会聚球面波圆孔衍射的一般积分式

 分别从菲涅尔-基尔霍夫和瑞利-索莫非衍射积分公式出发，导出了考虑倾斜因子后会聚球面波经圆孔衍射的一般衍射积分表达式。所得公式不仅可计算衍射场的焦移，而且对弱聚焦和强聚焦情况均适用。并与Li和Wolf公式的结果进行了比较，结果证实所得公式适用广泛。     

一种基于互易原理的超声功率新测量方法

本文从换能器的互易原理出发，利用平面波自易校准法获得换能器的自由场发送电流响应．根据平面活塞型换能器的衍射规律，推导出发射声功率的表达式．由此计算互易换能器在给定驱动电流（或电压）作用下的辐射超声功率．基于上述原理，使用自易校准装置测量了互易换能器的声功率一频率曲线．估计的测量不确定优于±20％．     

基于球壳内壁反射的球形换能器自易校准方法

基于球形换能器发射的脉冲球面声波及其在同心球壳内壁的反射,应用机电互易定理,导出了在球面波发射回波声场中,用于校准球形换能器的互易常数.以此为基础,提出一种使用封闭球壳反射器的自易校准方法,通过一次测量即可得到球形换能器的5个基本电声参数.进一步,将自易法校准所得的电压灵敏度换算成平面波声场中定义的标准灵敏度,给出了换...     

1-3型二维柱形凹面线聚焦换能器声场特性

设计并研制了柱面结构的1-3型复合材料凹面线聚焦换能器,在提高换能器带宽的同时,可以实现声场的线聚焦。将换能器内部PZT柱作为独立声源,应用瑞利积分和叠加原理,推导出了柱形凹面换能器总声场的理论表达式。通过仿真计算分析了换能器在聚焦线上的声场特点以及相关参数对聚焦性能的影响。对换能器参数做出合理设计,使换能器在实现线聚焦的同时,声场在聚焦线上的起伏较小,从而设计并制作出聚焦性能良好的线聚焦凹面换能器探头。实验测试结果表明采用本文方法计算得到的换能器声场与实测的声场分布基本符合,柱形凹面换能器在其几何焦点附近范围内均可实现聚焦,并在侧向上形成清晰的聚焦线,其聚焦线长度为换能器的侧向结构长度,在聚焦线上声场分布起伏较小。      

变厚度聚焦换能器对声焦域轴向长度影响的研究*

针对不同厚度的病变组织,改变声焦域轴向长度能提高高强度聚焦超声在临床治疗过程中的安全性和有效性。基于多频超声波叠加原理,该文提出了变厚度(多频)聚焦换能器,并设计了两种类型变厚度聚焦换能器。根据瑞利积分法推导了变厚度聚焦换能器声场,计算和分析了变厚度聚焦换能器的声焦域轴向长度,并与等厚度(单频)聚焦换能器声焦域轴向长度进行对比。结果显示,变厚度聚焦换能器中心到边缘的厚度变化趋势与声焦域轴向长度变化相关,中间薄两边厚换能器声焦域轴向长度缩短,中间厚两边薄换能器声焦域轴向长度变长,且实验验证了理论的正确性。研究结果可为变厚度聚焦换能器声场研究和高强度聚焦超声的临床治疗提供参考。     

空间频率对透射式全息图衍射率的影响

为研究干涉条纹空间频率与透射式全息图衍射率的关系,在相同条件下,拍摄以平面波、发散的和会聚的球面波分别作参考光、物光的透射式全息图,通过实验测量其衍射效率,同时计算了干涉条纹的空间频率。然后以会聚的球面波为物光,平面波为参考光,分别改变入射角和球面波会聚点到记录面的距离制作另外4块透射式全息图,并计算了它们的空间频率,测量了其衍射效率。结果表明：在相同条件下制作透射式全息图时,衍射效率只由空间频率决定,与使用何种参考光和物光无关,空间频率仅随参考光和物光的夹角变化而变化。     

振动声成像系统分辨率研究

本文从振动声成像的基本原理出发，通过引入点扩展函数PSF和定义轴向响应函数ARF，研究了由凹球面聚焦换能器分割而成的一种典型共焦换能器参数对振动声成像系统侧向分辨率和轴向分辨率的影响。计算研究表明：增大凹球面换能器的口径、减小几何焦距和提高中心频率均可以提高系统的侧向分辨率和轴向分辨率；但改变凹球面换能器的分割比例对两种分辨率影响不尽相同。综合考虑超声换能器激励、聚焦性能以及产生的辐射力效果等因素，则换能器应按等辐射面积原则分割为宜。文中还分析了介质的声衰减系数对实际轴向分辨率的影响。     

