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.     

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.     

带楔块二维面阵列超声相控阵声场特性分析

开展了带楔块二维面阵脉冲超声相控阵辐射声场特性的研究。将安装在一定角度斜楔块上二维面阵相控阵换能器声场问题简化为液固界面情况进行讨论。以单阵元在液固平界面条件下的辐射声场为基础,推导了聚焦偏转法则,给出了带楔块二维面阵超声相控阵声场计算方法。以检测材料为钢板,安装在倾斜角为36°有机玻璃楔块上的频率为5 MHz、8×8二维面阵相控阵的辐射声场计算为例,分析了在不同偏转角和不同聚焦深度下检测材料中的辐射声场特性。计算结果表明该方法可有效的分析带楔块二维面阵超声相控阵声场特性并用于指导二维超声面阵角束探头的设计。     

界面条件下线型超声相控阵声场特性研究

开展了界面条件下线型超声相控阵声场特性的研究.将带有楔块的超声相控阵问题合理简化为液固界面的情况进行讨论.根据射线声学理论,计算了单阵元在液固界面存在时的辐射声场,进而推导了聚焦法则,得到了超声线型阵在液固界面存在时的声场、位移场表达式.对安装在楔块上的相控阵换能器的辐射声场进行了仿真,并讨论了聚焦对换能器轴向和横向声场的影响,结果表明利用聚焦能提高分辨率和灵敏度,但聚焦区域之外声束性能更差,在实际检测中要合理利用聚焦. 关键词： 超声相控阵 界面 声场 聚焦     

An ultrasonic measurement model using a multi-Gaussian beam model for a rectangular transducer

To date, ultrasonic measurement models have primarily treated systems where circular transducers are used. Recently, however, a highly efficient ultrasonic beam model for a rectangular transducer has also become available where the transducer is represented as a superposition of a relatively few Gaussian beams. Thus, using the multi-Gaussian beams, we developed ultrasonic measurement models for systems where a rectangular transducer is employed. In this paper, we describe the developed models including the beam model, the efficiency factor for a rectangular transducer and far-field scattering models for some standard scatterers. Furthermore, the accuracy of the proposed model is verified by the comparison of the model-based predictions to the experimental measurements.     

Simulation of ultrasonic attenuation in theelastic mixing particle system

For the study of predicting ultrasonic attenuation of elastic, spherical mixing particles in the liquid-solid two-phase system, the Monte Carlo method(MCM) is introduced,serving as a probability and statistics technique to evaluate the inside ultrasonic events during the ultrasound propagation. On the basis of ultrasonic scattering and aborption, the continuous ultrasonic waves are represented as discrete and independent phonons. By recording the scattering events, tracing the trajectory of a moving phonon and calculating the number of phonons that finally reach the receiving transducer, the ultrasonic attenuation coefficient is obtained to be a frequence-dependent spectrum. Numerical investigations have been carried out to predict and compare the ultrasonic attenuation for a solid-liquid two-phase system with a single type particle. After verifing its feasibility, such a method is then appalied into mixing particle system, where the mixing iron particles and glass beads with various ratios are set as examples for the purpose of predicting ultrasonic attenuation for the monodisperse and polydisperse mixing particle systems. The results of MCM, the ECAH model, the Lloyd Berry(LB) model and the Waterman model match well when the particle volume concentration is lower than 10%,corresponding to iron particles and glass beads respectively. In the case of two-phase system with mixing particles, it is shown that as the particle volume concentration increases to 10%, the variation of the ultrasonic attenuation coefficient with mixing ratio yields a nonlinear tendency.The physical properties of particles can also influence ultrasonic attenuation significantly.     

