后,被探测器接收,转动转台,完成在入射平面的测量.利用Matlab对实验数据曲线拟合,给出了材料表面散射特性的数学表达式.实验结果表明,散射特性与表面粗糙度和入射角相关.当以中大角度照射时,粗糙表面不再严格遵守朗伯余弦定律,出现非镜向峰值现象,且峰值随着入射角的增大而增大.     

General equations with small parameter for the theory of current synthesis on arbitrary nonclosed surfaces

The inverse problem of restoring the space of currents on an arbitrary perfectly conducting surface is solved in the most general form. General equations with small parameter describing the synthesis of currents on arbitrary unclosed surfaces are derived.     

Reflective liquid-crystal displays with asymmetric incident and exit angles

The 2 x 2 matrix methods are extended to calculate the optical behaviors of reflective liquid-crystal displays with asymmetric incident and exit angles. Both the unfolding method and the backward-eigenwave method are employed to derive the 2 x 2 matrix representations. The simulation results for symmetric incident and exit angles from these two methods are identical and agree well with those obtained from the 4 x 4 matrix method when the air-panel surface reflections are neglected. Further, the derived 2 x 2 matrix methods are applied to the asymmetric cases with different incident and exit angles. The simulated results on the normally black vertical alignment and normally white mixed-mode twisted nematic reflective displays show reasonably good agreement with the reported experimental data. In addition, a rubbing effect related to contrast values is observed and analyzed in asymmetric reflective cases. We also find that this effect has a significant influence on the contrast ratios once the difference between the incident and exit angles becomes large.     

Contact and frictional behavior of rough surfaces using molecular dynamics combined with fractal theory

The microcontact behavior of a copper asperity on a diamond plate was carried out using a molecular dynamics (MD) simulation with the parallel algorithms atom decomposition method. The results show that the dynamic frictional force had an oscillated behavior when the flat diamond plane slipped through the copper asperity. The contact load, contact area, dynamic frictional force, and dynamic frictional coefficient increased as the contact interference increased at a constant loading velocity. The dynamic frictional force and dynamic frictional coefficient increased as the sliding velocity increased. Furthermore, the microcontact behavior can be evaluated between a rigid smooth flat plane and a rigid smooth hemisphere to a deformable rough flat plane by combining the deformed behavior of the asperity obtained from MD results and the fractal and statistic parameters.     

High-order perturbation theory for light scattering from a rough metal surface.

The angular distribution of the mean diffuse intensity scattered from a metal surface with one-dimensional roughness is studied with perturbation theory. From an approach based on the reduced Rayleigh equations in p polarization, exact perturbation terms up to eighth order in the height parameter are developed for surface roughness consistent with a stationary Gaussian process. The theory is evaluated for a number of cases in which surface plasmon polariton excitation is significant and produces effects such as backscattering enhancement. For surface roughness having a wide Gaussian power spectrum, it is found that the high-order terms lead to roughness-induced broadening of the backscattering peak. For rectangular spectra, two cases are studied in which backscattering effects are due to sixth- and eighth-order terms; both cases provide good comparisons with previously unexplained experimental results. Further, because of an eighth-order term, the diffuse intensity is shown to contain a specular peak that also relies on polariton excitation. This new effect is studied in detail and is found to arise from the constructive interference of contributions produced by multiple-scattering processes, although the time-reversed paths that produce backscattering enhancement are not essential to the specular effect.     

Contours of constant minimum-reflectance and maximum-reflectance angles in the complex plane of a dielectric constant for incident light of arbitrary polarization

The reflectance of an absorbing medium for incident light of arbitrary polarization can exhibit two extrema at angles of incidence φ(max) and φ(min). The behavior of iso-φ(max) and iso-φ(min) contours in the complex plane of a dielectric constant for various incident polarizations is analyzed.     

