Wideband imaging of extended targets with the decomposition of the time reversal operator

The weighted wideband imaging approach of full signal subspaces is proposed based on the decomposition of the time reversal operator(DORT). Although each singular vector of nonzero singular values does not correspond to one of the extended targets any more, the conventional approach of selective time reversal focusing still chooses one of the signal subspaces for imaging. Simultaneously, the time-reversal MUSIC imaging is carried out at a single frequency for wideband signal. The imaging of both methods has a high background fluctuation.In order to overcome these drawbacks, the number of signal subspaces is determined by the singular values of the time reversal operator, and then DORT imaging of full signal subspaces and entire bandwidth is achieved using the generalized reflectivity coefficients as the weighted parameters. The experimental result shows that the sidelobe level of this approach is extremely decreased.     

宽带扩展性目标时反算子分解成像

在时反算子分解技术的基础上,提出了宽带全信号子空间加权成像方法。虽然扩展性目标与时反算子的特征向量不再是一一对应关系,传统的时反选择性聚焦仍然选择某一特定的信号子空间成像,而时反MUSIC只利用某一频点成像,导致定位结果背景起伏较高。为克服这些缺陷,利用时反算子的特征值判断信号子空间的个数,以广义散射系数为加权系数,实现全宽带和全信号子空间成像。结果表明,此方法的旁瓣水平明显下降。      

Experimental detection and focusing in shallow water by decomposition of the time reversal operator

A rigid 24-element source-receiver array in the 10-15 kHz frequency band, connected to a programmable electronic system, was deployed in the Bay of Brest during spring 2005. In this 10- to 18-m-deep environment, backscattered data from submerged targets were recorded. Successful detection and focusing experiments in very shallow water using the decomposition of the time reversal operator (DORT method) are shown. The ability of the DORT method to separate the echo of a target from reverberation as well as the echo from two different targets at 250 m is shown. An example of active focusing within the waveguide using the first invariant of the time reversal operator is presented, showing the enhanced focusing capability. Furthermore, the localization of the scatterers in the water column is obtained using a range-dependent acoustic model.     

Detection of cracks in a thin air-filled hollow cylinder by application of the DORT method to elastic components of the echo

The DORT method (Decomposition de l'Opérateur de Retournement Temporel in French) is a scattering analysis technique which uses arrays of transducers. This method is efficient for detection of selective focusing on point-like scatterers. It has been also applied to analyze the scattering by an air-filled cylindrical steel shell immersed in water. It was shown that the diagonalization of the time reversal operator allows us to separate the different elastic components of the scattered field. Here, we apply the method to detect flaws in hollow cylinders. In this case, the dominant components are the three circumferential waves (A0, A1 and S0 Lamb modes). Each Lamb mode corresponds to an invariant of the time reversal operator. The dispersion curves of these waves are calculated from these invariants. Resonance frequencies of the shell are deduced from the frequency dependence of the eigenvalues of the time reversal operator. It is shown that the presence of a crack (0.2 mm in depth) affects significantly the eigenvalue distribution of the time reversal operator. Thus, the DORT method offers a new means for detecting defects in a shell.     

Real time inverse filter focusing through iterative time reversal

In order to achieve an optimal focusing through heterogeneous media we need to build the inverse filter of the propagation operator. Time reversal is an easy and robust way to achieve such an inverse filter in nondissipative media. However, as soon as losses appear in the medium, time reversal is not equivalent to the inverse filter anymore. Consequently, it does not produce the optimal focusing and beam degradations may appear. In such cases, we showed in previous works that the optimal focusing can be recovered by using the so-called spatiotemporal inverse filter technique. This process requires the presence of a complete set of receivers inside the medium. It allows one to reach the optimal focusing even in extreme situations such as ultrasonic focusing through human skull or audible sound focusing in strongly reverberant rooms. But, this technique is time consuming and implied fastidious numerical calculations. In this paper we propose a new way to process this inverse filter focusing technique in real time and without any calculation. The new process is based on iterative time reversal process. Contrary to the classical inverse filter technique, this iteration does not require any computation and achieves the inverse filter in an experimental way using wave propagation instead of computational power. The convergence from time reversal to inverse filter during the iterative process is theoretically explained. Finally, the feasibility of this iterative technique is experimentally demonstrated for ultrasound applications.     

