A Detailed Study of the Scattering of Scalar Waves from Random Rough Surfaces

A multiple scattering theory of scalar waves from random rough surfaces is presented. By using the Ewald-Oseen extinction theorem the scattering integral equation is solved by means of an expansion in σ powers (σ being the standard deviation of the corrugation). Values of the mean scattered intensity until the fourth order of σ are given. The quick convergence of this series for low σ permits us to deal with those situations of small roughness in which the Kirchhoff approximation given by Beckmann and Spizzichino [2] fails. These are the cases in which σ ? T and λ ? T (λ being the wavelength and T the surface correlation length). Thus this theory can give the intensity for white noise surfaces, and yields the conditions under which the single scattering Kirchhoff approximation works, as well as its percentage of error. As such it is shown that Beckmann's theory gives good results in all cases in which σ /T < 0·05 and, thus, the reason why it is valid for interpreting laser speckle measurements is given. All the analysis is done for normal statistics and a gaussian correlation function of the corrugation.     

Multiple Scattering from Rough Dielectric and Metal Surfaces Using the Kirchhoff Approximation

Abstract

The Kirchhoff double-scatter method for calculating the intensity distribution scattered from a rough surface is extended to dielectric and metal surface materials. The material properties are contained in the Fresnel reflection coefficients only. It is shown that the results agree well with calculations using the exact method for a surface of Gaussian statistics with standard deviation of height σ = 1·93λ and 1/e correlation length τ = 5·02λ.     

Effects of sensor locations on air-coupled surface wave transmission measurements across a surface-breaking crack

Previous studies show that the surface wave transmission (SWT) method is effective to determine the depth of a surface-breaking crack in solid materials. However, nearfield wave scattering caused by the crack affects the reliability and consistency of surface wave transmission measurements. Prior studies on near-field scattering have focused on the case where crack depth h is greater than wavelength λ of surface waves (i.e., h/λ > 1). Near-field scattering of surface waves remains not completely understood in the range of h/λ for the SWT method (i.e., 0 ≤ h/λ ≤ 1/3), where the transmission coefficient is sensitive to crack depth change and monotonically decreases with increasing h/λ. In this study, the authors thoroughly investigated the near-field scattering of surface waves caused by a surface-breaking crack using experimental tests and numerical simulations for 0 ≤ h/λ ≤ 1/3. First, the effects of sensor locations on surface wave transmission coefficients across a surface-breaking crack are studied experimentally. Data are collected from Plexiglas and concrete specimens using air-coupled sensors. As a result, the variation of transmission coefficients is expressed in terms of the normalized crack depth (h/λ) as well as the normalized sensor location (x/λ). The validity of finite element models is also verified by comparing experimental results with numerical simulations (finite element method). Second, a series of parametric studies is performed using the verified finite element model to obtain more complete understanding of near-field scattering of surface waves propagating in various solid materials with different mechanical properties and geometric conditions. Finally, a guideline for selecting appropriate sensor arrangements to reliably obtain the crack depth using the SWT method is suggested.     

Fast and accurate modelling of frequencyselective surfaces using a new modular neural network configuration of multilayer perceptrons

The authors consider the analysis and modelling of the scattering from frequency-selective surfaces (FSSs), in the 6-14-GHz band, as a function of its periodic array geometry of thin dipole elements on an anisotropic layer. The accurate full-wave electromagnetic (EM) analysis of each FSS was carried out using the method of moments. From the available EM data, the artificial neural network (ANN) models can be developed. The modelling problem was solved by using a new modular configuration of multilayer perceptrons (MLPs), which is an implementation of the proposal modified from the previous knowledge method of neuromodelling information. Each MLP in the modular configuration was trained separately from the others through the resilient backpropagation algorithm. Within the region of interest studied, the ANN model developed is able to estimate the resonance frequencies and the bandwidths of the FSS band-stop filters, with high accuracy and low computational cost. To verify the advantageous properties of the modular MLP/MLP model, a neural model using a simple MLP was developed in order to analyse the same learning task. A comparative study was done between these models in terms of training the convergence, the accuracy and the computational cost.     

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.     

Measurement of random processes at rough surfaces with digital speckle correlation

We present a detailed investigation of digital speckle correlation to measure small changes in the microstructure of random rough surfaces. The corresponding alterations in the scattered-light field are recorded by an electronic camera with subsequent numerical correlation. Among the classical theoretical approaches to describe the scattering at random rough surfaces, the composite-roughness model is advanced to calculate the speckle correlation in terms of parameters of the changes in surface microstructure. For an experimental verification, surfaces with similar microstructure are fabricated with a photolithographic technique. They are employed for comparative measurements with high-resolution scanning force microscopy and for correlation measurements under variation of experimental parameters. A good agreement between theoretically predicted and experimental correlation data can be observed. The results allow a quantitative whole-field monitoring of surface processes by remote optical means.     

