一种精确计算换能器空间脉冲响应的快速方法

空间脉冲响应被认为是最有效的瞬态声场计算方法,针对空间脉冲响应直接计算时需要很高的采样频率,导致数据量大、计算效率差的问题,推导了空间点与其在换能器平面的投影点脉冲响应之间的关系,提出了一种计算脉冲响应的快速算法,探讨了计算采样频率和插值采样频率对计算精度和计算效率的影响,研究发现,采用1000 MHz采样频率能够保证精度要求,采用500 MHz作为插值时的采样频率是较优的选择。该方法与直接求解相比,可提高计算效率18倍。      

A new analytic expression for fast calculation of the transient near and far field of a rectangular baffled piston

Essential to (cardiac) 3D ultrasound are 2D matrix array transducer technology and the associated (two-stage) beam forming. Given the large number of degrees of freedom and the complexity of this problem, simulation tools play an important role. Hereto, the impulse response (IR) method is commonly used. Unfortunately, given the large element count of 2D array transducers, simulation times become significant jeopardizing the efficacy of the design process. The aim of this study was therefore to derive a new analytical expression to more efficiently calculate the IR in order to speed up the calculation process. To compare accuracy and computation time, the reference and the proposed method were implemented in MATLAB and contrasted. For all points of observation tested, the IR with both methods was identical. The mean calculation time however reduced in average by a factor of 3.93 ± 0.03 times. The proposed IR method therefore speeds up the calculation time of the IR of an individual transducer element while remaining perfectly accurate. This new expression will be particularly relevant for 2D matrix transducer design where computation times remain currently a bottle neck in the design process.     

Beamforming with a reduced sampling rate

The beamforming process requires a high delay resolution to avoid the deteriorating effects of the delay quantization lobes on the image dynamic range and signal to noise ratio. Wideband transducers require delay resolutions in the order of 1/16 the signal period. If oversampling is used to achieve this timing resolution, a huge data volume has to be acquired and processed in real time. This is usually avoided by sampling just above the Nyquist rate and interpolating to achieve the required delay resolution. However this increases the hardware complexity. Baseband sampling has been alternatively proposed with sampling rates as low as the transducer frequency or even lower. This approach uses two A/D converters and processing chains for every channel, thus doubling the hardware requirements. Quadrature sampling can be used instead with a single A/D converter, but the sampling rate must be a multiple of four times the transducer frequency, decreasing the application flexibility. Furthermore, it produces relatively high errors in the detected envelope if wideband transducers are used. This work presents a new approach, the selective sampling technique (SST), which keeps the lowest sampling rate required by the imaging process or the signal bandwidth (whatever is larger) and, at the same time, provides a high delay resolution to keep the highest image dynamic range. The SST is based on a second order sampling process which, differently from the mentioned approaches, does not pose any constraints in the time interval between samples and produce lower errors in the detected envelope. The hardware requirements are low (a single A/D converter and processing chain for every transducer element), working at the lowest data rate compatible with the Nyquist criterion, thus reducing the data bandwidth. Furthermore, the sampling points can be also freely chosen, so that the SST simplify the usually required scan conversion process to a simple linear interpolation easily carried out by software in real-time.     

Synthetic aperture imaging using sources with finite aperture: deconvolution of the spatial impulse response

A method for ultrasonic synthetic aperture imaging using finite-sized transducers is introduced that is based on a compact, linear, discrete model of the ultrasonic measurement system developed using matrix formalism. Using this model a time-domain algorithm for deconvolution of the transducer's spatial impulse responses (SIRs) is developed that is based on a minimum mean square error (MMSE) criterion. The algorithm takes the form of a spatiotemporal filter that compensates for the SIRs associated with a finite-sized transducer at every point of the processed image. A major advantage of the proposed method is that it can be used for any transducer, provided that its associated SIRs are known. This is in contrast to the synthetic aperture focusing technique (SAFT), which treats the transducer as a point source. The performance of the method is evaluated with simulations and experiments, performed in water using a linear phased array. The results obtained using the proposed method are compared to those obtained with a classical time-domain SAFT algorithm. For a finite aperture source, it is clearly shown that the resolution obtained using the proposed method is superior to that obtained using the SAFT algorithm.     

̀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%.     

不同插值算法的光场重聚焦分析

光场数据重聚焦包括空间域重聚焦和频域重聚焦两种方法,在重聚焦过程中均需要进行插值计算,重聚焦精度与插值精度密切相关,而插值算法的复杂度会影响计算效率。在实际大量图像处理中,在重聚焦效果满足精度要求的前提下选择计算效率最高的方法,其中,插值精度对频域影响远大于空间域。介绍了空间域重聚焦和频域重聚焦的原理,以及传统3种插值方法和sinc函数插值法,分别用不同的插值方法对这两种重聚焦方法进行实验,比较其重聚焦效果并计算其效率。实验结果表明,在实际应用中为了满足计算效率的需求,在满足精度要求情况下,空间域重聚焦采用线性插值法最佳,频域采用采样半径为2像素的sinc插值最佳。对同一幅影像多次重聚焦时,频域方法优于空间域方法。     

