Time reversal of ultrasonic fields. I. Basic principles

Time reversal of ultrasonic fields represents a way to focus through an inhomogeneous medium. This may be accomplished by a time-reversal mirror (TRM) made from an array of transmit-receive transducers that respond linearly and allow the incident acoustic pressure to be sampled. The pressure field is then time-reversed and re-emitted. This process can be used to focus through inhomogeneous media on a reflective target that behaves as an acoustic source after being insonified. The time-reversal approach is introduced in a discussion of the classical techniques used for focusing pulsed waves through inhomogeneous media (adaptive time-delay techniques). Pulsed wave time-reversal focusing is shown using reciprocity valid in inhomogeneous medium to be optimal in the sense that it realizes the spatial-temporal matched filter to the inhomogeneous propagation transfer function between the array and the target. The research on time-reversed wave fields has also led to the development of new concepts that are described: time-reversal cavity that extends the concept of the TRM, and iterative time-reversal processing for automatic sorting of targets according to their reflectivity and resonating of extended targets.     

Time reversal of ultrasonic fields. Il. Experimental results

For pt.I see ibid., vol.39, no.5, p.555-66 (1992). A time-reversal mirror (TRM) is made of an array of transmit-receive transducers. The incident pressure field is sampled, digitized, stored, time-reversed and then re-emitted. This process can be used to focus, through inhomogeneous media, on a reflective target that may behave as an acoustic source after being insonified TRM experiments using a 64-channel prototype are described, and the results are given. Focusing experiments conducted on point targets through different aberrating media are described. The major result shows that the time-reversal focusing technique compensates for all the distortions whatever the TRM-aberrator distance. When the medium contains several targets, the authors show that the time-reversal process can be iterated in order to focus on the most reflective one. Lithotripsy applications are also discussed. Kidney stones are spatially extended targets and TRM experiments have been conducted on several kidney stones located behind inhomogeneous media. They show that the iterative TRM process is able to select one of the kidney stones and to focus on a small portion of it.     

Time-reversal of ultrasonic fields. III. Theory of the closed time-reversal cavity

For pt.II see ibid., vol.39, no.5, p.567-78 (1992). A theoretical model for time-reversal cavities to optimize focusing in homogeneous and inhomogeneous media is described. The concept of the cavity can be understood as the most realistic approximation to an exact three-dimensional (3-D) time-reversal of ultrasonic fields; it is also a generalization of the time-reversal mirrors realized experimentally in the laboratory. The proposed method is based on an approach in the transient regime that is more general than the monochromatic formalism used in optics to analyze the phase conjugation mirrors efficiency. This method uses impulse diffraction theory to obtain the impulse response of the cavity in any inhomogeneous medium. An original interpretation of the limitations due to diffraction observed in wave field propagation in terms of the different waves generated inside the cavity is also proposed. The time-reversal focusing process using a closed cavity in a weakly inhomogeneous medium is compared with more classical techniques to compensate wavefront distortions, thus illustrating the focusing improvement due to the time-reversal method.     

Ultrasonic nondestructive testing of scattering media using the decomposition of the time-reversal operator

In ultrasonic nondestructive testing, the iterative time-reversal process is an adaptive technique that can be used to detect flaws in complex samples with a large array of transducers. The decomposition of the time-reversal operator (DORT) method is a detection technique that is derived from the mathematical analysis of the iterative time-reversal process. Contrary to time-reversal techniques, the DORT method does not require programmable generators, and it allows the simultaneous detection and separation of several defects. In this paper, the method is applied to a Ti6-4 titanium cylindrical sample to separate the echo of a defect from the speckle due to microstructure contribution. The grain structure of this titanium alloy makes detection very difficult and, for large depths, conventional techniques do not allow the detection of small flaws with a satisfactory signal-to-noise ratio. The efficiency of the DORT method to detect a flat bottom hole with a diameter of 0.4 mm located at a depth of 140 mm in a titanium alloy sample is shown.     