圆柱类构件超声相控阵聚焦模型

在利用平面相控阵超声换能器对圆柱类构件检测时,受曲界面结构引起的入射波和回波时延的影响,扫描声束的波阵面产生弯曲,在利用传统迭代遍历算法计算延迟时间时效率低,无法发挥相控阵换能器检测优势。针对上述问题,建立了一种基于圆柱类构件特征和耦合介质特性的超声相控阵扫描成像的聚焦模型。该模型基于换能器、耦合介质、圆柱类构件材料特性和几何关系以及声线模型和折射定律,建立了耦合介质及被检构件的声速、曲面曲率半径、阵列与曲面间的距离等关联的延迟时间聚焦控制模型。利用该模型计算出的延时时间,对各阵元发射时间进行控制,从而实现扫描声束的聚焦。该文以液体和有机玻璃制介质楔块为例,对圆柱钢曲面的相控阵声束聚焦进行了仿真实验,结果表明该文方法计算效率显著提升,同时声束可以在预设位置实现聚焦,验证了该模型在计算效率上的优势与有效性。     

混合弹性颗粒体系声衰减数值模拟

采用概率统计方法——蒙特卡罗方法,建立一种预测液固两相体系中混合弹性球形颗粒声衰减的理论模型。在单颗粒声散射和吸收的基础上,将连续超声波抽象离散化为大量独立的声子,追踪声散射过程,通过统计接收器探测声子数最终确定声衰减系数。采用数值方法对单一球形颗粒的液固两相体系中声衰减进行预测和比较,确定了该方法的可行性后将该方法推广到混合颗粒体系中,对玻璃微珠/铁粉构成的混合颗粒及多分散混合颗粒体系进行数值研究。结果表明:在体积浓度低于10%时,蒙特卡罗法预测得玻璃微珠或铁粉颗粒声衰减和ECAH,Lloyd和Berry,Waterman等建立的模型结果吻合。对于混合颗粒构成的两相体系,算例中,随着体积浓度增大到10%,声衰减系数随混合颗粒数目比的变化呈现出了非线性的变化,同时颗粒物性也会影响不同组分颗粒对声衰减的贡献,算例中铁粉颗粒比玻璃微珠对声衰减的影响更大。     

Ultrasonic field modeling for immersed components using Gaussian beam superposition

The Gaussian beam (GB) superposition approach can be applied to model ultrasound propagation in complex-structured materials and components. In this article, progress made in extending and applying the Gaussian beam superposition technique to model the beam fields generated by transducers with flat and focused rectangular apertures as well as with circular focused apertures is addressed. The refraction of transducer beam fields through curved surfaces is illustrated by calculation results for beam fields generated in curved components during immersion testing. In particular, the following developments are put forward: (i) the use of individually determined sets of GBs to model transducer beam fields with a number of less than ten beams; (ii) the application of the GB representation of rectangular transducers to focusing probes, as well as to the problem of transmission through interfaces; and (iii) computationally efficient transient modeling by superposition of ‘temporally limited’ GBs.     

Experiments with neutron polarization analysis

Neutron polarization analysis experiments of the past 25 years are reviewed. In that time the technique has progressed from a curiosity to being a useful tool to be used when needed. In early experiments, the polarization of the scattered beam was analysed in the same direction as the polarization of the incident beam but, in some later experiments, full three-dimensional polarization analysis has been employed. This article starts by writing down the interactions which the neutron has with condensed matter and deriving the cross-sections for scattering and final polarizations of the scattered beam. This is done displaying the spin state functions of the neutron explicitly. A variety of experiments is then reviewed, commencing with the elastic and inelastic scattering experiments performed by Moon, Riste and Koehler in the late 1960s. Elastic scattering experiments where it is important to separate nuclear and magnetic cross-sections such as antiferromagnetic defect scattering are reviewed together with separation out of the nuclear spin scattering for various purposes. Of particular interest are the fully three-dimensional analysis experiments which reveal more about the structure and domain populations of certain antiferromagnets. Inelastic experiments for which polarization analysis is vital are those on paramagnets at high temperatures where it is necessary to discriminate against phonon scattering. Spin glasses are treated as frozen paramagnets. Polarization analysis also has another role to play in the separation of magnetic modes in both paramagnets and ordered magnets, and several of these experiments are reviewed. Finally it is possible to tag the polarization of a neutron beam in time and space and to measure the result at another time and place and this through various techniques yields information about the change in neutron energy on scattering. The techniques of pseudo-random flipping time of flight, neutron spectral modulation and neutron spin-echo spectroscopy are briefly reviewed but the techniques of polarized-neutron-beam management are left to another review.     

