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. I. Basic principles

SUMMARY

We draw connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, time-reversal imaging and finite-frequency ‘banana-doughnut’ kernels. We demonstrate that Frechet derivatives for tomographic and (finite) source inversions may be obtained based upon just two numerical simulations for each earthquake: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. For a given model, m, we consider objective functions χ(m) that minimize differences between waveforms, traveltimes or amplitudes. For tomographic inversions we show that the Frechet derivatives of such objective functions may be written in the generic form , where δ ln m=δm/m denotes the relative model perturbation. The volumetric kernel Km is defined throughout the model volume V and is determined by time-integrated products between spatial and temporal derivatives of the regular displacement field s and the adjoint displacement field s†; the latter is obtained by using time-reversed signals at the receivers as simultaneous sources. In waveform tomography the time-reversed signal consists of differences between the data and the synthetics, in traveltime tomography it is determined by synthetic velocities, and in amplitude tomography it is controlled by synthetic displacements. For each event, the construction of the kernel Km requires one forward calculation for the regular field s and one adjoint calculation involving the fields s and s†. In the case of traveltime tomography, the kernels Km are weighted combinations of banana-doughnut kernels. For multiple events the kernels are simply summed. The final summed kernel is controlled by the distribution of events and stations. Frechet derivatives of the objective function with respect to topographic variations δh on internal discontinuities may be expressed in terms of 2-D kernels Kh and Kh in the form , where Σ denotes a solid-solid or fluid-solid boundary and ΣFS a fluid–solid boundary, and ∇Σ denotes the surface gradient. We illustrate how amplitude anomalies may be inverted for lateral variations in elastic and anelastic structure. In the context of a finite-source inversion, the model vector consists of the time-dependent elements of the moment-density tensor m(x, t). We demonstrate that the Frechet derivatives of the objective function χ may in this case be written in the form , where e† denotes the adjoint strain tensor on the finite-fault plane Σ. In the case of a point source this result reduces further to the calculation of the time-dependent adjoint strain tensor e† at the location of the point source, an approach reminiscent of an acoustic time-reversal mirror. The theory is illustrated for both tomographic and source inversions using a 2-D spectral-element method.

Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels

The clinical part of these Guidelines and Recommendations produced under the auspices of the European Federation of Societies for Ultrasound in Medicine and Biology EFSUMB assesses the clinically used applications of all forms of elastography, stressing the evidence from meta-analyses and giving practical advice for their uses and interpretation. Diffuse liver disease forms the largest section, reflecting the wide experience with transient and shear wave elastography . Then follow the breast, thyroid, gastro-intestinal tract, endoscopic elastography, the prostate and the musculo-skeletal system using strain and shear wave elastography as appropriate. The document is intended to form a reference and to guide clinical users in a practical way.

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EFSUMB Guidelines and Recommendations on the Clinical Use of Ultrasound Elastography.Part 2: Clinical Applications

An ultrasonic array is a single transducer that contains a number of individually connected elements. Recent years have seen a dramatic increase in the use of ultrasonic arrays for non-destructive evaluation. Arrays offer great potential to increase inspection quality and reduce inspection time. Their main advantages are their increased flexibility over traditional single element transducer methods, meaning that one array can be used to perform a number of different inspections, and their ability to produce immediate images of the test structure. These advantages have led to the rapid uptake of arrays by the engineering industry. These industrial applications are underpinned by a wide range of published research which describes new piezoelectric materials, array geometries, modelling methods and inspection modalities. The aim of this paper is to bring together the most relevant published work on arrays for non-destructive evaluation applications, comment on the state-of the art and discuss future directions. There is also a significant body of published literature referring to use of arrays in the medical and sonar fields and the most relevant papers from these related areas are also reviewed. However, although there is much common ground, the use of arrays in non-destructive evaluation offers some distinctly different challenges to these other disciplines.

Ultrasonic arrays for non-destructive evaluation: A review

In the time-reversed counterpart to laser emission, incident coherent optical fields are perfectly absorbed within a resonator that contains a loss medium instead of a gain medium. The incident fields and frequency must coincide with those of the corresponding laser with gain. We demonstrated this effect for two counterpropagating incident fields in a silicon cavity, showing that absorption can be enhanced by two orders of magnitude, the maximum predicted by theory for our experimental setup. In addition, we showed that absorption can be reduced substantially by varying the relative phase of the incident fields. The device, termed a “coherent perfect absorber,” functions as an absorptive interferometer, with potential practical applications in integrated optics.

https://science.sciencemag.org/content/sci/331/6019/889.full.pdf

Time-reversed lasing and interferometric control of absorption.

The objective of this paper is to show that time reversal invariance can be exploited in acoustics to create a variety of useful instruments as well as elegant experiments in pure physics. Section 1 is devoted to the description of time reversal cavities and mirrors together with a comparison between time reversal and phase conjugation. To illustrate these concepts, several experiments conducted in multiply scattering media, waveguides and chaotic cavities are presented in section 2. Applications of time reversal mirrors (TRMs) in hydrodynamics are then presented in section 3. Section 4 is devoted to the application of TRMs in pulse echo detection. A complete theory of the iterative time reversal mode is presented. It will be explained how this technique allows for focusing on different targets in a multi-target medium. Another application of pulse echo TRMs is presented in this section: how to achieve resonance in an elastic target? Section 5 explores the medical applications of TRMs in ultrasonic imaging, lithotripsy and hyperthermia and section 6 shows the promising applications of TRMs in nondestructive testing of solid samples.

https://iopscience.iop.org/article/10.1088/0034-4885/63/12/202/pdf

Time-reversed acoustics

The decomposition of the time reversal operator (DORT) method is a selective detection and focusing technique using an array of transmit–receive transducers. It relies on the theory of iterative time reversal mirrors which was presented by Prada et al. [C. Prada, J. L. Thomas, and M. Fink, J. Acoust. Soc. Am. 97, 62–71 (1995)]. The time reversal operator was defined as K*(ω)K(ω), where ω is the frequency, * means complex conjugate, and K(ω) is the transfer matrix of the array of L transducers insonifying a time invariant scattering medium. It was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities, each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers. The DORT method consists in determining these eigenvectors and using them for the selective focusing. This paper presents a complete analysis of this method in the case of two scatterers. The...

Decomposition of the time reversal operator: Detection and selective focusing on two scatterers

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.

/pdf/of-the-time-reversal-operator-a-solution-to-selective-4dljmjqe4i.pdf

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

Focusing on a reflective target in an inhomogenous medium is difficult. In order to obtain good focusing properties, the concept of optical phase-conjugate mirrors, valid for monochromatic signals, is extended to large-bandwidth pulses such as those used in ultrasound echography. The transducer's linear response to the acoustic pressure allows replacement of the phase conjugation by a time-reversal operation on the pulse echo signals. The time-reversal mirror is an array of transmit-receive transducers. A first incident wave is reflected by the target. The received signals are stored in shift registers, reversed in times and then reemitted. The major advantage of this process is that the waves distorted by the aberrating medium are corrected by the mirror operation and the back propagation through the medium. When the medium contains several reflectors, this time-reversal process can be iterated in order to focus on the most-reflective one. >

Claire Prada

Papers

Time-reversed acoustics

Decomposition of the time reversal operator: Detection and selective focusing on two scatterers

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

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

Self focusing in inhomogeneous media with time reversal acoustic mirrors