Backscattering measurements from double-scale randomly rough surfaces

We present experimental measurements of light backscattered from double-scale randomly rough surfaces (oceanlike surfaces) with different statistical parameters illuminated at small and large angles of incidence. The surfaces are composed of a small-scale roughness superimposed on a slowly (large-scale) varying surface. The large-scale surfaces are diamond-machined periodic surfaces made on aluminum substrates and have either a sinusoidal or a Stokes wave profile. The small-scale roughness is added with lithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the backscattered light is strongly depolarized mainly at small angles of incidence and strong shadowing effects are present for large angles of incidence (θ(inc) > 60°).     

Light scattering by randomly rough isotropic dielectric surfaces

Abstract

An experimental investigation of the angular distribution of the light scattered by randomly rough, two-dimensional, isotropic dielectric surfaces is presented. The surfaces, whose profiles constitute good approximations to Gaussian random processes with Gaussian correlation functions, are fabricated in a photoresist and characterized by means of a mechanical profilometer. The substrates employed in the fabrication of the samples consist of thick parallel plates of filter glass that absorb the incident light and whose refractive index is close to that of the photoresist. This allows us to approximate experimentally a situation in which the light is scattered by a randomly rough interface between two semi-infinite dielectric media, illuminated from the air side. The results display features that can be attributed to multiple scattering. In particular, significant amounts of cross-polarized scattered light, as well as an enhanced backscattering peak, were observed in the scattering measurements.     

Coherent scattering by one-dimensional randomly rough metallic surfaces

A critical evaluation of various theoretical techniques for calculating the reflectivity of one-dimensional metallic randomly rough surfaces is presented. We proceed by comparing experimental and rigorous numerical results with those obtained with three perturbation theories and the Kirchhoff approximation. The samples were fabricated in photoresist, and their metallized surface profiles constitute good approximations to Gaussian-correlated, Gaussian random processes. The correlation lengths of these surfaces range from approximately one third to approximately three times the infrared wavelengths employed. The results show that the phase-perturbation theory has wider applicability than the other perturbation theories and the results based on the Kirchhoff approximation.     

Scattering measurements on curved rough surfaces

Abstract

A theoretical model is developed to examine light scattered from a curved optical surface with a defined surface form. The contribution of the surface form to scattering patterns is separated from that of the surface roughness. Experiments are carried out on a curved surface. Measurements are analysed and compared with theoretical calculations. The power spectrum density function and the autocorrelation function of the surface roughness are recovered from the measured scattering pattern.     

Jumplike variation of the contact area between randomly rough surfaces

A numerical model of the contact between two solid surfaces with statistically random roughness has been considered. As the two surfaces are brought in contact and pressed against each other, the real contact area initially increases in proportion to the normal force, with a proportionality factor dependent on the spectral density of the surface profile. As the pressing force grows further, the contact area exhibits two sequential jumps. This behavior is universal, being manifested for various spectral densities of the surface roughness in both two-and three-dimensional cases. The physical reasons for the observed features and their role in the mechanics of contact between soft materials (rubber, biological tissues) are discussed. The effect can be used for creating new adhesive systems capable of exhibiting strong adhesion upon application of a critical pressing force.     

Influence of shadowing on ellipsometric quantities of randomly rough surfaces and thin films

In this paper the formulae enabling us to calculate the values of the ellipsometric parameters of randomly rough surfaces and very thin films with randomly rough boundaries with respect to the influence of the shadowing between the irregularities of roughness are presented. These formulae are derived within the scalar diffraction theory of light. The first formula allows the calculation of the ellipsometric parameters using a numerical method, while the second formula is the approximative one but it expresses the ellipsometric parameters in a closed form. The numerical analysis of both formulae is performed for several examples of randomly rough surfaces and thin films. Moreover, the comparison of the results achieved using both formulae respecting the shadowing and an earlier formula not including this effect is performed. The experimental data of two samples of the randomly rough silicon surfaces covered with very thin surface layers are interpreted using all the formulae mentioned. Using this experimental study, the correctness of both formulae taking into account the shadowing, is confirmed.     