基于分形理论的两粗糙表面接触的黏滑摩擦模型EI北大核心CSCD

两粗糙表面的接触本质上是大量微凸体的接触,具有复杂的力学行为,连接界面的力学建模是重要的科学问题。从微观角度出发,对单个微凸体进行接触分析,并考虑了微凸体相互作用造成的基底面的下降,根据分形理论积分,建立了整个接触面的法向接触模型。利用该模型,可确定在给定法向预紧载荷下微接触截面积的概率密度函数;根据Mindlin模型、Masing准则和分形理论,建立了两粗糙表面接触的切向载荷与切向位移的关系,并研究了不同参数对系统能量耗散的影响。数值仿真结果表明,能量耗散随分形维数D增大而增大,随分形粗糙度参数G及法向预紧力增大而降低。     

Ray model of light scattering by flake pigments or rough surfaces with smooth transparent coatings

We derive expressions for the intensity and polarization of light singly scattered by flake pigments or a rough surface beneath a smooth transparent coating using the ray or facet model. The distribution of local surface normals is used to calculate the bidirectional reflectance distribution function (BRDF). We discuss the different distribution functions that can be used to characterize the distribution of local surface normals. The light-scattering model is validated by measurements of the BRDF and polarization by a metallic flake pigmented coating. The results enable the extraction of a slope distribution function from the data, which is shown to be consistent over a variety of scattering geometries. These models are appropriate to estimate or predict the appearance of flake pigment automotive paints.     

Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles

Adhesive or repulsive forces contributed by both meniscus and viscous forces can be significant and become one of the main reliability issues when the contacting surfaces are ultra smooth, and the normal load is small, as is common for micro/nano devices. In this study, both meniscus and viscous forces during separation for smooth and rough hydrophilic and hydrophobic surfaces are studied. The effects of separation distance, initial meniscus height, separation time, contact angle and roughness are presented. Meniscus force decreases with an increase of separation distance, whereas the viscous force has an opposite trend. Both forces decrease with an increase of initial meniscus height. An increase of separation time, initial meniscus height or a decrease of contact angle leads to an increase of critical meniscus area at which both forces are equivalent. An increase in contact angle leads to a decrease of attractive meniscus force but an increase of repulsive meniscus force (attractive or repulsive dependent on hydrophilic or hydrophobic surface, respectively). Contact angle has a limited effect on the viscous force. For asymmetric contact angles, the magnitude of the meniscus force and the critical meniscus area are in between the values for the two angles. An increase in the number of surface asperities (roughness) leads to an increase of meniscus force; however, its effect on viscous force is trivial. A slightly attractive force is observed for the hydrophobic surface during the end stage of separation though the magnitude is small. The study provides a fundamental understanding of the physics of the separation process and it can be useful for control of the forces in nanotechnology applications.     

Computations of the Mueller matrix elements for scattering from layered structures with rough surfaces, with applications to optical detection

A full-wave method is used to evaluate the Mueller matrix elements for scattering from layered structures with random rough surfaces. These provide a database for applications in optical detection over a broad range of rough surface statistical parameters. They can be used to determine the optimal frequencies and incident angles that provide most reliable measurements for optical detection. The elements of the Mueller matrix that are most sensitive to medium parameters of the layered structures can also be identified. Contributions from individual terms of the full-wave solutions are shown to have distinct physical interpretations.     

Scattering by layered structures with rough surfaces: comparison of polarimetric optical scatterometer measurements with theory

A laboratory model of a layered structure with a rough upper surface (a glass microscope slide cut with a diamond saw) is used to obtain optical polarimetric data. Scatterometer measurements were made of all the Mueller matrix elements associated with light scattered in arbitrary directions. (A preliminary measurement of scattering from a smooth opaque gold film on a silicon wafer was used to validate the calculation of the Mueller matrix elements.) These measurements are compared with corresponding analytical solutions based on the full-wave approach. Physical interpretations of the analytical solutions that account for scattering upon reflection and transmission across rough interfaces are given in a companion paper. The agreement between calculations and measurements suggests that the full wave, polarimetric solutions can provide a reliable database for electromagnetic detection of rough surfaces in remote-sensing applications.     

小斜率近似方法分析粗糙界面声散射问题

利用小斜率近似方法计算了起伏海面的声散射特性,得到了具有高斯分布粗糙海面的平均反射系数（即镜反射系数）计算公式,并与微扰法和Kirchhoff近似做了比较,结果表明小斜率近似是一种非常有效的分析起伏表面散射特性的近似方法。最后讨论了海面镜反射系数随海面的不平整度（波浪的均方根高度）、声波频率和声波入射方向的变化关系,得出了只有在声波波长和起伏波浪高度可比拟时,才有明显的镜反射的结论。这为分析浅海目标声散射特性时,选择是否需要考虑海面（海底）所引起的多途效应提供了理论依据。