Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.     

考虑晶粒分布的多晶体材料超声散射统一理论

现有超声散射统一理论可通过多晶体材料的微观结构和力学特性,实现全频域范围内衰减和相速度的正演建模,但其忽略晶粒尺寸分布的影响,进而降低了正演模型的计算精度.本文对不均匀介质的波动方程进行二阶Keller近似,用全频域格林函数推导介质中的平均波;以截断对数正态分布描述晶粒分布,构建加权的空间相关函数;结合材料的弹性模量协方差,建立含晶粒分布的超声散射统一理论,揭示晶粒分布对超声散射的影响规律;制备304不锈钢试块并开展超声散射实验.结果表明考虑晶粒分布特性后,纵波衰减谱和相速度谱相对于实验结果的相异性降低约49%和64%,横波衰减谱和相速度谱相对于实验结果的相异性降低约12%和4%.可见,本文的统一理论模型能有效修正晶粒分布导致的衰减谱和相速度谱偏差,为晶粒分布反演评价提供理论基础.     

Comparison of phase velocity in trabecular bone mimicking-phantoms by time domain numerical (EFIT) and analytical multiple scattering approaches

The corrected Waterman-Truell model and the Elastodynamic Finite Integration Technique were used to analyze the ultrasonic wave dispersion in trabecular bones mimicking phantoms. A simple two-phase model of the trabecular bone is assumed; the trabeculae structure and the bone marrow. The phase velocity for frequencies within the range from 400 kHz to 800 kHz were computed for different scatterer arrays varying their dimensions and number. The theoretical and numerical results were compared to experimental published data, obtained from a mimicking phantom composed by a periodic array of nylon shreds (trabeculae array) immersed in a water tank. Our results showed an excellent consistency when compared to experimental data. The negative dispersions of −8.48 m/s/MHz and −9.16 m/s/MHz were computed by the multiple scattering method and the numerical approach, respectively, where the latter is closer to the experimental dispersion of −12.09 m/s/MHz. Similar result has been reported in the literature, where the dispersion predicted by the Generalized Self-Consistent Method [J. Acoust. Soc. Am. 124 (2008) 4047] is −9.96 m/s/MHz.     

Note on Scattering of Electromagnetic Waves by Nonlinearly Screened Dust Grains in Plasmas

Although most experiments in complex plasmas correspond to non‐linear grain screening, the theoretical models of non‐linear screening have not been checked experimentally. Scattering of electromagnetic waves on a single nonlinearly screened dust grain in plasmas can serve as one of effective methods for investigation of non‐linear screening. In present paper we have developed a theory for electromagnetic wave scattering that includes both the effect of coherency of scattering for long wave range and the loss of coherency with a decrease of the wave length. It is valid for arbitrary non‐linearity in screening and demonstrates that the loss of coherency occurs for wave length less then the characteristic screening length for non‐linear screening being usually substantially larger than the linear Debye screening length. The effect is illustrated numerically using the most popular model of non‐linear screening. The dependence of the cross‐section of scattering on parameter of non‐linearity in screening is calculated numerically. The loss of coherency in scattering by a single grain can serve as effective diagnostic for checking the theoretical models of non‐linear screening. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

含双圆柱亚表面缺陷板条材料的表面温度分布

基于非傅里叶热传导方程,采用复变函数法和镜像法,研究了含双圆柱亚表面缺陷板条材料热波散射的温度场,并给出了热波散射温度场的解析解。分析了入射波波数、热扩散长度、缺陷的埋藏深度以及板条材料的厚度等对板条表面温度分布的影响。温度波由调制光束在材料表面激发,缺陷表面的边界条件为绝热。该分析方法和数值结果可为工程材料结构的传热分析、热波成像和材料内部缺陷评估,以及热物理反问题研究提供参考。     

