截断阶梯Legendre函数加权阵列恒定束宽波束特性分析*

连续Legendre函数加权的恒定束宽换能器(CBT)阵列可以在一定频率范围内采用与频率无关的简单阵元权重实现恒定束宽的波束特性。然而常规CBT阵列需要为每个阵元配置相应的阵元权重,当阵元数量较大时会增加复杂度。该文分析了截断阶梯Legendre函数加权的面阵列,包括球面阵、柱面阵和平面阵,并且分别分析了Legendre函数球面加权方法和Legendre函数柱面加权方法应用于上述阵列的性能。结果表明,截断阶梯Legendre函数加权对波束方向的影响可以忽略,而主要影响波束宽度。对于面阵列,当采样阶梯不大于3 dB,截断点不大于-21 dB时,截断阶梯Legendre函数加权能很好近似连续Legendre函数加权。因此截断阶梯Legendre函数加权可以在保证CBT阵列性能的前提下有效减少阵元加权系数的数量。     

Heating of biological tissues by two-dimensional phased arrays with random and regular element distributions

The effect of an irregularity of the element distribution in a two-dimensional phased array upon the efficiency of heating of biological tissue is studied in an ultrasonic surgery regime. Two arrays of 256 piston elements, which either form a regular square pattern or are positioned randomly on the surface of a spherical segment, are considered as a model. The formation and the steering of a set of nine foci along the array axis and in the direction perpendicular to it are investigated. The theoretical model includes the algorithm of determining a phase set at the array elements that is optimal for the formation of foci with equal intensities and a preset geometry, as well as the calculation of acoustic and temperature fields in a tissue. The results of numerical simulation are presented for the spatial distributions of ultrasonic intensity, temperature, and the corresponding thermal dose in tissue. It is demonstrated that an irregularity of the element distribution reduces the level of secondary intensity peaks in the field produced by the array. This provides an opportunity to avoid the overheating and ablation of tissue outside the target volume, even in the case of steering with the set of foci away from the array axis within a distance of ±7 mm. A nine-foci regime is studied with the parameters necessary to produce uniform thermal ablation in a volume that is evaluated on the basis of the thermal dose distribution.     

Improved beamforming using curved sparse 2D arrays in ultrasound

In this work we have investigated the effect of curving phase-steered sparse periodic two-dimensional arrays in one direction, and relate this effect to the geometry of the arrays. We have shown that curving is equivalent to removing some of the element periodicity, thus adding some “randomness” to the layout. Compared to flat phase-steered periodically sparse two-dimensional arrays, curving offers an even greater suppression of grating lobes located at directions along the curvature. The class of arrays yielding improved performance due to this suppression of grating lobes has been characterized.The point spread functions of some previously proposed array layouts, shown to be promising for ultrasonic imaging, have been simulated. The arrays have been simulated with various number of elements as well as various focal points, with array and field parameters typical to those in volumetric cardiac imaging. On a 48 × 48 element grid with a transducer center frequency of 3 MHz and the target at 40 mm, reductions in the peak sidelobe level of up to 12 dB were recorded for some critical steering directions, without significant differences in the beamwidth. The integrated sidelobe ratio was also examined, showing an almost equivalent performance as the flat array. This study shows that, without adding any complexity to the system, the overall image quality of a volumetric imaging system can be improved significantly by curving the array in one direction.     

Legendre函数加权的声纳宽频带恒定束宽波束特性分析*

为了处理水声信号,声纳阵列通常需要形成宽频带恒定束宽的波束。采用两种阵元加权方法分析二维圆弧形恒定束宽换能器声纳阵列:球面Legendre函数加权方法和柱面Legendre函数加权方法。分别对球面阵、柱面阵和平面阵这三种几何结构的声纳阵列进行分析,并且计算波束宽度和波束方向。结果表明,在宽频带范围内,除了柱面Legendre函数加权的球面阵之外,其余Legendre函数加权的声纳阵列均能利用简单的、不随频率变化的阵元权重和阵元延时,形成恒定束宽的波束,并且具有较小的旁瓣,此外波束方向与预设方向也较为一致。相对于其他恒定束宽波束形成方法,Legendre函数加权方法能利用较低的计算复杂度来实现良好的宽频带恒定束宽的波束特性。     

