利用散斑图像测量表面粗糙度的计算机模拟及实验

从菲涅耳-基尔霍夫衍射公式出发推导出了粗糙面近场衍射方程。通过对观察面散斑光强统计特性的分析,提出了采用镜射光强分量法测量表面粗糙度的思想。为验证该方法的有效性,首先用计算机模拟产生具有不同统计特性的随机表面,然后对由随机表面产生的散斑场及其光强分布进行计算。计算结果表明,与传统的散斑对比度法相比,散斑镜射光强分量法测量弱粗糙表面粗糙度具有更大的适用范围和更高的测量精度,克服了散斑对比度法易受表面横向相关长度影响的缺点。通过实验对计算机模拟结果进行了验证。     

Numerical computation of in-plane displacements and their detection in the near field by double-exposure objective speckle photography

A model of a rough surface to the scale of the optical wavelength is proposed, with randomly distributed zero-mean Gaussian heights. It is assumed that the aforesaid surface is illuminated by a coherent light beam of homogeneous intensity. An in-plane pure translation of this surface is simulated on a PC by means of the Matlab program. In the near-field optical regions the Fraunhofer approximation and the subsequent FFT are not suitable for application in the generation of a speckle pattern. Hence, with the aim of calculating the translation of the rough surface by means of double-exposure objective speckle photography using the point-wise filtering technique (PWFT), the Fresnel-Kirchhoff integral is first employed to obtain the speckle intensity near the surface on a photographic plate, and then the intensity pattern produced by the diffraction of the plate is determined in the far field (Fraunhofer), which suffices to calculate the modulus of displacement through the Young’s fringes. The results are analyzed according to surface roughness and the sample distance to the recording plane.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

Wave diffraction by a concave statistically rough surface

Abstract

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the ‘two-scale’ scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Statistical study of the radiation losses due to surface roughness for a dilectric slab deposited on a metal substrate

This paper presents an original method of analyzing radiation loss from dielectric slab with random wall imperfections. The method is based on Maxwell’s equations under their covariant form written in a non-orthogonal coordinate system. The solution is found by using a perturbation method applied to the smooth surface problem. The statistical characteristics of the radiation intensity, the average value and the probability density function, are analytically determined.     

Relation between statistical properties of surface roughness and the averaged speckle intensity in the diffraction field

A theoretical and experimental investigation is made on the relation between the statistical properties of a rough surface and the averaged speckle intensity in the diffraction field. The theoretical analysis is performed in some detail over a wide range of the random phase variation for various illuminated objects. The result gives an interpretation for the behavior of the averaged speckle intensity obtained experimentally for various states of rough surfaces.     

Characterization of chemically etched indium phosphide surfaces with light scattering

Scattering of light from chemically etched InP surfaces is studied in the present paper. A model is developed to describe the randomly rough surfaces produced by chemical etching and this model is used in a numerical simulation using the Kirchhoff approximation to calculate the scattered intensity distribution from the surfaces. Comparisons between the numerical results and experimental measurements for an incident wavelength of 633 nm show good agreement. Numerical simulation results are presented to show the variation of the scattered intensity distribution for surfaces with different times of chemical etching. These results are useful for characterization or control of this type of surface.     

Characterization of chemically etched indium phosphide surfaces with light scattering

Scattering of light from chemically etched InP surfaces is studied in the present paper. A model is developed to describe the randomly rough surfaces produced by chemical etching and this model is used in a numerical simulation using the Kirchhoff approximation to calculate the scattered intensity distribution from the surfaces. Comparisons between the numerical results and experimental measurements for an incident wavelength of 633 nm show good agreement. Numerical simulation results are presented to show the variation of the scattered intensity distribution for surfaces with different times of chemical etching. These results are useful for characterization or control of this type of surface.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

Statistics of travel time and intensity of two first arrivals of short pulses backscattered by a rough 3D surface

