Anisotropic Rough Surfaces Research Articles

High Frequency Roughness Scattering from Various Rough Surfaces: Theory and Laboratory Experiments

The scattering strength of isotropic and anisotropic rough surfaces was experimentally and theoretically investigated for high frequencies about 500 kHz. Emphasis was placed on studying the response from three two-dimensional rough surfaces which roughness was either isotropic (characterized by a Gaussian distribution) or anisotropic (characterized by a modified-sine surface). Theoretical predictions rely on the first-order small slope approximation either including a Gaussian structure function or a quasi-periodic structure function. The combination of true data and theoretical results indicates the importance of taking into account the anisotropy of a surface in a scattering prediction process. It is shown that the scattering strength varies a lot depending on the propagation plane. In the longitudinal direction of ripples, scattering strength is mostly in the specular direction, whereas in the transversal direction of the ripples, the scattering strength is spread in a very different way related to the particular features of the ripples, with several maxima and minima independent of the specular direction. Contrary to the isotropic surface, the scattering strength from an anisotropic rough surface is modified from one propagation plane to another, which explains why the entire rough surface should be taken into account without any simplification as it is often seen when dealing with scattering models. Compared to such a surface, positions of the emitter and of the receiver are naturally significant when measuring scattering strength.

Modelling of High-Frequency Roughness Scattering from Various Rough Surfaces through the Small Slope Approximation of First Order

The first-order small slope approximation is applied to model the scattering strength from a rough surface in underwater acoustics to account for seafloor for high frequencies from 10 kHz to hundreds of kilohertz. Emphasis is placed on simulating the response from two-dimensional anisotropic rough surfaces. Several rough surfaces are described based on structure functions such as the particular sandy ripples shape. The scattering strength is predicted by the small slope approximation and is first compared to a well known bistatic method, interpolating the Kirchhoff approximation and the small perturbations model, assuming that the rough interface is isotropic. Results obtained from the two different models are similar and show a higher level in the specular direction than in the other directions. For an isotropic surface, changing the propagation plane gives similar results. Then, SSA, which lets us adapt the structure function of the roughness straight away, is tested trough several anisotropic surfaces. In a longitudinal direction of ripples, the scattering strength is mostly in the specular direction, whereas in the transversal direction of ripples, the scattering strength prediction shows high values for different angular directions. Thus the scattering strength is spread in a very different way strictly related to the particular features of the ripples. Combine our results, indicates the importance of taking into account the anisotropy of a surface in a scattering prediction process, taking into account the positions of the emitter and of the receiver which are naturally significant when predicting scattering strength.

Light Scattering of Rough Orthogonal Anisotropic Surfaces with Secondary Most Probable Slope Distributions

We study the light scattering of an orthogonal anisotropic rough surface with secondary most probable slope distribution. It is found that the scattered intensity profiles have obvious secondary maxima, and in the direction perpendicular to the plane of incidence, the secondary maxima are oriented in a curve on the observation plane, which is called the orientation curve. By numerical calculation of the scattering wave fields with the height data of the sample, it is validated that the secondary maxima are induced by the side face element, which constitutes the prismoid structure of the anisotropic surface. We derive the equation of the quadratic orientation curve. Experimentally, we construct the system for light scattering measurement using a CCD. The scattered intensity profiles are extracted from the images at different angles of incidence along the orientation curves. The experimental results conform to the theory.

Contact Analysis for Joint Interfaces of Machine Tools Based on a 3-D Anisotropic Asperity Model

In this paper, a 3-D contact model for anisotropic rough surfaces based on 3-D statistically measurements is established and finite element contact analysis is conducted. The average height of the asperity (h), the average summit distances between two neighboring peaks of asperities (Sx and Sy) are selected as the characterized parameters of the rough surface. Finite element simulation results show that the normal contact pressure has an exponential relation with the normal deformation and an exact linear relationship between the normal deformation and the real contact pressure of the surfaces is obtained. At last, the normal contact stiffness of the joint interface is obtained empirically with the exponential relationship assumption.

Anisotropic charge transport in nonpolar GaN quantum wells: Polarization induced line charge and interface roughness scattering

Charge transport in GaN quantum well (QW) devices grown in non-polar direction has been theoretically investigated . Emergence of anisotropic line charge scattering mechanism originating as a result of anisotropic rough surface morphology in conjunction with in-plane built-in polarization has been proposed. It has shown that in-plane growth anisotropy leads to large anisotropic carrier transport at low temperatures. At high temperatures, this anisotropy in charge transport is partially washed out by strong isotropic optical phonon scattering in GaN QW.

