Optimal adaptive focusing through heterogeneous media with the minimally invasive inverse filter

The inverse filter is a technique used to adaptively focus waves through heterogeneous media. It is based on the inversion of the Green's functions matrix between the M transducers of a focusing array and N control points in the focal area. The inverse filter minimizes the pressure deposited around the focal point. However it is highly invasive, requiring the presence of N transducers or hydrophones in the focal area at the control points' locations to measure the Green's functions. This paper presents a way of reaching the inverse filter's focusing quality with a minimally invasive setup: only one transducer (at the desired focal location) is needed. This minimally invasive inverse filter takes advantage of the fact all the information about the propagation medium can be retrieved from the signals backscattered by the medium towards the focusing array, if the propagation medium is lossless. A numerical simulation is performed to test this minimally invasive inverse filter through a scattering, lossless medium. The focusing quality equals the conventional, highly invasive inverse filter's. The average spatial and temporal contrast is increased by up to 10 dB compared to the time reversal focusing.     

经颅超声聚焦方法和声场特性研究

基于高分辨的CT数据建立了非均匀颅骨仿真模型,该模型引入了颅骨的声衰减系数,深入研究和分析了声波时间反转法和超声相控阵法在颅脑中的聚焦方法及效果。颅骨具有较强的声波衰减特性,使用时间反转聚焦时需要进行幅度补偿,对于0.7MHz的频率信号,幅度补偿后的时间反转聚焦声场主瓣宽度窄、旁瓣低,焦点处声场比无幅度补偿的时间反转法提高8.86dB,比超声相控阵聚焦法提高7.89dB,具有很好的空间聚焦精度和聚焦效率。研究了颅骨衰减系数、声场焦点位置、声波频率、换能器阵列位置和方位等参数对聚焦声场的影响,结果表明,幅度补偿时间反转法比相控阵法具有更低的旁瓣,且高频时的聚焦效果比相控阵好,相控阵聚焦对换能器阵列的位置和方位比较敏感,而时间反转经颅超声聚焦对声传播路径和入射角具有更高的鲁棒性。      

基于时间反演技术的电磁器件端口场与内部场转换方法

随着电磁器件的集成化,器件搭载的模块、实现的功能愈发多样.各模块间的耦合难以忽略,设计难度陡然增加,传统设计方法逐渐力不从心,迫切需要寻找一种新的电磁综合设计方法.本文利用时间反演电磁波的时空同步聚焦特性,探索了将时间反演技术应用于器件设计的可能性.首先,基于通用的器件逆设计流程,利用时间反演技术、并矢格林函数及电磁学的基本原理,提出了将器件端口场分布转换为内部场分布的方法,并证明由端口期望场的时间反演场在空间某一位置获得的连续等效源的共轭分布可在端口处产生与期望场接近的场分布.且在单点频逆设计过程中,只需知道端口电场或磁场的切向分量即可完成端口场与内部场的转换.同时,借助格林函数的互易性对本文所提理论做适当变换后,进行数值仿真验证,分析讨论了不同初始信息条件下该方法的适用性.仿真结果与理论相符,证明了理论的正确性,为将时间反演技术应用于电磁器件的逆设计提供了可能.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

Unified Green's function retrieval by cross correlation

It has been shown by many authors that the cross correlation of two recordings of a diffuse wave field at different receivers yields the Green's function between these receivers. Recently the theory has been extended for situations where time-reversal invariance does not hold (e.g., in attenuating media) and where source-receiver reciprocity breaks down (in moving fluids). Here we present a unified theory for Green's function retrieval that captures all these situations and, because of the unified form, readily extends to more complex situations, such as electrokinetic Green's function retrieval in poroelastic or piezoelectric media. The unified theory has a wide range of applications in "remote sensing without a source."     

Time-reversed waves and super-resolution

Time-reversal mirrors (TRMs) refocus an incident wavefield to the position of the original source regardless of the complexity of the propagation medium. TRMs have now been implemented in a variety of physical scenarios from GHz microwaves to MHz ultrasonics and to hundreds of Hz in ocean acoustics. Common to this broad range of scales is a remarkable robustness exemplified by observations at all scales that the more complex the medium (random or chaotic), the sharper the focus. A TRM acts as an antenna that uses complex environments to appear wider than it is, resulting for a broadband pulse, in a refocusing quality that does not depend on the TRM aperture.Moreover, when the complex environment is located in the near field of the source, time-reversal focusing opens completely new approaches to super-resolution. We will show that, for a broadband source located inside a random metamaterial, a TRM located in the far field radiated a time-reversed wave that interacts with the random medium to regenerate not only the propagating but also the evanescent waves required to refocus below the diffraction limit. This focusing process is very different from that developed with superlenses made of negative index material only valid for narrowband signals. We will emphasize the role of the frequency diversity in time-reversal focusing. To cite this article: M. Fink et al., C. R. Physique 10 (2009).     

