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.     

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.     

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.     

Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.     

Flow of architectural coatings on complex surfaces; theory and experiment

A mathematical model is developed to predict the three-dimensional time-dependent flow of a non-Newtonian shear-thinning liquid coating on a non-planar substrate. The model employs the lubrication approximation and other simplifications. Results are compared with experimental observation of the drainage flow out of an axisymmetric indentation in a vertical substrate. A straightforward experimental method is developed to capture quantitative measurements of the evolving free-surface shapes. Two different architectural paints are used. The agreement between theory and experiment is good overall; however, agreement is better for one of the paints, presumably due to inadequate rheological modeling of the other. Improved understanding of the coating flow of these liquids can be expected to lead to improved products and processes.     

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。     

Conductivity of thin metal slabs with rough surfaces

The electrical conductivity of a slab whose thickness is small compared to the free electron path is calculated. A boundary condition proposed previously by the author is used. This condition describes the electron scattering on a rough surface. The result differs from the well-known Dingle formula, since relaxation in the volume and on the surface is correlated for the nearly tangentially incident electrons and the specularity coefficient depends on the angle between the electron momentum and the surface.     

Planar two-dimensional Bragg resonators with corrugated surfaces: Theory and experiment

The electrodynamic properties of a planar two-dimensional Bragg resonator with two-dimensional distributed feedback were studied. A high selectivity of the resonator with respect to the longitudinal and the transverse mode indices is demonstrated, the mode spectrum being significantly dependent on the surface relief pattern of the resonator plates. The theoretical results are confirmed by measurements under “cold” conditions.     

Diffuse and specular reflectance from rough surfaces

We present a reflection model for isotropic rough surfaces that have both specular and diffuse components. The surface is assumed to have a normal distribution of heights. Parameters of the model are the surface roughness given by the rms slope, the albedo, and the balance between diffuse and specular reflection. The effect of roughness on diffuse reflection is taken into account, instead of our modeling this component as a constant Lambertian term. The model includes geometrical effects such as masking and shadowing. The model is compared with experimental data obtained from goniophotometric measurements on samples of tiles and bricks. The model fits well to samples with very different reflection properties. Measurements of the sample profiles performed with a laser profilometer to determine the rms slope show that the assumed surface model is realistic. The model could therefore be used in machine vision and computer graphics to approximate reflection characteristics of surfaces. It could also be used to predict the texture of surfaces as a function of illumination and viewing angles.     

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.     

S. sanguinis adhesion on rough titanium surfaces: Effect of culture media

Bacterial colonization plays a key role in dental implant failure, because they attach directly on implant surface upon implantation. Between different types of bacteria associated with the oral environment, Streptococcus sanguinis is essential in this process since it is an early colonizer. In this work the relationship between titanium surfaces modified by shot blasting treatment and S. sanguinis adhesion; have been studied in approached human mouth environment. Bacteria pre-inoculated with routinary solution were put in contact with titanium samples, shot-blasted with alumina and silicon carbide, and adhesion results were compared with those obtained when bacteria were pre-inoculated with modified artificial saliva medium and on saliva pre-coated titanium samples. Our results showed that bacterial adhesion on titanium samples was influenced by culture conditions. When S. sanguinis was inoculated in routinary culture media, colonies forming unities per square millimeter presented an increment correlated with roughness and surface energy, but separated by the type of particle used during shot-blasting treatment; whereas in modified artificial saliva only a relationship between bacteria adhered and the increment in both roughness and surface energy were observed, regardless of the particle type. Finally, on human saliva pre-coated samples no significant differences were observed among roughness, surface energy or particle.     

Compressive imaging of subwavelength structures: periodic rough surfaces

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.     

Investigation of rough surfaces and transparent birefringent samples with Mueller-matrix scatterometry

Measurements made with an automated angle-resolved Mueller-matrix scatterometer are described. The instrument uses incident-polarization electro-optical modulation, division-of-amplitude photopolarimetry, and software-implemented Fourier-transform analysis of the detected signals to determine the scattered Mueller matrix of the sample. The measurement time is approximately 1 s per scattering angle. Applications to the control of surface roughness and structure on rough steel sheets (galvanized and uncoated) and of the properties of transparent birefringent optical elements (liquid-crystal devices) are discussed.     

Analysis of finite journal bearings with longitudinal and transversal rough surfaces

This paper represents a numerical iterative scheme for calculation of finite 360° journal bearings with longitudinal and transversal rough surfaces. A modified Christensen's Reynolds type equation is solved numerically under isothermal boundary condition. The Reynold's boundary condition assuming that the pressure and its derivative vanish near the point of location of the minimum film thickness is used in an iterative scheme to find out this location. Results of the analysis show the great influence of surface roughness on the bearing behaviour, especially when the bearing operates at its hydrodynamic limit.