Application of vernier thinning techniques to segmented annular arrays

Due to the aperture periodicity, the inter-element spacing of two-dimensional squared arrays is maintained near lambda/2 in order to avoid grating lobes. This condition gives rise to severe problems derived from the huge number of array elements and from their little size that causes the signal to noise ratio to bring down. Vernier techniques have been proposed to lower the number of active elements, but the drastic reduction of the ultrasonic energy is still a great problem for the image contrast. In this work, vernier techniques for segmented annular (SA) arrays are theoretically studied. SA arrays produce lower grating lobes than squared arrays and, therefore, allow the element size to be increased beyond the lambda/2 constraint. Using larger elements, SA arrays have advantage to squared arrays because they have larger active area and smaller thinning order for the same complexity (number of channels) of the image system. Theoretical results of the vernier techniques applied to SA arrays in both radial and tangential directions are presented and compared with the equivalent squared array.     

Two-dimensional phased arrays for surgery: Movement of a single focus

Numerical simulation and comparative analysis of acoustic fields generated by two-dimensional phased arrays designed for ultrasonic surgery is conducted. The case of movement of a single focus by an array with the surface shaped as a part of a spherical shell with the curvature radius 120 mm is considered. The influence of the number of elements (varying from 64 to 1024), their diameter (from 2.5 to 10 mm), frequency (from 1 to 2 MHz), and the degree of sparseness of the elements at the array surface on the field characteristics is studied. The calculations are performed for arrays with elements positioned at the surface both regularly (in square, annular, or hexagonal patterns) and randomly. Criteria for the evaluation of the “quality” of intensity distributions in the field generated by an array in the case of movement of a single focus are suggested. Of all arrays studied, the best quality of distributions is obtained for an array containing 256 elements of diameter 5 mm randomly positioned at the array surface. The quality of the intensity distributions for arrays consisting of 255, 256, and 1024 elements positioned regularly (in square, annular, and hexagonal patterns) is inferior to the corresponding quality for arrays with randomly positioned elements. The irregularity in elements’ positioning considerably improves the distribution quality by suppressing the secondary intensity peaks in the field generated by the array; or, alternatively, it provides an opportunity to obtain the same distribution quality with a fraction of the number of elements in the array. The effects of the number and shape of elements, errors in phase setting, frequency modulation of signals, and non-uniform distribution of amplitudes over the array surface on the distribution quality are analyzed.     

Array gain for a cylindrical array with baffle scatter effects

Cylindrical arrays used in sonar for passive underwater surveillance often have sensors surrounding a cylindrical metal baffle. In some operational sonars, the phones in each stave (i.e., each line of phones aligned with the cylinder axis) are hardwired together so that the array is equivalent to a baffled circular array of directional elements, where each element corresponds to a line array of omnidirectional phones steered to broadside. In this paper a model is introduced for computing the array gain of such an array at high frequencies, which incorporates baffle scatter using infinite, rigid cylinder scattering theory, and with ambient noise described by an angular spectral density function. In practice the phones are often offset from the baffle surface, and the acoustic field sampled by the staves is distorted at high frequencies due to interference between the incident and scattered fields. Examples are given to illustrate the resulting array gain degradation, using three noise distributions that are frequently used in sonar performance modeling: three-dimensional isotropic, two-dimensional isotropic, and surface dipole noise.     

Micromachined high frequency PMN-PT/epoxy 1-3 composite ultrasonic annular array

This paper reports the design, fabrication, and performance of miniature micromachined high frequency PMN-PT/epoxy 1-3 composite ultrasonic annular arrays. The PMN-PT single crystal 1-3 composites were made with micromachining techniques. The area of a single crystal pillar was 9 × 9 μm. The width of the kerf among pillars was ∼5 μm and the kerfs were filled with a polymer. The composite thickness was 25 μm. A six-element annular transducer of equal element area of 0.2 mm² with 16 μm kerf widths between annuli was produced. The aperture size the array transducer is about 1.5 mm in diameter. A novel electrical interconnection strategy for high density array elements was implemented. After the transducer was attached to the electric connection board and packaged, the array transducer was tested in a pulse/echo arrangement, whereby the center frequency, bandwidth, two-way insertion loss (IL), and cross talk between adjacent elements were measured for each annulus. The center frequency was 50 MHz and −6 dB bandwidth was 90%. The average insertion loss was 19.5 dB at 50 MHz and the crosstalk between adjacent elements was about −35 dB. The micromachining techniques described in this paper are promising for the fabrication of other types of high frequency transducers, e.g. 1D and 2D arrays.     

