Iterative Time Reversal Process Research Articles

Correcting for Target Motion in Time-Reversal Spectral Focusing

It is well-known that an iterative time-reversal (TR) process, applied via a distributed sensing system, can be used to produce a space-time waveform that maximizes the energy scattered from a stationary target back to the sensors. The TR process accomplishes this by automatically focusing energy, both spatially and spectrally, on the stationary target. When scatterers are moving, however, the TR focusing can break down. This article shows how to modify the TR process so that it automatically focuses energy on a moving target. This new TR process automatically generates a distributed beam that: 1) follows the target as it moves and 2) enhances the target resonances by concentrating the energy spectrally. This focusing occurs without a priori knowledge of the target’s location or spectral response. The new TR algorithm is derived through a careful analysis of the idealized case of a single isotropic moving point scatterer. This article includes simulations that compare the TR focus both with and without the new modification. Although the simulations are carried out for the electromagnetic case, the theory applies equally well to the acoustic case when the target speed is significantly less than the ambient sound speed. Appendices are included with details of the calculations and with analysis of the range of relative velocities for which the modified TR process should be used.

A distortion matrix framework for high-resolution passive seismic 3-D imaging: application to the San Jacinto fault zone, California

SUMMARYReflection seismic imaging usually suffers from a loss of resolution and contrast because of the fluctuations of the wave velocities in the Earth’s crust. In the literature, phase distortion issues are generally circumvented by means of a background wave velocity model. However, it requires a prior tomography of the wave velocity distribution in the medium, which is often not possible, especially in depth. In this paper, a matrix approach of seismic imaging is developed to retrieve a 3-D image of the subsoil, despite a rough knowledge of the background wave velocity. To do so, passive noise cross-correlations between geophones of a seismic array are investigated under a matrix formalism. They form a reflection matrix that contains all the information available on the medium. A set of matrix operations can then be applied in order to extract the relevant information as a function of the problem considered. On the one hand, the background seismic wave velocity can be estimated and its fluctuations quantified by projecting the reflection matrix in a focused basis. It consists in investigating the response between virtual sources and detectors synthesized at any point in the medium. The minimization of their cross-talk can then be used as a guide star for approaching the actual wave velocity distribution. On the other hand, the detrimental effect of wave velocity fluctuations on imaging is overcome by introducing a novel mathematical object: The distortion matrix. This operator essentially connects any virtual source inside the medium with the distortion that a wavefront, emitted from that point, experiences due to heterogeneities. A time reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each real geophone at the surface and each virtual geophone in depth. Phase distortions can then be compensated for any point of the underground. Applied to passive seismic data recorded along the Clark branch of the San Jacinto fault zone (SJFZ), the present method is shown to provide an image of the fault until a depth of 4 km over the frequency range 10–20Hz with an horizontal resolution of 80 m. Strikingly, this resolution is almost one eighth below the diffraction limit imposed by the geophone array aperture. The heterogeneities of the subsoil play the role of a scattering lens and of a transverse waveguide which increase drastically the array aperture. The contrast is also optimized since most of the incoherent noise is eliminated by the iterative time reversal process. Beyond the specific case of the SJFZ, the reported approach can be applied to any scales and areas for which a reflection matrix is available at a spatial sampling satisfying the Nyquist criterion.

Tuning to Resonances With Iterative Time Reversal

This paper considers a distributed wave-based sensing system that probes a scene consisting of multiple interacting idealized targets. Each sensor is a collocated transmit–receive pair that is capable of transmitting arbitrary wideband waveforms. We address the problem of finding the space-time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers. Our approach is based on earlier theoretical work that showed, for an idealized infinite half-space geometry, that the solution could be constructed by an iterative time-reversal (TR) process. In this paper, we give a more realistic example involving a two-sensor time-domain system. We show that for this system, the iterative TR process can be used to tune automatically to all the target resonances that are within the bandwidth of the interrogating radar system. We show that although obtaining eigenvalues (and hence resonances) of the scattering operator is in general unstable, using the iterative TR process to obtain the resonances is a stable process. Moreover, we show that these resonance frequencies are connected to the poles of the singularity expansion method.

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.

Experimental investigation of bottom target detection by single channel iterative time reversal.

Iterative time reversal process will gradually lead echo waves to converge to a dominant narrowband resonant mode of the target and enhance the return level in noisy and reverberant environment. This technique is used in bottom target detection and an experiment has been performed in the Yellow Sea, China. The experiment is in a monostatic configuration, and the target, which is a 53 cm external diameter and 260 cm long stainless steel cylindrical shell with concrete interior, is resting on the seafloor, and the directional transceiver, which is a transmitter and receiver couple, is located right above the target. First, a broadband interrogation pulse is launched, and the echo is measured and a bandpass filter is applied to avoid transceiver response peak, then the signal is time reversed and retransmitted, and repeat above procedures iteratively. The bottom reverberation will gradually be suppressed, and the center frequency of converged signal corresponds to a target resonance frequency, which is different from inhomogeneous bottom response in no target case. The existence of target is determined by this important acoustic signature, and the results illustrate the feasibility of this method. [Work partially supported by the CAS Innovation Fund.]