The time history of a pulse backscattered by a rough surface contains information about the position of the surface and the properties of the scatterers. This information is utilized successfully in a number of remote sensing techniques ranging from echo sounding of the ocean bottom to medical ultrasonics and satellite altimetry. In the current paper, statistical properties of backscattered waves are considered in a geometrical optics approximation. The probing pulse duration is assumed to be sufficiently short so that signals backscattered in the vicinity of individual specular points on a rough surface do not overlap in time. Theoretical results previously obtained for a 2D problem [I. M. Fuks and O. A. Godin, 2005, Waves in Random and Complex Media, 14, 539-562; M. I. Charnotskii and I. M. Fuks, 2005, Waves in Random and Complex Media, 15, 451-467] are extended to wave scattering by 3D rough surfaces by following a mathematical approach developed in stochastic geometry. Predictions of an asymptotic theory are verified against results of Monte-Carlo simulations. Probability density functions of travel times and intensities of the first and second arrivals of the backscattered wave are quantified in terms of statistical moments of roughness assuming normal distribution of elevations. It is found that, as in the 2D case, the travel time and the intensity are strongly correlated; on average, the earlier a signal arrives, the smaller is its intensity.     

Eigenvalue system for the scattering from rough surfaces - Saving in computation time by a physical approach

The curvilinear coordinate method is an efficient theoretical tool for analysing rough surfaces. It consists on solving Maxwell’s equations written in a nonorthogonal coordinate system. The C method leads to eigenvalue systems and the scattered fields can be expanded as a linear combination of eigensolutions. The boundary conditions allow the combination coefficients to be determined. The dominant computational cost for the C method is the eigenvalue problem solution which is of order of N³ where N is the size of eigenvalue systems. In this paper, we propose a new approach based on the association of the C method with the beam simulation method (BSM) in order to reduce the computational time. The BSM is based on decomposing a large incident beam into narrower subbeams and then synthesizing the large beam by coherent superposition. The adopted procedure consists of two stages. First, the surface fields are obtained by the C method associated with each elementary beam illuminating smaller surfaces. Second, the total surface field is deduced from a coherent superposition of elementary surface current densities. The far-field and the scattering coefficients are derived from the Huygens principle applied to the total surface fields. We confirm the efficiency and the validity of the approach and show that the BSM applied with the C method allows a significant saving in computation time.     

Scattering of electromagnetic radiation by surfaces with a fractal relief

The scattering indicatrix of electromagnetic waves for different types of rough surfaces and angles of incidence is calculated using the Kirchhoff scalar theory. The rough surfaces are modelled by a two dimensional Weierstrass function. The scattering index for a rough surface with a fractal relief is found to have a complicated structure with intensity bursts in directions quite far from the direction of mirror reflection.     

微粗糙圆柱的各向异性散斑特性研究

分析了高斯光束照射微粗糙圆柱在菲涅尔衍射区形成的散斑图像统计特性,给出了强度起伏自相关函数与表面曲率及粗糙程度等参数之间的关系.根据强度起伏自相关函数的离散化定义,实验并计算了圆柱轴向与径向结构有差异情况下的散斑强度起伏相关函数.结果表明,对于C1和C2圆柱沿垂直于圆柱轴向的散斑尺寸变长,强度起伏自相关函数沿平行和垂直于圆柱轴两个方向的波动相差较大;对于C3和C4圆柱两个方向上的散射特性基本相同;测量C1和C3的结果表明,散斑尺寸和形状依赖于圆柱表面的皱褶和圆柱表面曲率两个因素.研究结果对于如柱型管道、轴承等方面的机械制造的质量控制有重要的应用价值.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Considerations to Rayleigh’s hypothesis

In 1907 Lord Rayleigh published a paper on the dynamic theory of gratings. In this paper he presented a rigorous approach for solving plane wave scattering on periodic surfaces. Moreover he derived explicit expressions for a perfectly conducting sinusoidal surface, and for perpendicular incidence of the electromagnetic plane wave. This paper was criticized by Lippmann in 1953 for he assumed Rayleigh’s approach to be incomplete. Since this time there have been published several arguments, proofs, and discussions concerning the correctness and the range of validity of Rayleigh’s approach not only for plane wave scattering on gratings but also for light scattering on nonspherical structures, in general. In the paper at hand we will discuss the different point of views on what is called “Rayleigh’s hypothesis” as well as the relevance of a found theoretical limit for its validity. Furthermore we present a numerical treatment of the original scattering problem of a p-polarized plane wave perpendicularly incident on a perfectly conducting sinusoidal surface (i.e., the scalar Dirichlet problem). In doing so we emphasizes the near-field solution especially within the grooves of the grating up to points on the surface, and below the surface. Two different Green’s function formulations of Huygens’ principle are used as starting points. One of this formulation results in the general T-matrix approach which is considered to be affected by Rayleigh’s hypothesis especially for near-field calculations. The other formulation provides a conventional boundary integral equation which is in accordance with Lippmann’s point of view and free of problems with Rayleigh’s hypothesis. But the obtained results show that Lippmann’s argumentation do not withstand a critical numerical analysis, and that the independence of least-squares approaches from Rayleigh’s hypothesis, as understood and proven by Millar, seems to hold also for certain methods which does not fit into such an approach.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Investigation of Lamb elastic waves in anisotropic multilayered composites applying the Green’s matrix