一种二分迭代实时声线修正算法

为提高对水下目标的定位精度,提出并实现了一种二分迭代实时声线修正算法。首先通过二分迭代法快速搜索出水下声源所发出的定位声信号传播声线的初始掠射角,然后以该初始掠射角对应的唯一声线为基础,根据斯涅耳(Snell)声线折射定理计算得到声源与水下接收阵元的距离值,最终利用与声线相符的三路测距值进行交汇解算,完成实时声线修正定位。湖上试验结果表明,该算法简单易行、运算速度快,能够满足实时修正处理的要求,在复杂水文条件下提高了水声定位系统的定位精度。该算法具有良好的工程实用性和通用性,可推广应用于同类水声跟踪定位系统。     

多盲孔缺陷的超声兰姆波时域拓扑能量成像方法研究

传统超声成像方法受瑞利准则的约束，难以对缺陷间距小于成像分辨率阈值的多缺陷进行成像。提出了一种基于时域拓扑能量的超声兰姆波成像方法，将逆散射拓扑成像方法中的拓扑渐进过程转换成求解直接声场和伴随声场。然后通过将伴随声场进行时间反转，两个声场将具有在缺陷处聚焦，在非缺陷处不聚焦的特性。将直接声场和伴随声场进行融合，以时域拓扑能量值作为像素值进行成像，从而使表征缺陷的精度较高。建立了缺陷间距小于分辨率阈值的多盲孔缺陷有限元模型，通过“一发多收”的方式激发S0模式和采集缺陷散射信号，并进行时域拓扑能量成像。仿真结果表明：对于多盲孔缺陷，时域拓扑能量成像法能够获得比延时叠加法和时间反转成像法更高的分辨率，并且能在缺陷间距小于成像分辨率阈值时进行成像。     

Aberration correction by time reversal of moving speckle noise

Focusing a wave through heterogeneous media is an important problem in medical ultrasound imaging. In such aberrating media, in the presence of a small number of point reflectors, iterative time reversal is a well-known method able to focus on the strongest reflector. However, in presence of speckle noise generated by many non-resolved scatterers, iterative time reversal alone does not work. In this paper, we propose the use of the echoes coming from moving particles in a flow, such as red blood cells, to generate a virtual point reflector by iterative time reversal. The construction of the virtual point reflector is performed by a coherent addition of independent realizations of speckle coming from moving particles. After focusing on a virtual point reflector, ultrasound images can be locally corrected inside an isoplanatic patch. An application for the correction of power Doppler images is presented. A theoretical analysis shows that this iterative method allows focusing on the point of maximal insonification of the uncorrected beam.     

Optimal sound speed estimation using modified nonlinear anisotropic diffusion to improve spatial resolution in ultrasound imaging

In ultrasound exams of obese patients and the breast, the spatial and contrast resolutions of ultrasound images are severely deteriorated when a constant sound speed corresponding to soft tissue is used in receive dynamic beamformation. This degradation is due to the defocusing of the ultrasound beam because of the disparity in sound speed between soft tissue and fatty layers. To minimize the degradation, this paper proposes a new method of estimating an optimal sound speed that can be used to achieve the best beamforming performance in a region of interest (ROI). The proposed method employs a new focusing quality factor (FQF) as an indicator of how well the focusing is conducted with a given sound speed. The FQF is closely associated with the degree of edge conspicuity, which can be obtained using the proposed modified nonlinear anisotropic diffusion (MNAD) technique. To calculate FQF, ultrasound images are formed with different sound speeds ranging from 1400 to 1600 m/s and, subsequently, the ROI is chosen. In the ROI, the degrees of edge conspicuity (i.e., FQF) are calculated. The sound speed can be considered an optimal one for the ROI if it is used to construct the image that provides the maximum FQF. The performances of the proposed method were evaluated through simulation and in vitro experiments with a tissue-mimicking phantom. The performance was also compared with that of the conventional image-based method employed in a commercial ultrasound imaging system. The experimental results demonstrated that the proposed method is capable of estimating an optimal sound speed with an error of 10 m/s regardless of whether strong targets are included in the ROI or not. On the other hand, the conventional image-based method generated an estimation error of 60 m/s maximally in the case in which there were no strong targets in ROI. This indicates that the proposed method is a useful tool to improve ultrasound image quality for clinical applications, especially for ultrasound exams of obese patients and the breast.     