The reflection of ultrasound from partially contacting rough surfaces

Ultrasound is commonly used to detect and size cracks in a range of engineering components. Modeling techniques are well established for smooth and open cracks. However, real cracks are often rough (relative to the ultrasonic wavelength) and closed due to compressive stress. This paper describes an investigation into the combined effects of crack face roughness and closure on ultrasonic detectability. A contact model has been used to estimate the size and shape of scatterers (voids) at the interface of these rough surfaces when loaded. The response of such interfaces to excitation with a longitudinal ultrasonic pulse over a wide range of frequencies has been investigated. The interaction of ultrasound with this scattering interface is predicted using a finite-element model and good agreement with experiments on rough surfaces is shown. Results are shown for arrays of equi-sized scatterers and a distribution of scatterer sizes. It is shown that the response at high frequencies is dependent on the size, shape, and distribution of the scatterers. It is also shown that the finite-element results depart from the mass-spring model predictions when the product of wave number and scatterer half-width is greater than 0.4.     

Schlieren visualization of ultrasonic wave fields with high spatial resolution

The visualization of ultrasonic wave fields in optically transparent liquids using the acousto-optic interaction is a well proven tool for the experimental investigation of wave propagation including wave field interaction effects with certain discontinuities and obstacles like reflection, refraction, and diffraction effects as well as for transducer testing and design. For high resolution visualization of wave fields including pulsed waveforms, pulsed light sources and sensitive optical imaging sensors with certain specifications are needed. In this paper the technical requirements of optical and electronic components for high resolution visualization of ultrasound wave fields will be presented. Also, specifications and operation results of a new designed, inexpensive Schlieren optical system will be presented, which is capable of pulsed wave field visualization in the MHz frequency range. The spatial resolution is high enough, not only for accurate beam shape and wave pattern visualization, but also for a gray-scaled display of wave amplitudes including amplitude zero crossings in ultrasound pulses. Consequently, ultrasonic wavelengths can be visualized quantitatively as well as wavelength changes of the ultrasound pulses while traveling through transparent media with different sound velocities. Results to be presented will include 2 MHz and 10 MHz experiments using single transducers as well as linear arrays of commercial medical scanners during their standard operation showing the system beamforming characteristics.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.     

A tri-modal directional transducer

Acoustic transducers made from piezoelectric ceramic cylinders usually exploit the breathing or omnidirectional (omni) mode of vibration. However, with suitable voltage distribution, higher order extensional modes of the cylinder can be excited which produce directional radiation patterns. These modal radiation patterns can then be combined to synthesize desired beam patterns which may be steered by incrementing the excitation. This paper describes a model for the combined acoustic response of the extensional modes of vibration of a piezoelectric ceramic cylinder, a method of synthesizing a desired radiation pattern, and an experimental implementation of a directional transducer that uses these techniques. This tri-modal transducer is broadband and directional with a frequency independent beam pattern yet simple, small, and lightweight.     

Anomalous light scattering at the surface of growing ice crystals and thermodynamics of irreversible processes

The framework of nonequilibrium thermodynamics is used to study the phenomenon of enhanced Rayleigh scattering from the liquid-solid interface of a growing crystal. The scattering is treated as resulting from small objects of finite lifetime produced at the interface by the growth process and confined thereafter to one phase or the other. The thermodyanmic analysis leads to the formation, adjacent to the interface, of a boundary layer, various properties of which are studied. The analysis is then used to discuss the data obtained in two different experiments on the anomalous light scattering from the ice-water interface. It is found that the various data presented in these two experiments cannot be reconciled with each other in all respects.     