This article presents a numerical study of dispersion characteristics of some symmetric and antisymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer. The authors introduce a subsidiary boundary problem of three-dimensional elasticity theory for the system of partial differential equations describing the harmonic oscillations of the composite caused by a surface load. The problem reduces to a boundary problem for ordinary differential equations by employing the Fourier transform. An algorithm of constructing the Fourier transform of the Green’s matrix of the given boundary problem is presented. The wave numbers of Lamb waves propagating in composites, their phase velocity surfaces and group wave surfaces are presented through the poles of the transform of the Green’s matrix. The authors obtain the dispersion curves for different directions and frequencies and investigate the dispersion curves and surfaces of wave numbers, phase velocities and group wave surfaces for various composites. The numerical results are then compared with the results obtained by applying other methods.     

样品表面银膜的粗糙度对钛酸钡微球成像性能的影响

研究了样品表面镀有不同表面粗糙度的银膜对钛酸钡（BaTiO₃ glass,BTG）微球成像效果的影响,发现当银膜表面的粗糙度（RMS）从3.23 nm增大到6.80 nm时,用直径为15 μm的BTG微球观察直径为250和580 nm的微球阵列,样品的成像范围增大.另外,BTG微球还可以清晰分辨原本不可分辨的直径为200 nm的微球阵列.结果表明,粗糙银膜引起的散射作用和表面等离激元波的局域场增强效应,使得更多物体的高频信息耦合进微球,提高了微球成像的分辨率和成像范围.     

Radar backscattering from Gerstner's sea surface wave

In the framework of a two-scale scattering model, radar backscattering from the rough sea surface was considered. The sea surface was modelled as a superposition of a nonlinear, large-scale Gerstner's wave and small-scale resonant Bragg scattering ripples. The zero-order diffracted field was found by a geometrical optics approach, with shadowing taken into account, and by an 'exact' solution of the diffraction problem obtained numerically. For vertical and horizontal polarizations, the spatial distribution of specific scattering cross sections along the large-scale wave was obtained. The spatially averaged specific backscattering cross sections, as well as the mean Doppler frequency shifts at both polarizations, obtained by the geometrical optics approach are compared with those obtained by using the 'exact' solution of the large-scale diffraction problem. The roles of shadowing and multiple wave scattering processes are discussed, and qualitative explanations of the difference between these two approaches are given.     

Electrochemical machining of super-hydrophobic Al surfaces and effect of processing parameters on wettability

Super-hydrophobic aluminum (Al) surfaces were successfully fabricated via electrochemical machining in neutral NaClO₃ electrolyte and subsequent fluoroalkylsilane (FAS) modification. The effects of the processing time, processing current density, and electrolyte concentration on the wettability, morphology, and roughness were studied. The surface morphology, chemical composition, and wettability of the Al surfaces were investigated using scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS), white-light interferometry, roughness measurements, X-ray diffraction (XRD), Fourier-transform infrared spectrometry (FTIR), and optical contact angle measurements. The results show that hierarchical rough structures and low surface energy films were present on the Al surfaces after electrochemical machining and FAS modification. The combination of the rough structures and the low surface energy materials plays a crucial role in achieving super-hydrophobicity. Compared with the anodic oxidation and chemical etching method, the method proposed in our work does not require strong acid or alkali, and causes less harm to the environment and operators but with high processing efficiency. The rough structures required by the super-hydrophobic surfaces were obtained at 30-s processing time and the best super-hydrophobicity with 164.6^° water contact angle and 2^° tilting angle was obtained at 360 s. The resulting super-hydrophobic Al surfaces have a long-time stability in air and an excellent resistance to corrosive liquids.