Acoustical fields from rectangular ultrasonic transducers for non-destructive testing and medical diagnosis

Theoretical results are given for pressure and intensity in the acoustical field produced by rectangular ultrasonic transducers. Comparison between the fields of square, circular and rectangular transducers is made showing that the field of a rectangular transducer, by comparison with that produced by square and circular transducers, may be divided into three zones rather than two: the very nearfield, the nearfield and the farfield. Some experimental results are shown confirming the general shape of the predicted curves. Emphasis is put on the difficulty of interpreting quantitative ultrasonic results with rectangular probes.     

Some extensions of the Gaussian beam expansion: radiation fields of the rectangular and the elliptical transducer

A straightforward extension of Gaussian beam expansion is presented for calculation of the Fresnel field integral [J. J. Wen and M. A. Breazeale, J. Acoust. Soc. Am. 83, 1752-1756 (1988)]. The source distribution function is expanded into the superposition of a series of two-dimensional Gaussian functions. The corresponding radiation field is expressed as the superposition of these two-dimensional Gaussian beams and is then reduced to the computation of these simple functions. This treatment overcomes the limit that the shape of source is of circular axial-symmetry. The numerical examples are presented for the field of the (uniform) elliptical and the rectangular piston transducers and agree well with the results given by complicated computation.     

环形稀疏声源阵列声涡旋的优化与操控

提出和优化了环形稀疏声源阵列涡旋声场的形成方法,进行了涡旋声压,相位和振动速度的理论推导和特性分析。通过改变声源数、声源频率和观测距离等参数,对声涡旋场的模拟结果证明,声涡旋半径主要由信号波长决定,声源频率越高,声涡旋半径越小,能量越集中;涡旋声压随着声源数的增加而线性提高,随着传播距离的增加而减小;声涡旋环形相位分布的线性度随着声源数、声源波长和传播距离的增加而提高。建立了3/4/6/8声源实验系统,径向声压和相位分布以及环形相位分布的测量结果和模拟结果具有较好的一致性,同时悬吊泡沫盘的旋转证明了声涡旋角动量的传输。本研究中声涡旋场的特性分析和参数优化为粒子操控及其在生物医学中的应用提供了依据。      

Setting boundary conditions on the Khokhlov–Zabolotskaya equation for modeling ultrasound fields generated by strongly focused transducers

An equivalent source model is developed for setting boundary conditions on the parabolic diffraction equation in order to simulate ultrasound fields radiated by strongly focused medical transducers. The equivalent source is defined in a plane; corresponding boundary conditions for pressure amplitude, aperture, and focal distance are chosen so that the axial solution to the parabolic model in the focal region of the beam matches the solution to the full diffraction model (Rayleigh integral) for a spherically curved uniformly vibrating source. It is shown that the proposed approach to transferring the boundary condition from a spherical surface to a plane makes it possible to match the solutions over an interval of several diffraction maxima around the focus even for focused sources with F-numbers less than unity. This method can be used to accurately simulate nonlinear effects in the fields of strongly focused therapeutic transducers using the parabolic Khokhlov–Zabolotskaya equation.     

Calculation of radiation acoustical fields from phased arrays with nonparaxial multi-Gaussian beam model

A nonparaxial multi-Gaussian beam model based on the rectangular aperture is proposed in order to overcome the limitation of paraxial Gaussian beam model which losing accuracy in off-axis beam fields. With the method, acoustical field generated by an ultrasonic linear phased array transducer is calculated and compared with the corresponding field obtained by Rayleigh-Sommerfeld integral, paraxial multi-Gaussian beam model, and Fraunhoffer approximation method. Simulation examples show that nonparaxial multi-Gaussian beam model is not limited by the paraxial approximation condition and can predict efficiently and accurately the acoustical field radiated by a linear phased array transducer over a wide range of steering angles.     