64 elements two-dimensional piezoelectric array for 3D imaging

Ultrasound has a large potential on non-invasive inspection with main applications in medical imaging and non-destructive testing (NDT). The increasing interest in 3D imaging applications leads to investigate new solutions for two-dimensional (2D) ultrasonic arrays with an affordable number of electronic channels without resolution degradation. 2D segmented annular arrays (SAAs) are a good compromise between resolution--image quality--and number of electronically active channels. A 1-3 piezoelectric composites are used as basis material to manufacture the array transducers due to their low planar coupling and high electromechanical coupling coefficients. A 1.5 MHz SAA of 64 elements and 20 mm of diameter was designed, manufactured and tested. The design key point is the use of a flexible circuit with electrodes and tracks that define the array geometry. The piezocomposite was used as a monolithic support. Soft backing and one matching layer were used. The array elements have been tested electrically and acoustically showing good agreement with a KLM-based simulation model. Acoustical field measurements in water at different steering angles were made and compared with simulations performed with a model that uses an exact solution of the impulse response approach. Side lobes are important because the array geometry used was designed to work in metals for NDT purposes. Smaller array elements should be made for medical applications.     

Non-integral dimensions ultrasonic phased arrays in a borehole

The non-integral dimensions ultrasonic phased arrays and their scanning and testing methods in a borehole are studied. First, the focusing acoustic fields excited by the 1.25D, 1.5D, and 1.75D phased arrays are analyzed, and then the imaging resolution in the elevation direction and the influence of the dynamic elements are investigated. Second, the focusing and deflexion characteristics of the acoustic fields excited by the annular and segmented annular phased arrays are studied, and they are compared with those excited by the 2D surface array. The application method of the 1.25D, 1.5D, and 1.75D, annular and segmented annular phased arrays in acoustic logging are analyzed and discussed. It provides a theoretical foundation for the application of the ultrasonic phased arrays in acoustic logging.     

圆环形聚焦声场的构建与调控

提出了一种由径向振动模式的圆环形压电换能器晶片组成的圆柱形阵列换能器结构, 依据阵元激励信号的相位调控机理, 推导了圆环形聚焦声场的调控公式, 在三维空间中构建了圆环形聚焦声场, 实现了对其聚焦区域大小、聚焦圆环半径以及轴向位置移动的调控. 理论分析和仿真研究表明, 所提出的圆柱形阵列换能器实现了对圆环形聚焦声场的调控. 为检测超声、功率超声、医学超声等应用领域提供了一种可实现的新型圆环形可调控聚焦声场.     

Dynamics behavior of rotating bladed discs: A finite element formulation for the study of second and higher order harmonics

Annular finite elements for the computation of second and higher order harmonics modes of bladed rotating discs are developed. The elements take into account gyroscopic effect and stiffening due to centrifugal and thermal stresses (the latter not present in arrays of blades). The displacement field is expressed by a truncated Fourier series along the angle and by polynomial shape functions in the radial direction. This paper is the generalization of a previous study limited to zero- and first-order harmonics and deals only with second and higher order harmonics modes that are uncoupled from the modes involving the behavior of the rotor as a whole. Several cases have been studied to verify the accuracy of the disc and array of blades elements.     

Spherical harmonics MUSIC versus conventional MUSIC

With the three-dimensional symmetry and wide potential application, spherical array signal processing has been a hot research area for years. This paper devotes to the direction-of-arrival (DOA) estimation of the spherical arrays. Based on the orthogonality of the sensors’ location, MUSIC algorithm in spherical space is proposed, named as SH-MUSIC. Similar to beamspace MUSIC, spherical harmonics transformation is operated before MUSIC algorithm and a better performance is gotten because SH-MUSIC utilizes the array configuration’s orthogonality. On account of the transformation matrix’s orthogonality, spherical harmonics transformation is suggested to be operated firstly in other improved MUSIC algorithms without rejection, and it is demonstrated in beamspace MUSIC. In addition, owing to the tiny error between the steering vectors and the spherical harmonics with high order, sphere array data models including open sphere and rigid sphere are constructed. Simulation proves SH-MUSIC to be effective. Moreover, experimental data from a rigid sphere microphone array is dealt with by SH-MUSIC and the DOAs are estimated accurately.     