Perception of illuminance flow in the case of anisotropic rough surfaces

Perception of illuminance flow in the case of anisotropic rough surfaces

Statistical Models of Rough Surfaces for Finite Element 3D-Contact Analysis

The present study is divided in two parts. In the first one the complete elasto-plastic microcontact model of anisotropic rough surfaces is given. Rough surfaces are modelled as a random process in which the height of the surface is considered to be a two-dimensional random variable. It is assumed that the surface is statistically homogeneous. The description of anisotropic random surfaces is concentrated on strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids. The model is based on the volume conservation of asperities with the plasticity index modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a combination of the elastic, elasto-plastic and plastic components. The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness. The part two deals with the solution of the fully three-dimensional contact/friction problem taking into account contact stiffnesses in the normal and tangential directions. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two numerical examples are selected to show applicability of the method proposed.

Perception of illuminance flow in the case of anisotropic rough surfaces

Human observers estimate the illumination direction of rough surfaces rather precisely. When surfaces are rough, the illumination generates visible "texture" from differential shading at the level of the roughness, whereas differential illumination at the level of significant global surface curvature leads to the more familiar "shading". The shading is used in conventional shape-from-shading (SFS) algorithms, which ignore the illumination texture cue. Because of this simplification, SFS algorithms are typically formulated as global problems (partial differential equations, etc.). Human observers are likely to apply different methods than do these conventional SFS algorithms, however. When the roughness is not isotropic, one expects systematic errors in the visual detection of illumination direction, conceivably giving rise to erroneous shape estimates. Here we addressed this issue through systematic psychophysics on illumination direction detection as a function of the roughness anisotropy. Our expectations were fully borne out, in that the observers committed the predicted systematic errors. These results are precise enough to allow the inference that illumination direction detection is based on second-order statistics--that is, of edge detector (rather than line detector) activity.

Droplets on inclined rough surfaces

The behaviour of liquid droplets on inclined heterogeneous surfaces was simulated by the lattice-Boltzmann method using the Shan-Chen multiphase model. The effect of topography of the surface on the contact angle hysteresis was investigated. It is shown in particular, by using anisotropic rough surfaces, how surface topography and thereby the continuity of the three-phase contact line, affect this hysteresis. Our results clearly indicate that the superhydrophobicity of a surface cannot be judged by the contact angle alone.

Geometrical considerations in analyzing isotropic or anisotropic surface reflections

The bidirectional reflectance distribution function (BRDF) represents the evolution of the reflectance with the directions of incidence and observation. Today BRDF measurements are increasingly applied and have become important to the study of the appearance of surfaces. The representation and the analysis of BRDF data are discussed, and the distortions caused by the traditional representation of the BRDF in a Fourier plane are pointed out and illustrated for two theoretical cases: an isotropic surface and a brushed surface. These considerations will help characterize either the specular peak width of an isotropic rough surface or the main directions of the light scattered by an anisotropic rough surface without misinterpretations. Finally, what is believed to be a new space is suggested for the representation of the BRDF, which avoids the geometrical deformations and in numerous cases is more convenient for BRDF analysis.

Directional radiative properties of anisotropic rough silicon and gold surfaces

Recent studies have shown that the topography of some chemically etched microrough silicon surfaces is non-Gaussian and may be strongly anisotropic. However, the bidirectional reflectance distribution function (BRDF) of anisotropic surfaces has not been fully understood. The present study uses the Monte Carlo method to investigate the out-of-plane BRDF, multiple scattering, and the change of the polarization state upon reflection. Two ray-tracing algorithms are developed that incorporate the surface topography or slope distribution of the samples obtained by the use of an atomic force microscope. The predicted BRDFs for silicon surfaces with or without a gold coating are in reasonable agreement with the results measured using a laser scatterometer at a wavelength of 635 nm. The employment of surface topographic data is indispensable to the BRDF modeling of anisotropic surfaces. While first-order scattering makes the dominant contribution to reflections from the studied surfaces, it is critical to consider the polarization state change in order to correctly predict the out-of-plane BRDF. The versatile Monte Carlo modeling tools developed through the present study help gain a better understanding of the directional radiative properties of microrough surfaces and, furthermore, will have an impact on thermal metrology in the semiconductor industry.