无损检测用换能器灵敏度的测量

在无损检测领域中换能器的灵敏度应该是一个重要的特性,但对于超声探伤用的换能器的灵敏度至今还没有一个有效的方法来进行测量。本文把换能器看成是平面源,推得了它在远场条件下的互易参量。并采用互易技术在固体样品中校准了超声换能器的灵敏度,实验表明超声探伤用的换能器的发送和接收灵敏度是能够精确测量的,在一定的耦合条件下,测试总精确度在±1dB以内。     

反射层析激光雷达小系统成像模拟

对反射层析激光雷达近场小系统成像进行了理论分析与模拟验证,当目标处于瑞利-索末菲衍射区域,到达目标的波前属于球面波衍射。根据奈奎斯特定律对球面波反射层析图像重建所需角度采样数,单投影采样点数约束条件进行了推导。引入了折线的方法,用于避免平方开方的距离运算,缩短图像重建时间。数值模拟表明此方法可以在降低计算量的前提下实现图像重建,随着探测距离的拉长,折线重建图像与参考图像相似度越来越高。     

Cymbal换能器的力电性能

研究了Cymbal换能器的力电性能。在简单支承边界条件下,应用压电-弹性理论、克希霍夫薄板振动理论、瑞利-李兹理论和等效电路方法分析了Cymbal换能器的机电特性,给出了Cymbal换能器的近似解和串联共振频率方程,研究了Cymbal换能器在无负载条件下的等效电路及相关参数和Cymbal换能器空腔深度与空腔底部半径的比与谐振频率和机电耦合系数的关系。根据数值分析结果得到最佳机电耦合系数,为Cymbal换能器的优化设计提供了理论依据。     

A new algorithm for spatial impulse response of rectangular planar transducers

Previous solutions for spatial impulse responses of rectangular planar transducers require either approximations or complex geometrical considerations. This paper describes a new, simplified and exact solution using only trigonometric functions and simple set operations. This solution, which can be numerically implemented with a straightforward algorithm, is an exact implementation of the Rayleigh integral without any far field or paraxial approximation. Additionally, a nonlinear relationship was also established for spatial impulse responses from two field points which share the same projection point on the transducer surface plane. By incorporating this relationship in the algorithm, the computational efficiency of spatial impulse responses and continuous fields is improved about 20-folds and 14-folds, respectively. This algorithm has practical applications in designing l-D linear/phased arrays, 1.5-D arrays and 2-D arrays, as demonstrated through numerical simulations with array transducers. Experiments were also conducted to verify the new solution and results show that the algorithm is both accurate and efficient. The application of this method may include development of ultrasound imaging system for hard and soft tissue nondestructive assessment.     

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.     

̀Spatial impulse response of a rectangular double curved transducer

Calculation of the pressure field from transducers with both a convex and a concave surface geometry is a complicated assignment that often is accomplished by subdividing the transducer surface into smaller flat elements of which the spatial impulse response is known. This method is often applied to curved transducers because an analytical solution is unknown. In this work a semi-analytical algorithm for the exact solution to a first order in diffraction effect of the spatial impulse response of rectangular-shaped double curved transducers is presented. The solution and an approximation to it are investigated. The approximation reformulates the solution to an analytically integrable expression, which is computationally efficient to solve. Simulation results are compared to FIELD II simulations. Calculating the response from 200 different points yields a mean error for the different approximations ranging from 0.03% to 0.8% relative to a numerical solution for the spatial impulse response. It is also shown that the presented algorithm gives consistent results with FIELD II for a linear flat, a linear focused, and a convex nonfocused element. The solution involved a three-point Taylor expansion and gave an accuracy of 0.01%.     

Characterization of cylindrical ultrasonic transducers using acoustic holography

We present the results of studying the vibrational velocity distribution over the surface of cylindrical ultrasound transducers by acoustic holography. We describe two approaches for acoustic holography: the spatial spectrum method and the Rayleigh integral method. In the case of cylindrical sources the spectral method has a specific feature in comparison to the case of quasi-plane sources: small-scale spectrum components having the form of evanescent (nonpropagating) waves near the source, turn into propagating waves at a certain distance from the source. The use of such a mixed type of waves makes it possible to increase the holographic resolution. To conduct holography of cylindrical sources by the Rayleigh integral method, a modification consisting in the superimposing of boundaries on the integration region is proposed. We present the results of numerical simulation and physical experiments on holography of small cylindrical piezoelectric transducers. We demonstrate that the proposed methods of holography make it possible to recover the vibration structure of source surfaces up to order of the wavelength scales.     