高准确度多频调制激光测距算法研究

针对传统的激光测距仪测量准确度低、实时性差等问题,结合正交相位检测和坐标旋转数字式计算机角度解算方法,设计了一种多频激光测距系统.系统中采用改进的正交算法对噪音环境下的测距相位差的正切值进行计算,再通过坐标旋转数字式计算机角度解算方法计算出测距相位差,该方法有效地提高了测距准确度并大大降低了系统的运算量.在采样频率500 MHz、计算字长16位、回波信噪比14 dB时,测量范围为150 m,相位测量误差为0.026 4°,距离测量准确度达到0.11 mm.     

Plate impulse response spatial interpolation with sub-Nyquist sampling

Impulse responses of vibrating plates are classically measured on a fine spatial grid satisfying the Shannon-Nyquist spatial sampling criterion, and interpolated between measurement points. For homogeneous and isotropic plates, this study proposed a more efficient sampling and interpolation process, inspired by the recent paradigm of compressed sensing. Remarkably, this method can accommodate any star-convex shape and unspecified boundary conditions. Here, impulse responses are first decomposed as sums of damped sinusoids, using the Simultaneous Orthogonal Matching Pursuit algorithm. Finally, modes are interpolated using a plane wave decomposition. As a beneficial side effect, these algorithms can also be used to obtain the dispersion curve of the plate with a limited number of measurements. Experimental results are given for three different plates of different shapes and boundary conditions, and compared to classical Shannon interpolation.     

Development of the new approach to the Brownian coagulation theory: Transition regime

The new approach for calculation of the collision frequency function in the two limiting regimes (continuous and free molecular) proposed in the previous paper [1] is extended to the general case including the intermediate transition regime. The collision frequency function in the transition regime is numerically calculated without using semi-empirical assumptions (from the literature). The best fit to the numerically calculated points can be attained with the new interpolation formulas that have a simpler form and higher accuracy in comparison with the semi-empirical models.     

Comparison of the performance of different tools for fast simulation of ultrasound data

Simulation of ultrasound data is often performed for developing new ultrasound data processing techniques. The spatial impulse response method (as implemented in FieldII) has typically been used as the gold standard due to its excellent accuracy in the linear domain. When scatterer numbers become significant and when 3D volumetric data sets need to be computed, calculation time can become an issue however. In order to solve this problem, two alternative methods have recently been proposed both of which are based on the principle of convolving a set of point scatterers with a point spread function. “FUSK” operates in the frequency domain while “COLE” runs in the spatio-temporal domain. The aim of this study was to directly contrast both methodologies in terms of accuracy and processing speed using FieldII as a reference.     

水浸超声检测的平面波频域快速成像算法

给出了一种基于一步相移法的水浸超声检测快速频域算法,以适用于液浸式相控阵成像。通过在阵列信号频域乘以相移因子,将阵列虚拟延拓至水浸工件表面,再进行单介质频域成像。相比时域延时叠加算法,节省了计算界面折射点的用时。对于垂直入射平面波检测,提出一种网格匹配的方法,通过调整傅里叶变换的点数,使阵列信号频域和图像频域的采样网格相重合,有效地减少了频域插值误差和伪像,进一步降低了运算次数.实验结果表明,网格匹配频域算法的运算次数仅为时域平面波算法的1/60,为水浸式超声实时检测提供了一种可行方案。      

球形阵列自适应网格分层定位算法

刚性球形传声器阵列可以在无空间模糊的条件下进行球谐域数据处理,基于球形阵列的可控波束形成器导向响应功率(SRP)算法定位精度高,但是计算量大,计算效率低。通过将球面致密的全局网格搜索替换为分层搜索策略可以有效减小SRP算法的计算量。提出MRE-SRP算法保持球形阵列SRP定位精度的同时降低计算量,首先通过球谐域MUSIC(SH-MUSIC)算法判断入射声源的数量减小搜索区域;其次将相对熵模型引入球谐域SRP(SH-SRP)定位算法中,提取网格分层前后的信息增益,设计自适应网格选择判据,实现分层多分辨率网格的精准再细分,从而降低计算量。实验验证了所提出算法的性能,结果显示在单双声源定位中,该算法可以实现较高的定位精度,精准选择分层网格,计算量减少75%以上。     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

聚焦换能器自由场互易校准的冲击响应积分法衍射系数计算

在聚焦换能器的会聚球面波自由场互易校准法中，衍射损失修正系数是获得互易常数的一个关键参数。本文利用冲击响应函数积分法系统地计算了超声治疗头、机械扫描B超探头以及多普勒诊断探头的衍射损失系数，得出了一些典型参数下的计算曲线，可供不同类型的聚焦换能器会聚球面波互易校准时引用。与传统的瑞利积分法分析比较显示，本文中所采用的冲击响应函数积分法显著地提高了运算速度，同时基本保持了与瑞利积分算法计算结果的一致性。     