Measurement and Modeling of the Bidirectional Reflectance of SiO2 Coated Si Surfaces

An understanding of the variation of directional radiative properties of rough surfaces with dielectric coatings is important for temperature measurements and heat transfer analysis in many industrial processes. An experimental study has been conducted to investigate the effect of coating thickness on the bidirectional reflectance distribution function (BRDF) of rough silicon surfaces.Silicon dioxide films with thicknesses of 107.2, 216.5, and 324.6 nm were deposited using plasma-enhanced chemical vapor deposition onto the rough side of two Si wafers. The wafer surfaces exhibit distinct anisotropic characteristics as a result of chemical etching during the manufacturing process. A laser scatterometer measures the BRDF at a wavelength of 635 nm, after improvement of the signal-to-noise ratio. The slope distribution function obtained from the measured BRDF of uncoated Si surfaces was used in an analytical model based on geometric optics for rough surface scattering and thin-film optics for microfacet reflectance. The predicted BRDFs are in reasonable agreement with experimental results for a large range of coating thicknesses. The limitations of the geometric optics for modeling the BRDF of coated anisotropic rough surfaces in the specular direction are demonstrated. The results may benefit future radiative transfer analysis involving complicated surface microstructures with thin-film coatings.

Elasto-plastic statistical model of strongly anisotropic rough surfaces for finite element 3D-contact analysis

The complete elasto-plastic microcontact model of anisotropic rough surfaces is proposed. The description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain. The present model is based on the volume conservation of asperities in which the plasticity index is modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a mixture of both the elastic and plastic components. For low nominal pressures both the elastic and elasto-plastic contact stiffness is found to be almost linear in relation to the normal load. The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness.

Unpolarized infrared emissivity with shadow from anisotropic rough sea surfaces with non-Gaussian statistics

The emissivity of two-dimensional anisotropic rough sea surfaces with non-Gaussian statistics is investigated. The emissivity derivation is of importance for retrieval of the sea-surface temperature or equivalent temperature of a rough sea surface by infrared thermal imaging. The well-known Cox-Munk slope probability-density function, considered non-Gaussian, is used for the emissivity derivation, in which the skewness and the kurtosis (related to the third- and fourth-order statistics, respectively) are included. The shadowing effect, which is significant for grazing angles, is also taken into account. The geometric optics approximation is assumed to be valid, which means that the rough surface is modeled as a collection of facets reflecting locally the light in the specular direction. In addition, multiple reflections are ignored. Numerical results of the emissivity are presented for Gaussian and non-Gaussian statistics, for moderate wind speeds, for near-infrared wavelengths, for emission angles ranging from 0 degrees (nadir) to 90 degrees (horizon), and according to the wind direction. In addition, the emissivity is compared with both measurements and a Monte Carlo ray-tracing method.

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: II. comparison with numerical results

This second part presents illustrative examples of the model developed in the companion paper, which is based on the first- and second-order optics approximation. The surface is assumed to be Gaussian and the correlation height is chosen as anisotropic Gaussian. The incoherent scattering coefficient is computed for a height rms range from 0.5λ 1λwhere λ is the electromagnetic wavelength), for a slope rms range from 0.5 to 1 and for an incidence angle range from 0 to 70°. In addition, simulations are presented for an anisotropic Gaussian surface and when the receiver is not located in the plane of incidence. For a metallic and dielectric isotropic Gaussian surfaces, the cross- and co-polarizations are also compared with a numerical approach obtained from the forward.backward method with a novel spectral acceleration algorithm developed by Torrungrueng and Johnson (2001, JOSA A 18). (Some figures in this article are in colour only in the electronic version)

Multiple scattering in the high-frequency limit with second-order shadowing function from 2D anisotropic rough dielectric surfaces: I. Theoretical study

In this paper the first- and second-order Kirchhoff approximation is applied to study the backscattering enhancement phenomenon, which appears when the surface rms slope is greater than 0.5. The formulation is reduced to the geometric optics approximation in which the second-order illumination function is taken into account. This study is developed for a two-dimensional (2D) anisotropic stationary rough dielectric surface and for any surface slope and height distributions assumed to be statistically even. Using the Weyl representation of the Green function (which introduces an absolute value over the surface elevation in the phase term), the incoherent scattering coefficient under the stationary phase assumption is expressed as the sum of three terms. The incoherent scattering coefficient then requires the numerical computation of a ten- dimensional integral. To reduce the number of numerical integrations, the geometric optics approximation is applied, which assumes that the correlation between two adjacent points is very strong. The model is then proportional to two surface slope probabilities, for which the slopes would specularly reflect the beams in the double scattering process. In addition, the slope distributions are related with each other by a propagating function, which accounts for the second-order illumination function. The companion paper is devoted to the simulation of this model and comparisons with an ‘exact’ numerical method.