Time reversal mirrors and invariants of the time reversal operator: Application to detection and imaging in biological media

Acoustic time reversal mirrors have been developed in the Laboratoire Ondes et Acoustique for several years. In inhomogeneous media and especially in the presence of multiple scattering, these systems provide outstanding focusing properties. While used in pulse echo mode, the time reversal process can be iterated, leading to selective focusing on the most reflective point among a set of scatterers. This iteration is also used to enhance the echo from a defect like a kidney stone or a microcalcification in the breast. The iterative time reversal process is described by a matrix call the Time Reversal Operator (TRO). The eigenvectors of this matrix provide the invariants of the iterative time reversal process, their analysis is the base of the D.O.R.T. method. It allows the separation of the echoes from several scatterers in an inhomogeneous medium and the selective focusing on any of them. Furthermore, when an estimate of the medium’s Green function is available, high‐resolution and low‐noise images can be achieved using the backpropagation of the dominant eigenvectors. The principle of acoustic time reversal mirrors and the D.O.R.T. method will be described through several examples.

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.

Time reversal techniques in ultrasonic nondestructive testing of scatteringmedia

Time reversal techniques are adaptive methods that can be used in nondestructiveevaluation to improve flaw detection through inhomogeneous and scatteringmedia. Two techniques are presented: the iterative time reversal process and theDORT (French acronym for decomposition of the time reversal operator) method.In pulse echo mode, iterative time reversal mirrors allow one to accurately controlwave propagation and focus selectively on a defect reducing the speckle noise dueto the microstructure contribution. The DORT method derives from themathematical analysis of the iterative time reversal process. Unlike time reversalmirrors, it does not require programmable generators and allows the simultaneousdetection and separation of several defects. These two procedures are presentedand applied to detection in titanium billets where the grain structure rendersdetection difficult. Then, they are combined with the simulation codePASS (phased array simulation software) to form images of the samples.

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.

Iterative time reversal in the ocean

The iterative time-reversal process focusing on the strongest scatterer in a multitarget medium has been described theoretically in terms of eigenvalues and eigenvectors of a time-reversal operator K*K in ultrasonics [Prada et al., J. Acoust. Soc. Am. 97, 62–71 (1995)]. In this paper, we extend the concept of iterative time-reversal to waveguide propagation in the ocean. For a single target, the iterative time-reversal process results in a minor improvement in spatial focusing. However, data from a recent experiment in the Mediterranean Sea [Kuperman et al., J. Acoust. Soc. Am. 103, 25–40 (1998)] illustrates the importance of the waveguide and source transducer characteristics even in the single target case. When the ocean contains several reflectors, iterative time-reversal focuses on the target corresponding to the largest eigenvalue of the time-reversal operator, which depends not only on the reflectivity of the targets, but also on the complex propagation effects between the targets and time-reversal mirror. Analysis of the experimental data for a single target and simulation results with multiple targets in the ocean are presented.

Iterative time reversal in the ocean

The efficiency of an iterative time reversal process in the ocean has been demonstrated in an experiment conducted in the Mediterranean Sea during April 1996. [See Kuperman et al. in this session.] The iterative time reversal process consisted of initiating a 50-ms pulse with equal amplitudes on all elements from SRA to VRA, capturing the signal at 75-m depth on a single hydrophone of VRA, and retransmitting it from SRT at the same depth to SRA, reversing the received signal in time and retransmitting it from all the SRA sources back to VRA. This process was repeated many times over an hour. Although this was not the intended mode of operation of iterative phase conjugation as in the free-field case with many scatterers [Prada et al., J. Acoust. Soc. Am. 90, 1119–1129 (1991)], it shows that an iterative process can enhance the focusing of a single target in the ocean. Comparisons of data with simulations and theoretical analysis will be presented and discussed.

The iterative time reversal process: Analysis of the convergence

The efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated. In a multitarget media, the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown [C. Prada, F. Wu, and M. Fink, J. Acoust. Soc. Am. 90, 1119 (1991)]. The theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of L transducers in a given medium as a linear system of L inputs/L outputs. The system is characterized at each frequency by its transfer matrix K and the time reversal iterative process is then described by a time reversal operator K*K. Because of the reciprocity principle, this operator is Hermitian. The following result is shown: If the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator K*K with nonzero eigenvalue corresponds to one of the targets in the set and provides the optimum phase law to focus on it. Furthermore, the eigenvalue is proportional to the reflectivity of the target. In particular, the ‘‘brightest’’ target is associated to the eigenvector of greatest eigenvalue so that the iterative time reversal process leads to a wave focusing on this target. This analysis is illustrated by numerical and experimental results.

Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media

The iterative time reversal mirror provides an elegant way of focusing in multiple target media on the most reflective one. This paper presents a method to focus on the other targets. It is derived from a theoretical study of the iterative time reversal process. The iterative process can be described at each frequency by a time reversal operator which can be diagonalized. The eigenvectors of this operator are eigenmodes of the time reversal process. In the case of well resolved targets of different “brightness”, the rank of the time reversal operator is equal to the number of targets and each eigenvector of non zero eigenvalue provides the optimal phase and amplitude law to focus on the corresponding target. An experimental validation of these results is given.

Problèmes inverses en diffusion acoustique avec des miroirs à retournement temporel

Time-reversal mirror (T.R.M.) utilizes time-reversal invariance of wave equation. Acoustic T.R.M. are made of large transducer arrays allowing the incident acoustic field to be sampled, time-reversed, and re-emitted. Such a process allows an original way of studying acoustical sources. This paper describes an application of T.R.M. to the characterization of extended scatterer illuminated by broad band pulse. The ability of T.R.M. to time-reverse separetely each scattered waves permits to isolate spatially and temporally the equivalent sources of extended scatterer. We investigate more particularly the problem of a cylindrical scatterer: we show that T.R.M. allows to characterize simply the different sources of backscattered waves and especially the mode conversion of incident wave into circumferential waves. Besides, we show that iterative time reversal process allows to generate any particular circumferential wave