Backscattering grain noise modelling in ultrasonic non-destructive testing

Abstract

Many materials present an internal grain microstructure. When these materials are subjected to ultrasonic non-destructive testing, the grains behave like scattering centres producing unwanted backscattered noise that can make the detection of true defects difficult. This paper is devoted to the modelling of the probability density and the spacetime correlation functions of the grain noise complex envelope. Assuming statistical independence between any pair of grains, the authors derive analytical expressions for the above functions. Specifically, the envelope comes to be K-distributed, the parameters of the distribution may be related, under reasonable simplifying assumptions, to the material characteristics (grain density, grain size distribution, propagation velocity). The spacetime correlation function is a separable function. It may be expressed as the product of a spatial factor due to the spatial correlation introduced by the non-zero beamwidth, and a time factor due to the time correlation introduced by the non-zero pulse duration. The analytical expressions are verified by means of real data measured in austenitic stainless steel specimens.     

The scattering of electromagnetic waves in fractal media

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous two-dimensional medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterer concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman–Truell model, and the more recent Conoir–Norris model.     

Statistically stable ultrasonic imaging in random media

Analysis of array data from acoustic scattering in a random medium with a small number of isolated targets is performed in order to image and, thereby, localize the spatial position of each target. Because the host medium has random fluctuations in wave speed, the background medium is itself a source of scattered energy. It is assumed, however, that the targets are sufficiently larger and/or more reflective than the background fluctuations so that a clear distinction can be made between targets and background scatterers. In numerical simulations nonreflective boundary conditions are used so as to isolate the effects of the host randomness from those of the spatial boundaries, which can then be treated in a separate analysis. It is shown that the key to successful imaging is finding statistically stable functionals of the data whose extreme values provide estimates of scatterer locations. The best ones are related to the eigenfunctions and eigenvalues of the array response matrix, just as one might expect from prior work on array data processing in complex scattering media having homogeneous backgrounds. The specific imaging functionals studied include matched-field processing and linear subspace methods, such as MUSIC (MUtiple SIgnal Classification). But statistical stability is not characteristic of the frequency domain, which is often the province of these methods. By transforming back into the time domain after first diagonalizing the array data in the frequency domain, one can take advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.     

Rain induced attenuation for 3mm wave band and its measurement system

In this paper, the effect of rain induced attenuation for millimeter wave is discussed. The theory of multiple scattering is used to obtain the solution for the plane wave propagation through a plane parallel medium of thickness L containing randomly distributed nonspherial particles. The coherent field and the total field are studied, respectively. The numerical results are good agreement with experimental data and the multiple scattering effects must be included. A 3mm wave propagation measurement system was made on a 0.8km terrestrial link.     

Decorrelation and phase-shift of coda waves induced by local changes: multiple scattering approach and numerical validation

We report on theoretical predictions of the decorrelation and phase-shift of coda waves induced by local changes in multiple scattering media. Using the multiple scattering formalism, we show that both expressions (decorrelation and phase-shift) involve a same sensitivity kernel based on the intensity transport in the medium. We compare the kernels based on the diffusion approximation with the ones based on the radiative transfer approximation, showing that the latter is more accurate at short times or for changes located close to the source or the receiver. We also perform a series of numerical simulations of wave propagation (finite differences) to validate our models in different configurations.     

表面粗糙度对固体内部超声背散射的影响

超声背散射法可通过多晶体金属内部的空间方差信号,实现微观结构参数的无损评价,但表面粗糙度对评价模型的精度及实用性存在显著影响.基于高斯声束理论推导垂直入射粗糙界面的纵波声场,以此研究声能的Wigner分布规律;在超声的波长远大于粗糙度的前提下,构造表面粗糙度修正系数,并建立粗糙界面的单次散射响应模型,揭示粗糙度对超声波背向散射的影响规律.用304不锈钢制备轮廓均方根值为0.159μm的光滑试块和25.722μm的粗糙试块开展超声背散射实验,结果表明模型在粗糙度修正前后均可实现光滑试块的晶粒尺寸有效评价,但未经修正的传统模型对粗糙试块的晶粒尺寸评价结果与金相法结果的相对误差高达-21.35%,而本模型的评价结果与金相法结果符合得很好,相对误差仅为1.35%.可见,本模型能有效补偿粗糙度引起的超声背散射信号衰减,从而提高晶粒尺寸无损评价的精度.     