时间反转镜DOA-AT成像算法

超声成像中广泛应用的DOA算法容易受到介质的不均匀性和多途效应的影响,纵坐标分辨率较差。在时间反转法理论的基础上,提出在随机媒质中采用时间反转镜超声成像的DOA-AT新算法。新算法通过对散射中接收信号的到达时间和响应矩阵频域奇异值进行分解,将时域内目标函数DOA估计与到达时间估计结合起来,使成像目标的纵坐标估计得到明显改善,对目标检测能力增强。     

A study on the reconstruction of moderate contrast targets using the distorted born iterative method

Previous tomographic methods using ultrasound for reconstructing sound speed and attenuation images suffered from convergence issues for targets with moderate speed of sound contrast. Convergence problems can be overcome by the use of the multiple frequency, distorted Born iterative method (DBIM). The implementation of DBIM for measurement configurations in which receiver positions are fixed was studied, and a novel regularization scheme was developed. The regularization parameter needed to stabilize the inversion process initially was found through the Rayleigh quotient iteration, then relaxed according to the relative residual error between the measured and estimated scattered fields. The DBIM was successfully stabilized for both full and partial receiver angular coverage without a significant loss in spatial resolution. The effects of variable density in the reconstructions were briefly explored through simulations. The ability to reconstruct targets with moderate contrast was validated through experimental measurements. Speed of sound profiles for balloons filled with saline in a background of water were reconstructed using multiple frequency DBIM techniques. The mean squared error for speed of sound reconstructions of the balloon phantoms with 16.4% sound speed contrast was 1.1%.     

Vector diffraction problem of focusing a category 1 aberrated wavefront through a multilayered lossless medium

Abstract

In optical storage and other imaging applications, a laser beam is focused through a transparent lossless medium of different refractive index. Applications include optical and magneto-optical recording. It is highly likely that, in the near future, conventional magnetic recording will transition to optically/thermally assisted magnetic recording technology. In all these applications, it is necessary to ascertain the quality of the image formed by the focusing apparatus on an imaging surface when in the neighbourhood of the focus, the focused beam of light passes through a stratified lossless medium. This paper examines the vector diffraction problem of focusing radiation through a multilayered medium. The solution is accomplished by first deriving a general solution of the focusing problem in any homogenous medium. This solution is then used to obtain the solution in the multilayered medium by applying continuity of the electric and magnetic fields at the interfaces. The technique used here allows one to calculate the field quantities in the entire image space. Furthermore, the focusing lens may have Seidel aberrations of the fourth order. The salient feature of this method is that the vector diffraction problem is solved only once - for the zeroth layer, immediately next to the exit pupil. In the remaining layers, the results are obtained by solving linear algebraic equations. The solution of the algebraic equations is obtained in closed form.     

Dynamic tomography with a priori information

We present "dynamic tomography" algorithms that allow for the high-resolution, time-resolved imaging of dynamic (i.e., continuously time evolving) complex systems at existing x-ray micro-CT facilities. The behavior of complex systems is constrained by the underlying physics. By exploiting a priori knowledge of the geometry of the physical process being studied to allow the use of sophisticated iterative reconstruction techniques that incorporate constraints, we improve on current frame rates by at least an order of magnitude. This allows time-resolved imaging of previously intractable processes, such as two-phase fluid flow. We present reconstructions from experimental data collected at the Australian National University x-ray micro-CT facility.     

A k-space method for large-scale models of wave propagation in tissue

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for “slow” (c(x)⩽c₀) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed     

Sources of image degradation in fundamental and harmonic ultrasound imaging: a nonlinear, full-wave, simulation study

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain. This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-and-sum beamforming is used to generate point spread functions (PSFs) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is due to reverberation from near-field structures. Compared with fundamental imaging, reverberation clutter in harmonic imaging is 27.1 dB lower. Simulated tissue with uniform velocity but unchanged impedance characteristics indicates that for harmonic imaging, the primary source of degradation is phase aberration.     

Position and time-delay calibration of transducer elements in a sparse array for underwater ultrasound imaging

This paper describes a novel method for the calibration of the position and time delay of transducer elements in a large, sparse array used for underwater, high-resolution ultrasound imaging. This method is based on the principles used in the global positioning system (GPS). However, unlike GPS, in which the wave propagation speed is generally assumed known, the sound propagation speed in the water usually is unknown and it is calibrated simultaneously in this method to achieve high calibration accuracy. In this method, a high-precision positioning system is used to scan a single hydrophone (used for transmission) in the imaging field of the array. The hydrophone transmits pulses at selected positions, and the transducer elements in the sparse array receive the transmitted signals. Time of flight (TOF) values between transducer elements and hydrophone positions then are measured. From a series of measured TOF values, the position and time delay values for each transducer element as well as the propagation speed can be calibrated. The performances of the calibration algorithm are theoretically analyzed and evaluated with numerical calculations and simulation studies. It is found that this method is capable of calibrating the positions and time delays of transducer elements with high accuracy.     