Pulse compression technique for simultaneous HIFU surgery and ultrasonic imaging: a preliminary study

In an ultrasound image-guided High Intensity Focused Ultrasound (HIFU) surgery, reflected HIFU waves received by an imaging transducer should be suppressed for real-time simultaneous imaging and therapy. In this paper, we investigate the feasibility of pulse compression scheme combined with notch filtering in order to minimize these HIFU interference signals. A chirp signal modulated by the Dolph-Chebyshev window with 3-9 MHz frequency sweep range is used for B-mode imaging and 4 MHz continuous wave is used for HIFU. The second order infinite impulse response notch filters are employed to suppress reflected HIFU waves whose center frequencies are 4 MHz and 8 MHz. The prototype integrated HIFU/imaging transducer that composed of three rectangular elements with a spherically con-focused aperture was fabricated. The center element has the ability to transmit and receive 6 MHz imaging signals and two outer elements are only used for transmitting 4 MHz continuous HIFU wave. When the chirp signal and 4 MHz HIFU wave are simultaneously transmitted to the target, the reflected chirp signals mixed with 4 MHz and 8 MHz HIFU waves are detected by the imaging transducer. After the application of notch filtering with pulse compression process, HIFU interference waves in this mixed signal are significantly reduced while maintaining original imaging signal. In the single scanline test using a strong reflector, the amplitude of the reflected HIFU wave is reduced to −45 dB. In vitro test, with a sliced porcine muscle shows that the speckle pattern of the restored B-mode image is close to that of the original image. These preliminary results demonstrate the potential for the pulse compression scheme with notch filtering to achieve real-time ultrasound image-guided HIFU surgery.     

三维大型任意阵列宽带波束指向性图的快速计算

为解决常规频域直接方法计算大型三维阵列宽带波束图(BP)速度较慢,无法满足大型三维宽带阵优化设计需求的问题,提出了一种适用于大型三维任意阵列的宽带BP图的快速算法.在利用二维非均匀快速傅里叶变换(NUFFT)伴随操作实现二维阵列BP频域快速计算方法的基础上,引入第三空间频率变量,将与阵元纵向坐标有关的相位因子转化为第三...     

空间插值在功率谱密度计算中的应用

 为了提高光学元件波前中频PSD计算的精度和有效频谱宽度,提出了填补波前无效数据的双线性插值法和抑制欠采样噪声的六采样点插值法。模拟计算和实验结果表明：双线性插值法有效地保证了填充数据与真实数据的一致性,抑制了零填充方法引入的虚假中高频信息,使得填补后的PSD与原始PSD较好地吻合;六采样点插值法有效地分离了信号和欠采样噪声,使得有效PSD频谱上限从1/2 Nyquist频率提高到Nyquist频率。     

Optimization of the transfer function of an acoustooptic cell with an apodized piezoelectric transducer

It is shown that an apodized piezoelectric transducer can significantly reduce the side lobe level of the acoustooptic cell transfer function. Series and symmetric connections of the transducer sections and measures to suppress the effect of spurious elements arising in the electric circuit are proposed. In particular, the effect of spurious capacitances and inductances on the frequency response of the transducer is studied. It is shown that they violate the optimal condition for the suppression of the transfer function side lobes, especially at high frequencies. It is shown by calculations that the effect of spurious elements can be eliminated by the insertion of additional capacitors at 80 and 150 MHz.     

压电陶瓷复合换能器固有频率的有限差分法*

为丰富换能器固有频率的研究理论,以及提供一种新的计算方法供工程人员选择,提出了计算其固有频率的有限差分法。以由径向极化的压电陶瓷圆管与金属预应力管沿径向复合而成的二元压电陶瓷复合换能器为例,建立并推导了其向振动的数学模型及其有限差分形式,给出了换能器径向振动的特征方程。利用MTALAB对计算实例的径向振动的固有频率进行编程计算,理论计算结果与已有实验结果符合很好,验证了有限差分法计算压电陶瓷复合换能器固有频率的可行性及准确性。通过仿真计算,给出了换能器径向振动固有频率与其结构尺寸的影响关系：换能器径向振动的固有频率随压电陶瓷圆管内径的增大而降低,随换能器壁厚比的增大而降低。该文所建立的换能器径向振动固有频率的有限差分法同样适用于结构形式相近的换能器及其他元器件。     

Nonlinear elastic imaging using reciprocal time reversal and third order symmetry analysis

This paper presents a nonlinear imaging method for the detection of the nonlinear signature due to impact damage in complex anisotropic solids with diffuse field conditions. The proposed technique, based on a combination of an inverse filtering approach with phase symmetry analysis and frequency modulated excitation signals, is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only one broadcasting transducer and one receiving transducer, was used to insonify the defect taking advantage of multiple linear scattering as mode conversion and boundary reflections. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel, and the nonlinear source, induced by low-velocity impact loading, was retrieved with a high level of accuracy. Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behavior.