Measurement method of particle concentration and acoustic properties in suspension using a focused ultrasonic impulse radiated from a plano-concave transducer

As a method to measure the concentration and property of a particle suspension, we proposed an ultrasonic measurement method using a plano-concave ultrasonic transducer. To carry out the experiment, we used a focused ultrasonic impulse with a broad frequency bandwidth radiated from the transducer, instead of utilizing continuous waves as in the conventional method. By analyzing the frequency components of the echo returned from the reflector put at the focal region of the transducer in suspension, we measured the concentration, etc., from variations of attenuation in the frequency spectrum. As specimens, we used some substances containing fine particles for which the acoustic properties or sizes are heterogeneous to each other. Specifically, the milk fat included in milk was examined in detail to characterize the best-tasting milk. In conclusion, we determined that the particle concentration and acoustic properties were easily and instantaneously measurable using the frequency spectrum obtained from pulse echoes passed through the specimen liquid, and the plano-concave transducer was advantageous in these measurements.     

Model-based optimization of ultrasonic transducers

Numerical simulation and automated optimization of Langevin-type ultrasonic transducers are investigated. These kind of transducers are standard components in various applications of high-power ultrasonics such as ultrasonic cleaning and chemical processing. Vibration of the transducer is simulated numerically by standard finite element method and the dimensions and shape parameters of a transducer are optimized with respect to different criteria. The novelty value of this work is the combination of the simulation model and the optimization problem by efficient automatic differentiation techniques. The capabilities of this approach are demonstrated with practical test cases in which various aspects of the operation of a transducer are improved.     

Development of phased array techniques to improve characterization of defect located in a component of complex geometry

Ultrasonic inspection of complex geometry components has to cope with different problems: limited access of the area assumed to be insonified, beam misorientation and distortions, loss of sensitivity. Those harmful effects can lead to inspection performance degradations, especially in terms of defect detection and characterization. Phased array techniques may be used to overcome such difficulties, as they can provide an optimal mastering of the ultrasonic beam radiated through the inspected component. This paper presents some applications of phased array inspections carried out by the French Atomic Energy Commission (CEA) and the French Company of Electricity (EDF) in the framework of R&D studies. Inspections of components with varying profile (of planar and cylindrical parts, misalignment and local depression), and containing artificial reflectors have been carried out with pulse echo immersion techniques, using standard and phased arrays transducers. Optimal delay laws have been applied to preserve the beam characteristics in spite of the varying profile geometry encountered as the phased array transducer was moved over the component. Those delay laws allow to efficiently compensate the beam distortions generated by the profile geometry. They were computed using a specific model and compared to experimental delays obtained using through transmission tests. Experimental and simulation results showed that the defect detection and characterization performances were greatly enhanced using phased array techniques. In the presented examples, with standard transducers, defects located below the irregular parts of the specimen were partially detected, in accurately located or even missed, whereas phased array inspections enabled to detect and locate all of these defects.     

超声检测用压电换能器瞬态特性可控可调

超声检测用压电换能器瞬态特性主要包括瞬态空间响应和瞬态时间响应。本文通过调整控制换能器和激励源,实现瞬态空间响应和瞬态时间响应的某些特性的可控可调。其中包括在空间响应方面消除边缘波以获得平行声束和消除平面波以获得聚焦绳声束;在时间响应方面,调整换能器的背衬阻抗以获得可调首次波幅比和调整换能器结构和激励电信号以获得任意检测信号等。     

非近轴近似多高斯声束模型的相控阵换能器声场计算

针对近轴近似的多高斯声束模型无法准确计算离轴区域声场的问题,我们提出了一个矩形源的非近轴近似多高斯声束模型,用于计算偏转聚焦时线性相控阵换能器辐射的声场。利用该方法计算了由矩形阵元组成的相控线阵的辐射声场,并与瑞利积分、近轴近似方法及夫琅和费近似方法进行了分析和对比,计算结果表明该方法克服了常规近轴近似条件的限制,可以准确、快速地计算较大偏转范围内的换能器辐射声场,在计算相控阵换能器偏转聚焦声场中具有独特的优势。