Transmission mode time-reversal super-resolution imaging

The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, "Super-resolution imaging using time-reversal and MUSIC," J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, "The iterative time reversal process: Analysis of the convergence," J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., "Decomposition of the time reversal operator: Detection and selective focusing on two scatterers," J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth's surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with "classical" backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.     

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.     

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.     

Imaging in the presence of grain noise using the decomposition of the time reversal operator

In this paper, we are interested in detecting and imaging defects in samples of cylindrical geometry with large speckle noise due to the microstructure. The time reversal process is an appropriate technique for detecting flaws in such heterogeneous media as titanium billets. Furthermore, time reversal can be iterated to select the defect with the strongest reflectivity and to reduce the contribution of speckle noise. The DORT (the French acronym for Decomposition of the Time Reversal Operator) method derives from the mathematical analysis of the time reversal process. This detection technique allows the determination of a set of signals to be applied to the transducers in order to focus on each defect separately. In this paper, we compare three immersion techniques on a titanium sample, standard transmit/receive focusing, the time reversal mirror (TRM), and the DORT method. We compare the sensitivity of these three techniques, especially the sensitivity to a poor alignment of the array with the front face of the sample. Then we show how images of the sample can be obtained with the TRM and the DORT method using backpropagation algorithm.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Echo-to-reverberation enhancement based on decomposition of time reversal operator with forward and backward reverberation nulling constrains

Combined the decomposition of time reversal operator and the time reversal reverberation nulling, a new time reversal processing approach for echo-to-reverberation ratio enhancement is proposed. In this method, a 2-dimensional signal subspace for the range of the target and two bottom focusing weight vectors for the ranges near the target are obtained by the decomposition of time reversal operator. From the signal subspace and focusing weight vectors, a constrained optimal excitation weight vector of source receiver array can be deduced to null the acoustic energy on the corresponding bottom and maximize the energy at the tar- get. This method remedies the shortages of conventional time reversal processing, time reversal reverberation nulling and time reversal selective focusing method. It focuses sound energy at the target and nulls the energy at the bottom near the target range simultaneously, therefore enhancing the echo-to-reverberation ratio without probe source and prior-knowledge of the relative scattering intensity of target and bottom. Numerical simulations in typical shallow water environments showed the effectiveness of the proposed method and its improved performance for echo-reverberation enhancement than conventional time reversal processing.     

Automatic determination of the number of targets present when using the time reversal operator

Acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources. The DORT method is a derivation of the time reversal process, which allows for focusing on multiple targets. An important step in this process is the determination of the number of targets or sources present. This is achieved by examining the eigenvalues of the time reversal operator (TRO). The number of significant eigenvalues is then chosen as the number of sources present. However, as mentioned in [N. Mordant, C. Prada, and M. Fink, J. Acoust. Soc. Am. 105, 2634-2642 (1999) and C. Prada, M. Tanter, and M. Fink, in Proceedings of the IEEE Symposium, 1997, pp. 679-683], factors such as low signal to noise ratio (SNR), small data sample, array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues. This paper proposes a robust method of automatically determining the number of targets even in the presence of a small number of snapshots. For white Gaussian noise, the profile of the ordered eigenvalues is seen to fit an exponential law. The observed eigenvalues are then compared to this model and a mismatch is detected between the observed profile and the noise-only model. The index of the mismatch gives the number of scatterers present.     

Green's function estimation in speckle using the decomposition of the time reversal operator: application to aberration correction in medical imaging

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Green's function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Green's functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Green's function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.     

Adaptive projection method applied to three-dimensional ultrasonic focusing and steering through the ribs

An adaptive projection method for ultrasonic focusing through the rib cage, with minimal energy deposition on the ribs, was evaluated experimentally in 3D geometry. Adaptive projection is based on decomposition of the time-reversal operator (DORT method) and projection on the "noise" subspace. It is shown that 3D implementation of this method is straightforward, and not more time-consuming than 2D. Comparisons are made between adaptive projection, spherical focusing, and a previously proposed time-reversal focusing method, by measuring pressure fields in the focal plane and rib region using the three methods. The ratio of the specific absorption rate at the focus over the one at the ribs was found to be increased by a factor of up to eight, versus spherical emission. Beam steering out of geometric focus was also investigated. For all configurations projecting steered emissions were found to deposit less energy on the ribs than steering time-reversed emissions: thus the non-invasive method presented here is more efficient than state-of-the-art invasive techniques. In fact, this method could be used for real-time treatment, because a single acquisition of back-scattered echoes from the ribs is enough to treat a large volume around the focus, thanks to real time projection of the steered beams.     