A method for determining relative ionization gauge sensitivities using cross section measurements

The authors propose an original molecular collision method for the determination of vacuum ionization gauge sensitivity coefficients. The knowledge of scattering gas pressure p is necessary to determine absolute scattering cross sections σ, using molecular beam techniques. Inversely the knowledge of σ allows the absolute measurement of the pressure. The cross section σ is first measured using a beam of molecules A and a target gas B for which the gauge calibration is known. By interchanging A and B the gauge can be calibrated for the gas A. Theoretical conditions of application of this method are discussed, the principal point being that the beam has to be effusive. Sensitivity coefficients have been determined for several gases.     

Characterization of 1D diffractive optical elements by phase inversion

Abstract

We consider the feature dimensions of selected 1D diffractive optical elements (DOE) such that the Fourier transform based Gerchberg-Saxton (GS) iterative scalar phase retrieval algorithm, as calibrated by the results of vector coupled-wave theory, may be used for phase reconstruction. We consider examples only of continuous surface relief and binary (two level, not multi-level) phase-only DOE. Experimental phase distribution for rectangular and blazed gratings with ～ 5λ period agree within experimental limits with scalar theory, and, for the rectangular grating, were shown to agree also with the vector theory. Phase distributions are considered for a continuously varying linear blazed grating with 10λ periodicity, its sampled binary equivalent with minimum feature sizes of 0.1λ and for continuous linear blazed gratings with period varied from ～ 16λ to ～ 2λ. The vector calculations show an average linear dependence of the phase on grating period, but the vector curves are displaced to lower values from the scalar results by an increasing amount as the grating period is reduced. Grating performance is more influenced by the size of the grating period than the subwavelength size of the features in a binary representation. Reasonable equivalence is found in the prediction of correct phase distributions between scalar and vector theory for grating periods > ～ 5λ.     

A New Electromagnetic Theory for Scattering from Shallow Rough Surfaces

A new approximate theory for scattering from arbitrary rough surfaces is presented. It is shown that this theory gives the exact result, to the first order, when the depth of the asperities tends to zero. On the other hand, we prove that this is not the case for formulae relying upon the Kirchhoff approximation, even in cases for which many authors have claimed their validity. Many applications can be envisaged, in particular to direct or inverse scattering from random rough surfaces.     

Ultrasonic wave scattering from rough,imperfect interfaces. Part I. Stochastic interface models

A theoretical model for ultrasonic wave scattering by geometrically irregular and imperfectly bonded interfaces is presented. In Part I, the normal stiffness of interfaces formed by the partial contact of solids with rough surfaces is estimated for two models of contacting surfaces with random roughness in one dimension only. The first model considers nonconforming surfaces with a single-scale of roughness, while double-scale roughness characterizes the surfaces of the second model, which are conforming at the large scale and nonconforming at the smaller scale. The surfaces' profiles are described by Gaussian probability and spectral densities. The surfaces at each contact are modeled by two cylinders under a compressive load and the normal stiffness per unit area of the interface is evaluated by averaging the stiffness of all the contacts, assuming they do not interact with each other. It is shown that the smaller the roughness, the softer the interface; the larger the autocorrelation length, the softer the interface; and the smaller the initial aperture, the stiffer the interface. Furthermore, interfaces described by the second model appear much stiffer than those described by the first model. The interface characterizations and normal stiffness models developed in Part I will be used in Part II to study the scattering of ultrasonic plane waves by such an interface.     

Wave Scattering from Fractal Surfaces

Abstract

In this paper, a normalized band-limited Weierstrass function is presented for modelling 2D fractal rough surfaces. Some conventional statistical parameters, namely the root mean square and the correlation length of rough surfaces, are used to assess between fractal parameters and the roughness of surfaces. An analytic solution of the scattered light field from these fractal surfaces is derived based on Kirchhoff theory. Three statistical parameters, namely the average scattering coefficient, the average intensity of scattered field, and the root mean square of scattered field, are introduced to study the influence of various fractal parameters on the scattered field by theoretical analysis and numerical calculations.     