脊加载椭圆波导的多项式表示分析方法

采用Rayleigh-Ritz方法和多项式表示对脊加载椭圆波导的传输特性进行了分析.数值计算与电磁仿真软件结果能很好地符合.研究了不同尺寸对脊波导带宽的影响，对这类结构的优化具有指导意义.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Generation of the basis sets for multi-Gaussian ultrasonic beam models--an overview

By using a small number of Gaussian basis functions, one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of Gaussian beams. Since Gaussian beams can be transmitted through complex geometries and media, such multi-Gaussian beam models have become powerful simulation tools. In previous studies the basis function expansion coefficients of multi-Gaussian beam models have been obtained by both spatial domain and k-space domain methods. Here, we will give an overview of these two methods and relate their expansion coefficients. We will demonstrate that the expansion coefficients that have been optimized for circular piston transducers can also be used to generate improved field simulations for rectangular probes. It will also be shown that because Gaussian beams are only approximate (paraxial) solutions to the wave equation, a multi-Gaussian beam model is ultimately limited in the accuracy it can obtain in the very near field.     

Formation of a pulsed electron beam in a plasmacathode system under forevacuum pressures

Results of an experimental study of the features of the production of pulsed beams by a plasma electron source operating in the forevacuum pressure range (5–15 Pa) are presented. For this pressure range, the emission properties of the plasma are substantially affected by the backward ion flow generated in the regions of formation and transport of the electron beam. It has been shown that in experimental conditions the ratio of the current of backward ions to the current of the electron beam can reach 10%, which is an order of magnitude greater than the same parameter for electron sources operating in the pressure range that is conventional for devices of this type (0.01–0.1 Pa). The principal factors that impose an upper limit on the beam current in a plasma-cathode source are analyzed.     

Acoustic field imaging by light reflection at the free surface of a liquid

In this paper we present a novel technique for acoustic field imaging. This technique is based on reflection of a collimated laser beam at the free surface of a liquid. The reflected beam becomes phase modulated by the acoustic wave as in acoustical holographic systems. We do not use a reference acoustical beam for holographic reconstruction but we observe this phase modulation using dark-field techniques. It gives a measurement of the acoustic field power as a function of the position. The authors have built an optical imaging system and carried out experiments with piezocomposite transducers. The technique presented in this work is able to give fast quantitative information about the performance of individual ceramic rods of the piezocomposite.     

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.     

Influence of source directivity on noise levels in industrial halls: Simulation and experiments

Noise exposure of workers in industrial halls is mainly induced by noisy machines whose acoustical features are often globally known by Sound Pressure Level. The evaluation of the directivity of these noise sources can help to anticipate specific solutions for noise reduction.This study shows how the directivities of three wood-working machines have been characterized. Some characterisations have been achieved with a simple and fast acoustical intensity mapping which meets the constraints of industrial areas.When source directivity is evaluated, its influence on the noise field in industrial halls can be assessed. Some simulations and some experiments allowed the estimation of the noise field induced in workshops by both directional and omnidirectional sources. Comparison of the fields prove that the noise distribution is influenced by the source directivity if the halls are empty. As soon as the halls contain scattering objects, the directivity effect is reduced a lot and the noise field remains nearly the same far from the source whatever source used. Nevertheless, workers close to a machine are exposed to noise according to their position with respect to the machine. Exposure at the workplace can vary from 4 to 8 dB(A) according to the directivity of machines such as those measured in the trials.     

Scatterer size estimation in pulse-echo ultrasound using focused sources: calibration measurements and phantom experiments

In a companion paper [T. A. Bigelow and W. D. O'Brien Jr., J. Acoust. Soc. Am. 116, 578 (2004)], theory, supported by simulations, showed that accurate scatterer size estimates could be obtained using highly focused sources provided that the derived generalized attenuation-compensation function was used and the velocity potential field near the focus could be approximated as a three-dimensional Gaussian. Herein, the theory is further evaluated via experimental studies. A calibration technique is developed to find the necessary equivalent Gaussian dimensions for a focused source using reflections obtained from a rigid plane scanned through the focus. Then, the theoretical analysis of focused sources is validated experimentally using three spherically focused ultrasound transducers to estimate the radius of glass beads imbedded in tissue mimicking phantoms. Both the impact of focusing (f/1, f/2, and f/4) and the effect of scatterer type (comparing glass bead results to simulation results that used scatterers with Gaussian impedance distributions) were tested. The simulated differences agree with the measured differences to within 2.5% provided that the comparison is made between the same scatterer type and sources with the same equivalent Gaussian dimensions. The improvement provided by the generalized attenuation-compensation function is greatly influenced by the type of scatterer whose size is being estimated and decreases as the wavelength dependence of the Gaussian depth of focus is reduced.     