Optimal focusing by spatio-temporal inverse filter. I. Basic principles

A focusing technique based on the inversion of the propagation operator relating an array of transducers to a set of control points inside a medium was proposed in previous work [Tanter et al., J. Acoust. Soc. Am. 108, 223-234 (2000)] and is extended here to the time domain. As the inversion of the propagation operator is achieved both in space and time, this technique allows calculation of the set of temporal signals to be emitted by each element of the array in order to optimally focus on a chosen control point. This broadband inversion process takes advantage of the singular-value decomposition of the propagation operator in the Fourier domain. The physical meaning of this decomposition is explained in a homogeneous medium. In particular, a definition of the number of degrees of freedom necessary to define the acoustic field generated by an array of limited aperture in a focal plane of limited extent is given. This number corresponds to the number of independent signals that can be created in the focal area both in space and time. In this paper, this broadband inverse-focusing technique is compared in homogeneous media with the classical focusing achieved by simple geometrical considerations but also with time-reversal focusing. It is shown that, even in a simple medium, slight differences appear between these three focusing strategies. In the companion paper [Aubry et al., J. Acoust. Soc. Am. 110, 48-58 (2001)] the three focusing techniques are compared in heterogeneous, absorbing, or complex media where classical focusing is strongly degraded. The strong improvement achieved by the spatio-temporal inverse-filter technique emphasizes the great potential of multiple-channel systems having the ability to apply completely different signal waveforms on each transducer of the array. The application of this focusing technique could be of great interest in various ultrasonic fields such as medical imaging, nondestructive testing, and underwater acoustics.     

Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis

We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles.     

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.     

Time reversed reverberation focusing in a waveguide

Time reversal mirrors have been applied to focus energy at probe source locations and point scatterers in inhomogeneous media. In this paper, we investigate the application of a time reversal mirror to rough interface reverberation processing in a waveguide. The method is based on the decomposition of the time reversal operator which is computed from the transfer matrix measured on a source-receiver array [Prada et al., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. In a similar manner, reverberation data collected on a source-receiver array can be filtered through an appropriate temporal window to form a time reversal operator. The most energetic eigenvector of the time reversal operator focuses along the interface at the range corresponding to the filter delay. It is also shown that improved signal-to-noise ratio measurement of the time reversal operator can be obtained by ensonifying the water column with a set of orthogonal array beams. Since these methods do not depend upon a priori environmental information, they are applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide demonstrate this method.     

基于虚拟源时间反转的经颅超声精确聚焦*

针对经颅超声难以精确聚焦的问题,本文研究了基于虚拟源的时间反转方法,建立颅骨二维数字模型,在聚焦目标处设置虚拟声源,利用时域有限差分法模拟超声时间反转过程,并考察基于虚拟源时间反转方法的聚焦效果。数值仿真结果表明,基于虚拟源的时间反转方法可以实现经颅超声的精确聚焦,聚焦强度和精度好于传统的相控聚焦;换能器中心频率和数量对聚焦效果的影响规律与相控聚焦时类似;该方法可以同时向多个焦点聚焦,并自适应调节各焦点处声压幅度。     

Robust time reversal focusing based on Maximin criterion in a waveguide with uncertain water depth

Time reversal processing(TRP) might be regarded as matched field processing with known environmental knowledge.However,the performance of TRP is degraded in an uncertain environment.A technique based on the Maximin criterion is proposed for enhancing the robustness of TRP in a waveguide with uncertain water depth.The relationship between the water depth and the focal spot translation is examined based on the waveguide-invariant theory.Then the time reversal transmission scheme with the Maximin criterion is performed to maximize the minimum transmission power on a target of interest.At the receiving end,coherent summation operation is carried out over the received data by a reception focusing bank.If it is necessary to enhance the target echo further,the iterative time reversal can be considered where the target echo corresponding to the first time reversal transmission is regarded as a secondary source.Numerical simulations and experimental results of the target localization in a waveguide tank have verified the effectiveness of robust TRP.