The focusing performance with a horizontal time- reversal array at different depths in shallow water

The performance of time-reversal focusing with a horizontal line array at different depths is investigated by normal mode modeling and computer simulation.It is observed that the focusing performance of a bottom-mounted horizontal time-reversal array is much better than that of a horizontal time-reversal array at other depths in shallow water.The normal mode modeling is used to explain this result.The absolute values of the modes at different depths are compared.It is shown that the number of modes whose absolute values close to zero is smaller at the bottom than that at other depths.It means that the horizontal time-reversal array deployed at the bottom can sample more modes,obtain more information of the probe source and achieve better focusing performance.The numerical simulations of time-reversal focusing performance under various conditions,such as different sound speed profiles,and different bottom parameters,lead to similar results.     

Acoustic emission localization in complex dissipative anisotropic structures using a one-channel reciprocal time reversal method

This paper presents an imaging method for the localization of the impact point in complex anisotropic structures with diffuse field conditions, using only one passive transducer. The proposed technique is based on the reciprocal time reversal approach (inverse filtering) applied to a number of waveforms stored into a database containing the experimental Green's function of the structure. Unlike most acoustic emission monitoring systems, the present method exploits the benefits of multiple scattering, mode conversion, and boundaries reflections to achieve the focusing of the source with high resolution. Compared to a standard time reversal approach, the optimal refocusing of the back propagated wave field at the impact point is accomplished through a "virtual" imaging process. The robustness of the inverse filtering technique is experimentally demonstrated on a dissipative stiffened composite panel and the source position can be retrieved with a high level of accuracy in any position of the structure. Its very simple configuration and minimal processing requirements make this method a valid alternative to the conventional imaging Structural Health Monitoring systems for the acoustic emission source localization.     

Time reversal and its application to tomography with diffracting sources

An exact time-domain method is proposed to time reverse a transient scalar wave using only the field measured on an arbitrary closed surface enclosing the initial source. Under certain conditions, a time-reversed field can be approximated by retransmitting the measured signals in a reversed temporal order. Exact reconstruction for three-dimensional broadband diffraction tomography (a linearized inverse scattering problem) is proposed by time-reversing the measured field back to the time when each secondary source is excited. The algorithm is verified by a numerical simulation. Extension to the case using Green's function in a heterogeneous medium is discussed.     

Time reversal of elastic waves in soft solids

When a scalar far-field wave is time reversed, it starts to converge toward its initial point source location, then collapses and finally diverges. Without evanescent waves, the symmetric focus spot is limited by the Rayleigh criterion. We present an experimental observation of a time-reversal elastic wave in a soft solid cavity using the transient elastography technique. It is observed that the time-reversed far field wave collapses and gives birth to near fieldlike effects. Elastodynamic Green's functions computation confirms the experimental conclusions: the diffraction limit implies a direction dependant Rayleigh criterion.     

Telecommunication in a disordered environment with iterative time reversal

Abstract

We present a method to transmit digital information through a highly scattering medium in a MIMO-MU (multiple input multiple output multiple users) context. It is based on iterations of a time-reversal process, and permits us to focus short pulses, both spatially and temporally, from a base antenna to different users. This iterative technique is shown to be more efficient (lower inter-symbol interference and lower error rate) than classical time-reversal communication, while being computationally light and stable. Experiments are presented: digital information is conveyed from 15 transmitters to 15 receivers by ultrasonic waves propagating through a highly scattering slab. From a theoretical point of view, the iterative technique achieves the inverse filter of propagation in the subspace of non-null singular values of the time-reversal operator. We also investigate the influence of external additive noise, and show that the number of iterations can be optimized to give the lowest error rate.

(Some figures in this article are in colour only in the electronic version)     

Optimal focusing by spatio-temporal inverse filter. II. Experiments. Application to focusing through absorbing and reverberating media

To focus ultrasonic waves in an unknown heterogeneous medium using a phased array, one has to calculate the optimal set of signals to be applied on the transducers of the array. (In most applications of ultrasound, medical imaging, medical therapy, nondestructive testing, the first step consists of focusing a broadband ultrasound beam deeply inside the medium to be investigated.) Focusing in a homogeneous medium simply requires to compensate for the varying focus-array elements geometrical distances. Nevertheless, heterogeneities in the medium, in terms of speed of sound, density, or absorption, may strongly degrade the focusing. Different techniques have been developed in order to correct such aberrations induced by heterogeneous media (time reversal, speckle brightness, for example). In the companion to this paper, a new broadband focusing technique was investigated: the spatio-temporal inverse filter. Experimental results obtained in various media, such as reverberating and absorbing media, are presented here. In particular, intraplate echoes suppression and high-quality focusing through a human skull, as well as hyper-resolution in a reverberating medium, will be shown. It is important to notice that all these experiments were performed with fully programmable multichannel electronics whose use is required to fully exploit the spatio-temporal technique.     

Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.     

Spatio-temporal invariants of the time reversal operator

The decomposition of the time reversal operator, known by the French acronym DORT, is a technique to extract point scatterers' monochromatic Green's functions from a medium. It is used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. A limitation of the method arises from its single-frequency nature, when the signals used in acoustics are often broadband. Reconstruction of the broadband Green's functions from the single-frequency Green's functions can be very difficult when numerous scatterers are present in the medium. Moreover, the method does not take advantage of the axial resolution associated with broadband signals. Time domain methods are investigated here as an answer to these problems. It is shown that the time reversal operator in the time domain takes the form of a tensor. The properties of the invariants are discussed. It is shown they do not have all the expected properties. Another method is proposed that requires a priori information on the medium.     

The determination of the relative permittivity of periodic stratified media based on the iterative time-reversal method

In this paper, we present a new method to determine the relative permittivity of periodic stratified media using the iterative time-reversal method. Based on transmission line theory, the focal peak value of iterative time-reversal electro- magnetic waves, which contain information about the periodic stratified medium, is computed in pulse-echo mode. Using the relationship between the focal peak value and the relative permittivity of the periodic stratified medium, the relative permittivity can be obtained by measuring the focal peak value. Numerical simulations are conducted, and the results demonstrate the feasibility of the proposed approach to the measurement of the relative permittivity of a periodic stratified medium.     

Modeling of wave propagation in inhomogeneous media

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surrounding the medium. Following a predictable initial computational effort, Green's functions between arbitrary points in the medium can be computed as needed using a simple cross-correlation algorithm.     

Amplitude degradation of time-reversed pulses in nonlinear absorbing thermoviscous fluids

The linear wave equation in a lossless medium is time reversible, i.e., every solution p(x, t) has a temporal mirror solution p(x, -t). Analysis shows that time reversal also holds for the lossless nonlinear wave equation. In both cases, time-reversal invariance is violated when losses are present. For nonlinear propagation loses cannot normally be ignored; they are necessary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pulse at the array elements also leads to a violation of time reversal even for lossless nonlinear acoustics. Numerical simulations are used to illustrate the effect of nonlinearity on the ability of a time-reversal system to effectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical results confirm that both shock generation (with the accompanying absorption) and amplification at the array, adversely affect the ability of a time-reversal system to form strong retrodirective sound fields.     

Limits of time-reversal focusing through multiple scattering: long-range correlation

Experimental results of time-reversal focusing in a high-order multiple scattering medium are presented and compared to theoretical predictions based on a statistical model. The medium consists of a random collection of parallel steel rods. An ultrasonic source (3.2 MHz) transmits a pulse that undergoes multiple scattering and is recorded on an array. The time-reversed waves are sent by the array back to the source through the scattering medium. The quality of temporal focusing is very well predicted by a simple statistical model. However, for thicker samples, persistent temporal side-lobes appear. We interpret these side-lobes as a consequence of the growing number of crossing paths in the sample due to high-order multiple scattering. As to spatial focusing, the resolution is practically independent from the array's aperture. With a 16-element array, the resolution was found to be 30 times finer than in a homogeneous medium. Resolutions of the order of the wavelength (0.5 mm) were attained. These results are discussed in relation with the statistical properties of time-reversal mirrors in a random medium.     

Effect of Media on the Electric Field of a Rhombic Nanostructure Array

Electric field distribution is an important parameter for nanostructure arrays in nanobiosensing appfications. It can influence the sensitivity and the resolution of nanobiosensors. We focus on the effect of media on the electric field distribution of a rhombic silver nanostructure array. The finite-difference time-domain algorithm- based numerical calculation method is used to monitor the electric field distribution of the silver nanostructures when the refractive index of the medium around the nanostructure array is changed. The calculated results show that tuning the refractive index of the medium around silver can have a considerable influence on the electric field distribution in the reflection and transmission directions. This effect can be used to increase the extinction efficiency and to improve the resolution of the spectra for nanobiosensing.     

任意半径圆形电流在径向成层介质中产生的电磁场

采用递推矩阵方法计算径向成层介质中的二维Green函数.根据层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解.只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的二维Green函数,并进而得到具有任意半径的圆形电流在介质中产生的电磁场.本文给出的Green函数具有表达方式简洁的优点.