Analytical method for evaluating the quality of acoustic fields radiated by a multielement therapeutic array with electronic focus steering

The paper presents an analytical method for calculating and analyzing the quality of 3-D acoustic fields of multielement phased arrays used in noninvasive ultrasound surgical devices. An analytical solution for the far field of each of its elements is used when calculating the array field. This method significantly accelerates calculations while preserving the high accuracy of results as compared to conventional direct numerical integration. Radiation from typical phased arrays is calculated using this approach, and the quality of their dynamic focusing is analyzed. Undesired diffraction effects caused by electronic focus steering are considered: an amplitude decrease in the main maximum and the appearance of grating lobes. The quality of dynamic focusing of the acoustic fields of two practically interesting arrays with a quasi-random element distribution (256 and 1024 elements, respectively), as well as of the regular array consisting of 256 elements is compared. In addition as well, a study is made of how the dimensions of the array elements and their spatial distributions affect the dimensions of the areas in which dynamic focusing is possible without occurrence of strong grating lobes and significant decrease in pressure amplitude at the main focus.

     

Steering vector sensor array elements with linear cardioids and nonlinear hippioids

The purpose of this work is to study the impact due to individual vector sensor element steering patterns on linear array beamforming. Standard, linear beamformers employ cardioid beampatterns for each vector sensor. In this work, a class of vector sensor element steering patterns beyond the standard cardioid was examined. The element weighting is nonlinear but nonadaptive, making it simple to implement in hardware processing. The new sensor steering patterns, referred to as hippioids, are products of cardioids and various powers of hippopedes. The angular resolution of individual sensors, the impact on angular resolution from arrays of varying aperture, and peak-to-sidelobe levels will serve as performance measures. An example of the differences in vector sensor steering patterns is provided using measured directional frequency and recorded buoy data.     

Analysis of transient responses in a laminated piezoelectric cylindrical shell

A hybrid numerical method is proposed for analysis of transient responses in a multilayered piezoelectric cylindrical shell.In the present method,the associated equations of the displacement field and the electro-potential field are developed using an analytical-numerical method.The piezoelectric cylindrical shell is discretized into layered annular elements along the wall thickness direction.The governing equations are determined by Hamilton's Principle considering the coupling between the elastic and elec...     

Two-dimensional phased arrays for application in surgery: Scanning by several focuses

Numerical simulation and comparative analysis of acoustic fields formed by two-dimensional phased arrays designed for ultrasonic surgery are conducted for the case of scanning by several focuses (in particular, by nine focuses arranged in a line and also by an array of nine focuses forming a 3×3 square grid). Calculations are performed for arrays with elements positioned at the surface both regularly (in square, ring, or hexagonal patterns) and randomly. Criteria for evaluating the “quality” of the intensity distributions in the field formed by the array in the case of scanning by several focuses are proposed. The quality of the intensity distributions for arrays containing 255 and 256 elements 5 mm in diameter arranged in regular patterns on the array’s surface (in square, ring, or hexagonal patterns) is inferior to that for arrays containing 256 randomly positioned elements. Among the regular arrays, the highest quality of intensity distributions is obtained for ring arrays, and the lowest quality is obtained for arrays with elements arranged in square or hexagonal patterns. The irregularity in the element positioning the array’s surface improves the quality of intensity distributions by reducing the secondary intensity peaks in the field formed by the array and, primarily, in the focal plane.     

FPGA-based implementation of steerable parametric loudspeaker using fractional delay filter

Parametric loudspeaker enables high directivity sound along the radiation direction to be generated by the nonlinear effects of ultrasonic waves in air. Based on the theory of phased array, the beams of parametric loudspeakers can be steered to other directions. In this paper, the Fractional Delay (FD) filter is introduced to generate any arbitrary delay to accurately control the steering angle of the beam. Field Programmable Gate Array (FPGA) is a better choice for the system of steerable parametric loudspeaker due to its strong capability of parallel and real-time processing. The algorithms have been realized easily and quickly by combining the tools of Matlab simulink and DSP Builder. Finally, the validity of the system is verified through comparing the theoretical simulations with the experimental results.     

Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid

We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.