Sources of image degradation in fundamental and harmonic ultrasound imaging using nonlinear, full-wave simulations

A full-wave equation that describes nonlinear propagation in a heterogeneous attenuating medium is solved numerically with finite differences in the time domain (FDTD). This numerical method is used to simulate propagation of a diagnostic ultrasound pulse through a measured representation of the human abdomen with heterogeneities in speed of sound, attenuation, density, and nonlinearity. Conventional delay-andsum beamforming is used to generate point spread functions (PSF) that display the effects of these heterogeneities. For the particular imaging configuration that is modeled, these PSFs reveal that the primary source of degradation in fundamental imaging is reverberation from near-field structures. Reverberation clutter in the harmonic PSF is 26 dB higher than the fundamental PSF. An artificial medium with uniform velocity but unchanged impedance characteristics indicates that for the fundamental PSF, the primary source of degradation is phase aberration. An ultrasound image is created in silico using the same physical and algorithmic process used in an ultrasound scanner: a series of pulses are transmitted through heterogeneous scattering tissue and the received echoes are used in a delay-and-sum beamforming algorithm to generate images. These beamformed images are compared with images obtained from convolution of the PSF with a scatterer field to demonstrate that a very large portion of the PSF must be used to accurately represent the clutter observed in conventional imaging.     

Sound field calculations for an ultrasonic linear phased array with a spherical liquid lens

Lenses are often used to provide focusing in the elevation dimension of ultrasonic linear phased-array transducers. The use of a liquid lens in this application adds a variable geometric focusing capability, determined by the radius of curvature of the lens surface and speed of sound in the liquid, to the electronic focusing produced by the linear phased array. An efficient method to calculate the sound field radiated from the linear phased-array transducer through the liquid lens is presented. It treats the lens surface as a secondary source distribution according to Huygens's principle, and employs a modified form of the rectangular radiator method to calculate the field. The appropriate phases for the array elements to focus and steer the beam are calculated by considering the refraction on the lens surface. Comparisons of computer simulations and experimental measurements of the field intensity distribution of a prototype linear array transducer with a liquid lens demonstrate the accuracy of the proposed method.     

基于改进FISTA的高分辨率声源定位方法

为提高快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm, FISTA)在反卷积波束形成中的空间分辨率以及计算速度,采用基于快速傅里叶变换的声学模型,引入过松弛方法和“贪婪”重启策略,提出两种改进的快速迭代收缩阈值算法,即基于快速傅里叶变换的过松弛单调快速迭代收缩阈值算法(Over-relaxed MonotoneFast Iterative Shrinkage-Thresholding Algorithm based on Fast Fourier Transform, FFT-OMFISTA)和基于快速傅里叶变换的“贪婪”快速迭代收缩阈值算法("Greedy" Fast Iterative Shrinkage-Thresholding Algorithm based on Fast FourierTransform, FFT-GFISTA),并应用于反卷积波束形成的求解过程中。设计了单声源和双声源的仿真与实验,验证了所提算法的有效性与优越性。结果表明,两种所提算法都具有良好的性能,都能在声源定位中实现更高的空间分辨率以及更快的计算速度。     

基于分辨力空间变化的自动聚焦方法

在获取数字化图象的过程中,快速、有效地实现自动聚焦十分重要。提出一种加快对焦判断的方法,模仿人眼视觉系统中视网膜的空间变化分辨力,建立了模拟模型并进行了数据分析。实验表明,利用所提出的模型,在保持高分辨力的同时又有一个大视场和较少的数据处理量,在保证了为精度的同时又提出了原有的处理速度,在对焦策略上有一定的先进性,在机器人视觉系统和数字成象系统中具有很好的应用前景。     

层状无砟轨道结构脱层缺陷超声成像

无砟轨道是典型的层状混凝土结构,脱层缺陷是其最常见的损伤形式,影响着高速列车的安全运行。传统的合成孔径聚焦成像方法是基于恒定声速的超声检测方法,忽略层间的声阻抗差异以及声波在层间界面处的折射,导致声束难以在缺陷处聚焦,声波在层状结构中传播的时间误差较大。鉴于此,提出了一种多层结构合成孔径聚焦成像方法,充分考虑多层结构中的层间声速差异,采用射线追踪方法准确获取声波在多层结构中的传播时间。在此基础上,分析了不同入射波模式以及不同激发频率对多层结构合成孔径聚焦成像结果的影响。结果表明：采用多层结构合成孔径聚焦成像方法,使用频率为50 kHz的横波入射成像分辨率更高,对无砟轨道脱层缺陷检测效果更好。该研究为该类缺陷检测提供了理论支撑。