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.     

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.     

Diversity detection of speckles for double-wavelength interferometry on rough surfaces

When the topography of a rough surface is measured with a double-wavelength interferometer, the phase error of the signal corresponding to the synthetic wavelength increases in the vicinity of dark speckles. To overcome this problem we perform an amplitude-dependent averaging of the synthetic phase over independent speckles (diversity detection). We either use spatially neighboring speckles or in the case of depolarizing surfaces, we use speckles of the same spatial mode, but with orthogonal polarizations. For the latter case the lateral resolution stays unaffected. The reduction of the speckle noise is demonstrated experimentally for a laterally scanning double-wavelength interferometer with superheterodyne detection of the synthetic phase.     

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°).     

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.     

Study of the formation of contact between rough surfaces based on the particle method

A model is proposed for the rough surface of a solid based on the particle method. Although the particle size is selected arbitrarily in this study, the evolution of the actual area of contact and the change in stress at the points of contact show fairly good agreement with concepts derived from experimental investigations. The experiments show that as two surfaces converge, the pressure at the contacts is considerably higher than the nominal value, and this leads to plastic deformation of the surface layers much greater than the bulk deformation. The model clearly shows the controlling factors and how the stressed state of the surface layer is formed. The model can be used to analyze interaction between surfaces, not only for the stationary case, but also when these undergo relative displacement. Pis’ma Zh. Tekh. Fiz. 24, 28–32 (March 12, 1998)     

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.     

Experimental light-scattering measurements from large-scale composite randomly rough surfaces

We present experimental measurements of the angular distribution of light scattered from large-scale composite 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 microlithographic techniques, and the surfaces are then gold coated. For a linearly polarized incident beam, it is found that the diffusely scattered light is strongly depolarized and that its pattern is rather different for each large-scale surface profile. Enhanced backscattering is also observed.     

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.     

Near-field intensity distribution of waves scattered from slightly rough surfaces

The near fields of electromagnetic waves scattered from two-dimensional slightly rough surfaces are studied by using the stochastic functional approach. The correlation coefficient between the surface and the intensity of the scattered-wave field is investigated to estimate the fidelity of near-field intensity images. We show that the fidelity depends on both the polarization and the angle of incidence and that high fidelity can be obtained by a TM-polarized incident wave whose incident angle is not close to the critical angle of the total reflection.     

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.     

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.     

Refrigeration aspects of magnetic particle suspensions

This study examines the feasibility of using magnetic particles in liquid suspension as a working fluid to achieve room temperature refrigeration with a permanent magnetic field source. Potential advantages include facilitation of regenerative heat transfer while avoiding wear, drag, and leakage problems of mechanical sliding seals associated with the use of a solid magnetic working substance. Rheological properties are evaluated in defining an appropriate composition, and performance estimates developed for a conceptual embodiment.     

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.     

Study of speckle size of light scattered from cylindrical rough surfaces

The autocorrelation function of the intensity scattered from cylindrical rough surfaces is analytically obtained with the Kirchhoff scalar diffraction theory. It is shown that, in contrast to the case in which planar rough surfaces scatter radiation, this function, related to the speckle size, depends on the statistical parameters that characterize the surface and on the scattering direction. This result suggests a new, to our knowledge, optical method that can be applied to the characterization of cylindrical rough surfaces, such as in on-line quality assessment, in manufacturing processes. The calculated theoretical expression was tested, showing good agreement with experiments.     

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.     

Characterization of random rough surfaces from scattered intensities by neural networks

Abstract

Optical scatterometry, a non-invasive characterization method, is used to infer the statistical properties of random rough surfaces. The Gaussian model with rms-roughness [sgrave] and correlation length σ is considered in this paper but the employed technique is applicable to any representation of random rough surfaces. Surfaces with wide ranges of Λ and σ, up to 5 wavelengths (λ), are characterized with neural networks. Two models are used: self-organizing map (SOM) for rough classification and multi-layer perceptron (MLP) for quantitative estimation with nonlinear regression. Models infer Λ and σ from scattering, thus involving the inverse problem. The intensities are calculated with the exact electromagnetic theory, which enables a wide range of parameters. The most widely known neural network model in practise is SOM, which we use to organize samples into discrete classes with resolution ΔΛ = Δσ = 0.5λ. The more advanced MLP model is trained for optimal behaviour by providing it with known parts of input (scattering) and output (surface parameters). We show that a small amount of data is sufficient for an excellent accuracy on the order of 0.3λ and 0.15λ for estimating Λ and σ, respectively.