Contact between a smooth microsphere and an anisotropic rough surface

This article discusses the effects of asperities on elastic and adhesive contact between a smooth sphere and a rough surface. Two numerical methods are introduced: an asperity-superposition method and a direct-simulation method. In the first method, geometric parameters such as asperity heights, orientations, and radii of curvature are identified by a least-squares regression of neighboring surface heights measured using an atomic force microscope. The rough surface is reconstructed by the superposition of these asperities. The modeling of adhesive and elastic contacts begins with the modeling of a single parabolic-shaped asperity contact. A generalized JKR model for an arbitrary parabola is developed to suit this purpose. The contact between the rough surface (represented by the supposition of parabolic-shaped asperities) and the sphere consequently is modeled bythe mapping and integration of individual asperity contacts. In the second method, pure-elastic contact is modeled by half-space elastic theory. A contact-search algorithm is used to find solutions on the displacement and the contact-pressure distribution that satisfy both the load-displacement equation and the contactboundary conditions. Results from both methods are compared to reveal the effects of asperities on adhesion and elastic-contact pressure.

Shadowing function with single reflection from anisotropic Gaussian rough surface. Application to Gaussian, Lorentzian and sea correlations

In this paper, the monostatic (transmitter and receiver are located at the same place) and bistatic (transmitter and receiver are distinct) statistical shadowing functions from an anisotropic two-dimensional randomly rough surface are presented. This parameter is especially important in the case of grazing angles for computing the bistatic scattering coefficient in optical and microwave frequencies. The objective of this paper is to extend the previous work (Bourlier C, Berginc G and Saillard J 2002 Waves Random Media 12 145–74), valid for a one-dimensional surface, to a two-dimensional anistropic surface by considering a joint Gaussian process of surface slopes and heights separating two points of the surface. The monostatic average (statistical shadowing function average over the statistical variables) shadowing function is then performed in polar coordinates with respect to the incidence angle, the azimuthal direction and the surface height two-dimensional autocorrelation function. In addition, for a bistatic configuration, it depends on the incidence angle and azimuthal direction of the receiver. For Gaussian and Lorentzian correlation profiles and practically important power-type spectra such as the Pierson–Moskowitz sea roughness spectrum, the numerical solution, obtained from generating the surface Gaussian elevations (Monte Carlo method), is compared with the uncorrelated and correlated models. The results show that the correlation underestimates the shadow slightly, whereas the uncorrelated results weakly overpredict the shadow and are close to the numerical solution.

Statistical model of strongly anisotropic rough surfaces for finite element contact analysis

Statistical model of strongly anisotropic rough surfaces for finite element contact analysis

A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfaces

We generalize the so-called wavelet transform modulus maxima (WTMM) method to multifractal image analysis. We show that the implementation of this method provides very efficient numerical techniques to characterize statistically the roughness fluctuations of fractal surfaces. We emphasize the wide range of potential applications of this wavelet-based image processing method in fundamental as well as applied sciences. This paper is the first one of a series of three articles. It is mainly devoted to the methodology and to test applications on random self-affine surfaces (e.g., isotropic fractional Brownian surfaces and anisotropic monofractal rough surfaces). Besides its ability to characterize point-wise regularity, the WTMM method is definitely a multiscale edge detection method which can be equally used for pattern recognition, detection of contours and image denoising. Paper II (N. Decoster, S.G. Roux, A. Arneodo, to be published in Eur. Phys. J. B 15 (2000)) will be devoted to some applications of the WTMM method to synthetic multifractal rough surfaces. In paper III (S.G. Roux, A. Arneodo, N. Decoster, to be published in Eur. Phys. J. 15 (2000)), we will report the results of a comparative experimental analysis of high-resolution satellite images of cloudy scenes.