Measurement of sound insulation of acoustic louvres by an impulse method

This paper presents results of a study of the sound attenuation of acoustic louvres. At the core of the study is an alternative method of measuring sound insulation, impulse response analysis, which circumvents the limitations imposed by standard and proposed standard methods. Using the impulse method, the sound transmission coefficient is measured at different angles of incidence and the angular dependency of transmission loss obtained. In the low frequency range, the transmission is governed by a mass layer effect. The value of transmission loss is independent of angle of incidence. For the mid and high frequencies, diffraction, interference and absorption determine louvre performance and an angular dependency is observed. The transmission at the angle of incidence, corresponding to a line-of-sight through the louvre blades, is the dominant contribution to the angle average value and a single measurement at the pitch of the louvre approximates the overall transmission loss. For the case considered, the geometry of the blades has little influence on the transmission at low frequencies and the mass of the blades has little influence at higher frequencies. In a companion paper, the impulse data are used to predict the insertion loss provided by the louvre when installed in a plant room.     

Diffraction of spherical waves at an annular aperture in the use of the boundary diffraction wave theory: A comparison of different diffraction integral approaches

The integral expression for divergent spherical waves diffracted at an annular aperture is derived based on the theory of the boundary diffraction wave. The expressions for divergent spherical waves diffracted at a circular aperture and a disk, and the axial field are treated as the special cases of our general one. Numerical calculation results for axial and transversal intensity distributions are given to compare our results with the Kirchhoff diffraction integral, first and second Rayleigh diffraction integrals. As expected, our results are in agreement with those in the use of the Kirchhoff diffraction integral, but the computer time is reduced greatly by using the boundary diffraction wave theory. The four diffraction formulae are shown to be consistent for axial and transversal intensity distributions, if the source and observation points are positioned equally from the aperture, or the observation point is located enough far from the aperture. Otherwise, the mean value of the first and second Rayleigh diffraction integrals is equal to the result of the boundary diffraction wave theory.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

Apparent transducer non-reciprocity in an ultrasonic flow meter

This paper investigates the effects of non-identical ultrasonic transducers on reciprocity and zero-flow calibration in transit time flow meters. According to the theorem of reciprocity, there should not be any difference between the up- and downstream acoustic times of flight in a zero-flow situation. This would thus eliminate zero-flow estimation drifts. The flow meter is modeled as a one dimensional system with equivalent electrical circuits and simulated with simulation program with integrated circuits emphasis. The work shows that variations between the two transducers cause false estimates of flow and indicate which parameters have the largest influence. It indicates that reciprocity holds only for identical transducers.     

Minimum radiation force target size for power measurements in focused ultrasonic fields with circular symmetry

The time-averaged ultrasonic power emitted by medical ultrasonic equipment is mostly measured using a radiation force balance, and the question of the necessary target size is of practical importance. The question is answered here by calculations based on a Rayleigh integral algorithm for fields from circular, focusing transducers. This case occurs particularly in the field of high-intensity therapeutic ultrasound. The calculation yields the necessary size of an absorbing target so that the radiation force is 98% of that exerted on an absorber of infinite lateral size, and this as a function of the transducer-to-target distance, of the transducer radius in comparison with the wavelength and of the focus (half-)angle. Several distributions of the transducer vibration amplitude are considered. The Rayleigh integral strictly applies only to planar transducers, but among the amplitude distributions there is also one that allows the simulation of the spherically curved transducer type often found in practice.     

Focused, phased-array plane piston and spherically-shaped concave piston transducers: comparison for the same aperture and focal point

It has sometimes been assumed that the phased-array plane piston transducer and the spherically-shaped concave piston transducer are equivalent structures when both have the same aperture and focal point. This assumption has not been previously examined, nor has an expression for the on-axis impulse response of the focused, phased-array plane piston transducer been derived. It is shown in this paper how such an expression can be obtained. Comparisons of the impulse response for both structures show similarities, as well as some differences that could be significant as the observation point approaches the focal point. Comparisons are also performed for wide-band pulses close to the focus as well as for sinusoidal excitation. A physical explanation for the cause of the impulse response discrepancy is shown to be due to the nature of the piston focusing delay and its effect on the Rayleigh integral.