Observation of light transmission through randomly rough glass surfaces beyond the critical angle

In this series of experiments we study the transmission of laser light through a randomly rough interface between air and ground-glass diffusers. We verify the refractive index suppression predicted by Dogariu and Boreman [Opt. Lett.21, 701 (1996)]. We also observe and quantify transmission beyond the critical angle for total internal reflection defined by Snell's law. In particular, these results may be applied to the ANITA experiment, which detects astrophysical neutrino interactions via radio waves produced under the ice. These radio waves must pass through the rough surfaces of the Antarctic ice sheets and shelves.     

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.     

Large-angle in-plane light scattering from rough surfaces

An in-plane light scattering setup that is capable of measuring large azimuthal scattering angles is presented. This type of measurement makes it easier to probe large k(parallel) at a fixed k(perpendicular) value (k(parallel) and k(perpendicular) are momentum transfer vectors parallel and perpendicular to the surface, respectively). Therefore the system allows us to explore small lateral scale and large vertical roughness (approximately lambda, the wavelength of the probe beam) of a rough surface. In-plane intensity measurements from a rough backside Si wafer and a Cu thin-film surface are reported. The structure factor that is related to surface roughness parameters is obtained from the measured in-plane intensity profiles. Both scalar (Beckmann-Kirchhoff) and vector (Rayleigh-Rice) theories have been applied to interpret the experimental data. The roughness parameters obtained from the scattering measurements are compared with those measured by atomic-force microscopy.     

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.     

Experimental investigation of the contact mechanics of rough fractal surfaces

The nonstationary character of roughness is a widely recognized property of surface morphology and suggests modeling several solid surfaces by fractal geometry. In the field of contact mechanics, this demands novel investigations attempting to clarify the role of multiscale roughness during physical contact. Here we review the results we recently obtained in the characterization of the contact mechanics of fractal surfaces by depth-sensing indentation. One class of experiments was conducted on organic thin films, load-displacement curves being acquired by atomic force microscopy using custom-designed tips. Another class of experiments focused on well-defined crystalline and mechanically polished ceramic substrates probed by a traditional nanoindenter. We observed the first-loading cycle to be considerably affected by surface roughness. Plastic failure was found to dominate incipient contact while contact stiffness increased on decreasing fractal dimension and roughness. Our findings suggest fractal parameters to drive contact mechanics whenever the penetration depth is kept below the interface width.     

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.     

Statistics of specular points at a randomly rough surface

Statistical parameters are obtained for an ensemble of specular points at a randomly rough Gaussian statistically isotropic surface at normal incidence. The joint probability density functions (PDFs) of specular point heights and total curvatures are derived separately for maxima, minima, and saddle points. The joint PDFs of brightness and surface elevations of specular points of different types are obtained analytically in an explicit form.     

4He atom reflection from rough liquid4He surfaces

When an atom is evaporated from or added to a free liquid surface there is a density perturbation of the surface. We have detected this surface spoiling using a⁴He atomic beam at glancing angles to the surface. With a perfect free liquid surface some of the atoms reflect specularly and some condense. We find that the specular reflection coefficient decreases as the surface is spoiled by another beam of⁴He atoms. The degree of spoiling as measured by the decrease in reflectivity, is initially proportional to the spoiling beam flux, but at higher fluxes the spoiling saturates. A phenomenological model is developed to describe this behaviour.     

Monte Carlo simulation of the field back-scattered from rough surfaces

A novel approach for the simulation of the field back-scattered from a rough surface is presented. It takes into account polarization and multiple scattering events on the surface, as well as diffraction effects. The validity and usefulness of this simulation is demonstrated in the case of surface topology measurement.     

Speckle size of light scattered from slightly rough cylindrical surfaces

This research is an extension of the optical method of quality control presented in a previous paper [Appl. Opt. 39, 5811 (2000)] to the case of slightly rough cylindrical surfaces. Applying the Kirchhoff scalar diffraction theory yields an analytical expression of the autocorrelation function of the intensity scattered from slightly rough cylindrical surfaces. This function, which is related to speckle size and shape, is shown to depend on the surface correlation length, unlike for plane surfaces for which the speckle depends on the illuminated area only. The theoretical expression is compared with that for the speckle produced by the light scattered from a cylindrical bearing and from various high-quality wires, showing that the method allows the correlation lengths of high-quality cylindrical surfaces to be determined.