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array’s transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.     

Determination of optical characteristics of biological tissues by temporal distribution of an ultrashort laser pulse passed through homogeneous scattering layer

The determination of optical characteristics of biological tissues by the temporal distribution of an ultrashort laser pulse passed through a homogeneous scattering layer is considered. Four nonstationary models used to describe passing of laser pulses through a highly scattering medium are compared for the first time. The domains of applicability for the diffusion models are determined. It has been shown that the determination of optical characteristics of highly scattering media by experimental temporal distributions leads to different numerical values depending on the used model. Nevertheless, any of these models can be used because the performed study does not permit one to give preference to any of them. However, in determining optical characteristics of the scattering samples, it is necessary to specify the used model, as well as the conditions under which the initial experimental data (in particular, the thickness of the layer of a studied sample) are obtained.     

SRS generation of anti-Stokes radiation under phase quasi-matching conditions

New methods of generation of anti-Stokes radiation of stimulated Raman scattering in media with changeable parameters of the third-order nonlinearity χ⁽³⁾ along the longitudinal coordinate are proposed. The conditions of obtaining phase quasi-matching in different media and reaching the maximum efficiency of conversion into the anti-Stokes component of stimulated scattering are determined by numerical methods. The dependence of the efficiency of energy transfer from the pump wave to the anti-Stokes wave on the ratio of intensities of the pump and Stokes waves at the input of the medium is studied. The models of the media in which the efficiency of generation of anti-Stokes radiation exceeds 30% are obtained. The results of the investigation can be used for the development of new efficient nonlinear optical devices upconverting the laser radiation frequency.     

Numerical simulation of soot optical diagnostics in non-optically thin media

The global aim of this paper consists of quantifying the effect of optically thick media on LII measurements. The paper emphasises in a simple, general two-phase case, the potential “signal trapping” due to the multiple scattering of light by soot particles. A statistical Monte Carlo approach has been used in the frame of a parametric study. This method allows testing separately the distinct influences of parameters like soot volume fraction, sphere diameter, optical path length or aggregate shape. As a first result of this numerical study, the theoretical validity range of experimental techniques can be determined when applied to a larger domain than the strictly optically thin one. A numerical tool for a better understanding of mixed and complex phenomena has been realised. Here the approach is validated on the simplest geometrical configuration; it will be applied to a real combustion chamber configuration later. PACS 78.70.-g     

声学宽带多焦点聚焦

针对声学宽带多焦点聚焦的问题,设计出结构简洁的声学人工结构。通过控制细槽深度,对反射声波的波前进行任意操控。数值仿真结果验证了所设计的声人工结构的聚焦效果。这种人工结构还允许对焦点的相对位置及数目进行精确而自由的调控,当尺寸大于波长的障碍物存在时仍可通过合理设计来产生聚焦效果。该方案具有设计简洁及焦点可控等优点,有望在生物医学及无损检测等场合产生广泛应用。      

Scattering model of a cylindrical shell with internal axisymmetric frames by using the Circumferential Admittance Approach

A numerical model is proposed for predicting scattering pressure by a fluid-loaded cylindrical shell stiffened by axisymmetric internal frames and impacted by an acoustic plane wave. The proposed developments are based on the Circumferential Admittance Approach (CAA) which allows us assembling a numerical model of the fluid loaded shell with finite element models of the internal frames. The scattering pressure model deduced with the CAA can then take into account: (a) internal frames having a cross section with a complex geometry and thickness variations (like T-shaped stiffeners, bulkheads, and hemispherical end caps); (b) variations of frame spacings; and (c) frame-shell coupling in the three translational directions and tangential rotation. Comparison with the numerical and experimental results of the literature for a periodic stiffened shell shows that the scattering from Bragg, Bloch–Floquet, and Helical waves is correctly predicted. The effects on the backscattering pressure of axial and tangential coupling forces are highlighted. Finally, an example of a non-periodically stiffened shell is presented to highlight the versatility of the approach proposed.