Time reversal of ultrasonic fields. I. Basic principles
01 Jan 1992-IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control (IEEE Trans Ultrason Ferroelectr Freq Control)-Vol. 39, Iss: 5, pp 555-566
TL;DR: 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 inhomogeneity propagation transfer function between the array and the target.
Abstract: 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. >
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TL;DR: In this article, the authors used strongly scattering materials to focus, shape and compress waves by controlling the many degrees of freedom in the incident waves in complex media such as white paint and biological tissue.
Abstract: In complex media such as white paint and biological tissue, light encounters nanoscale refractive-index inhomogeneities that cause multiple scattering. Such scattering is usually seen as an impediment to focusing and imaging. However, scientists have recently used strongly scattering materials to focus, shape and compress waves by controlling the many degrees of freedom in the incident waves. This was first demonstrated in the acoustic and microwave domains using time reversal, and is now being performed in the optical realm using spatial light modulators to address the many thousands of spatial degrees of freedom of light. This approach is being used to investigate phenomena such as optical super-resolution and the time reversal of light, thus opening many new avenues for imaging and focusing in turbid media
1,322 citations
TL;DR: In this article, the authors show that the Frechet derivatives of the objective function can be obtained for tomographic and (finite) source inversions based on 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.
Abstract: 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.
904 citations
Cites background or methods from "Time reversal of ultrasonic fields...."
...The concept of ‘time-reversal mirrors’, in which an acoustic signal is recorded by an array of transducers, time-reversed and retransmitted, has been made popular by Fink (Fink et al. 1989; Fink 1992, 1997)....
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...It is analogous to the approach taken in time-reversal imaging (Fink et al. 1989; Fink 1992, 1997), where one retransmits a time-reversed acoustic signal to locate its origin....
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TL;DR: In this article, a pitch-catch method using a pair of piezoelectric actuator and sensor is introduced to generate a damage indeX which can be used to characterize damage at a known location.
Abstract: This study presents active sensing methods in structural health monitoring, for detecting cracks and debonds in metallic and composite structures, which can be potentially implemented into airframe structures. First, a pitch-catch method using a pair of piezoelectric actuator and sensor is introduced to generate a damage indeX which can be used to characterize damage at a known location. Tests on airbus fuselage panels are conducted to verify the method and damage indeX. The damage indeX relates changes in the energy content of a specific Lamb wave mode selected by group velocity analysis to the eXtent of damage. Second, an imaging method based on multiple pitch-catch information, a network of piezoelectric actuator/sensors, is presented for characterizing damage (location and size) without need for a structural or damage model. The imaging method with an autofocusing feature is applied to aluminum plates and a stiffened composite panel for method verification.
574 citations
TL;DR: In this paper, the authors 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, and they describe time reversal cavities and mirrors together with a comparison between time reversal and phase conjugation.
Abstract: 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.
573 citations
TL;DR: In this article, the applicability of the time-reversal concept to guided waves in plate-like structures, where the stress waves are dispersive and of multi-modes, was investigated.
Abstract: This paper presents an experimental and theoretical investigation of the applicability of the time-reversal concept to guided waves in plate-like structures, where the stress waves are dispersive and of multi-modes. It is shown that temporal and spatial focusing can be achieved through time reversal, although the dispersive behaviour of the flexural waves renders it impossible to exactly reconstruct the waveform of the original excitation. Based on the principle of the time-reversal concept, a digital imaging method suitable for distributed sensor/actuator networks has been developed. This new method, which overcomes the limitation of the conventional phased array method that operates under pulse-echo mode, provides an efficient imaging method for locating and approximate sizing of structural damages. In addition, it has been shown that signal strengths can be considerably enhanced by applying the present synthetic time-reversal method, thus reducing the number of sensors and actuators required to achieve a given signal-to-noise ratio.
504 citations
References
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TL;DR: In this article, an approach to compute the near and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle is presented.
Abstract: An approach is presented to compute the near‐ and farfield transient radiation resulting from a specified velocity motion of a piston or array of pistons in a rigid infinite baffle. The approach, which is based on a Green's function development, utilizes a transformation of coordinates to simplify the evaluation of the resultant surface integrals. A simple expression is developed for an impulse response function, which is the time‐dependent velocity potential at a spatial point resulting from an impulse velocity of a piston of any shape. The time‐dependent velocity potential and pressure for any piston velocity motion may then be computed by a convolution of the piston velocity with the appropriate impulse response. The response of an array may be computed using superposition. Several examples illustrating the usefulness of the approach are presented. The farfield time‐dependent radiation from a rectangular piston is discussed for both continuous and pulsed velocity conditions. For a pulsed velocity of time duration T it is shown that the pressure at several of the field points can consist of two separate pulses of the same duration, when T is less than the travel time across the piston.
580 citations
TL;DR: The method presented here has no need for a beacon or an ideal point reflector to act as a source for estimating phase errors, and uses signals from random collections of scatterers to determine phase aberrations accurately.
Abstract: Methods for correction of phase aberrations induced by near-field variations in the index of refraction are explored. Using signals obtained from a sampled aperture (i.e. transducer array), phase aberrations can be accurately measured with a correlation approach similar to methods used in adaptive optics and radar. However, the method presented here has no need for a beacon or an ideal point reflector to act as a source for estimating phase errors. It uses signals from random collections of scatterers to determine phase aberrations accurately. Because there is no longer a need for a beacon signal, the method is directly applicable not only to medical ultrasound imaging but also to any coherent imaging system with a sampled aperture, such as radar and sonar. >
517 citations
TL;DR: 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.
Abstract: 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. >
416 citations