Acoustic radiation from a viscoelastic beam impacted by a steel sphere

The acoustic radiation from a viscoelastic beam impacted by a steel sphere has been studied both theoretically and experimentally. Transverse vibrations of free-free viscoelastic beams have been analyzed by employing the modal analysis technique and an approximate method, with the Hertz theory used to evaluate impact forces. The wave equation was solved to determine the acoustic pressure radiated from impacted beams of circular and elliptical cross-sections. The theoretical predictions are compared with the experimental results for the radiation from PMMA beams of circular and rectangular cross-sections. It is shown that for beams of circular cross-sections the theoretical and experimental results are in good agreement and that for beams of rectangular cross-sections the radiation is well predicted by modeling them as beams with elliptical cross-sections.     

Underwater hybrid near-field acoustical holography based on the measurement of vector hydrophone array

Hybrid near-field acoustical holography(NAH) is developed for reconstructing acoustic radiation from a cylindrical source in a complex underwater environment. In hybrid NAH,we combine statistically optimized near-field acoustical holography(SONAH) and broadband acoustical holography from intensity measurements(BAHIM) to reconstruct the underwater cylindrical source field. First,the BAHIM is utilized to regenerate as much acoustic pressures on the hologram surface as necessary,and then the acoustic pressures are taken as input to the formulation implemented numerically by SONAH. The main advantages of this technology are that the complex pressure on the hologram surface can be reconstructed without reference signal,and the measurement array can be smaller than the source,thus the practicability and efficiency of this technology are greatly enhanced. Numerical examples of a cylindrical source are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than conventional NAH. Then,an experiment has been carried out with a vector hydrophone array. The experimental results show the advantage of hybrid NAH in the reconstruction of an acoustic field and the feasibility of using a vector hydrophone array in an underwater NAH measurement,as well as the identification and localization of noise sources.     

3 mm波段二次谐波渐变复合腔回旋管的非线性模拟

 利用含电流的传输线方程,并在考虑多模注-波互作用及多模耦合的情况下,利用自主开发的多模高次谐波渐变结构复合腔回旋管的注-波互作用数值模拟软件,对3 mm波段二次谐波渐变复合腔回旋管进行了自洽非线性模拟,分析了H₀₂-H₀₃模式对下磁场系数、电流、电子注速度比对注-波互作用效率的影响。计算结果表明,在合适的腔体结构尺寸下,以及合适的磁场系数、电流、速度比下,注-波互作用效率可达27％。     

Configurations of high-frequency ultrasonics complex vibration systems for packaging in microelectronics

Ultrasonic high-frequency complex vibrations are effective for various ultrasonic high-power applications. Three types of ultrasonic complex vibration system with a welding tip vibrating elliptical to circular locus for packaging in microelectronics were studied. The complex vibration sources are using (1) a longitudinal-torsional vibration converter with diagonal slits that is driven only by a longitudinal vibration source, (2) a complex transverse vibration rod with several stepped parts that is driven by two longitudinal vibration source crossed at a right angle and (3) a longitudinal vibration circular disk and three longitudinal transducers that are installed at the circumference of the disk.     

The processes of formation and nonstationary dynamics of a virtual cathode in a nonrelativistic electron beam in the decelerating field (two-dimensional approximation)

We present the results of studies within the framework of a two-dimensional numerical model of nonlinear nonstationary processes in a nonrelativistic electron beam in the mode of formation of a virtual cathode in the decelerating field without focusing of the electrons by a magnetic field (low-voltage vircator). The results of numerical simulation were qualitatively confirmed by the experiment. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 843–852, October 2006.