Fast Coherence Scanning Interferometry for Measuring Smooth,Rough and Spherical Surfaces

Abstract

Coherence scanning interferometry is a useful instrument for measuring the geometry of a wide range of surfaces with high resolution. By introducing two objectives with a high numerical aperture in both arms of a Michelson interferometer it is possible to investigate spherical and aspherical surfaces. In addition to classical interferometry, the method can be applied to smooth, rough or separated surfaces.     

Estimation of scattering from a moist rough surface with spheroidal dust particles

The scattering from moisture rough surface with spheroidal dust particles having surface with spheroidal dust particles has recently received much attention. In part due to the recent prediction and observation of the spheroidal dust particles in rough surfaces under elastic wave by the Kirchhoff scattering model and scalar approximation with slope. Our analysis shows that the scattering depends on the moisture (2–4·5%) with spheroidal dust particles. At slightly moisture rough surface the dielectric properties increase with change in field amplitude in a rough surface with spheroidal dust particles.     

Influence of orientation of rough grooves on spectral reflectivity of a surface in the thermal radiation wavelength range

Roughness is one of the principal factors influencing reflectance of a surface that takes place in radiation heat transfer. In the present work, we investigate the influence of the orientation of single-oriented roughness grooves on the directed–directed spectral reflectance of surfaces within the wavelength range of 0.2–20.0 μm. The surfaces have a mean square deviation of the roughness (σ) of 0.2 μm and 2.0 μm and the areas exceed the size of the incident light beam. The angles of reflection are equal to the angles of incidence and are equal to 50° and 70°. The degree of influence of the groove orientation on the reflectance is defined as the ratio of the reflectances of one and the same surface with the grooves oriented parallel and perpendicular to the plane of incidence. In the theoretical investigation, we engage the unidimensionally rough surface model. An experimental study by means of physical modeling was performed: the degree of influence of the groove orientation on the spectral reflection of the surface was estimated, within the investigated wavelength range, according to the degree of influence of the groove orientation on the monochromatic reflectance of the reference ground surfaces within the σ-range of 0.01–4.33 μm on the wavelength 0.405 μm. The studies performed show that the spectral range of the groove orientation influence on the surface reflectance increases with an increase in σ and a decrease in the angle of incidence; the degree of that influence has a maximum the value of which increases with the increase in the angle of incidence. We determine the conditions of agreement of the theory and the experiment.     

Formation and characteristics of coarsening resistant cubic sigma phase in AI-4.2Cu-1.6Mg-0.2Si

Abstract

The precipitation and coarsening characteristics of an alloy of nominal composition (wt-%) AI-4.2Cu-l.6Mg-0.2Si were investigated at 200, 265, and 305°C for times up to 650 h. All aging conditions produced a mixture of homogeneously nucleated S′ and the cubic phase σ. The quench rate did not alter appreciably the volume fraction of cubic phase. The lattice parameter of the σ phase was 0.831 ± 0.005 nm and the aspect ratio of the σ precipitates was 1.4 ± 0.1 for treatments at 200 and 265°C, increasing to 1.8 for the specimens aged at 305°C for 24 h. The precipitated σ phase exhibited better resistance to coarsening and dissolution in long term aging treatments at 265°C than the concurrently precipitated S′, although the S′ was a more effective precipitation. hardener.     

Modelling of materials properties in duplex stainless steels

Abstract

Work is being undertaken to develop a new multiplatform software programme for predicting a wide range of materials properties for various alloy types. These properties include thermophysical and physical properties, mechanical properties, time–temperature transformation (TTT)/continuous cooling transformation diagrams etc. and the calculations are being applied to a variety of multicomponent alloy types, such as Ni based superalloys, steels, Ti alloys, Al alloys. The current paper concentrates on duplex stainless steels and describes the scientific background used for the calculation of TTT diagrams and mechanical properties for these materials. It is shown that there is very good agreement between the calculated TTT diagrams and the observed results from the literature for the formation of the σ, χ, and the chromium rich α' phase, while the calculated proof stress, tensile stress and hardness are in good agreement with the available experimental data. The effects of solution treatment temperature and the volume fraction of σ phase on mechanical properties are also discussed.     

粗糙表面散射基模高斯光束的散射特性实验研究

本文介绍良导体二维粗糙表面对红外激光束的散射分布;讨论不同偏振方式入射时散射光的分布特点,以及中等粗糙表面和弱粗糙表面散射能量在不同入射角下的变化趋势;分析表面参数对分布的影响。文章对观察到的弱粗糙表面散射在镜反射方向附近的边凸现象作了简述;这一现象由散射光的相干叠加而引起,有深入研究的价值。