Didier Cassereau

Time-reversed acoustics

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.

Self focusing in inhomogeneous media with time reversal acoustic mirrors

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 transducers 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.<<ETX>>

Time reversal techniques in ultrasonic nondestructive testing of scattering media

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

The role of the coupling term in transient elastography

The transient radiation of low-frequency elastic waves through isotropic and homogeneous soft media is investigated using the Greens function approach. A careful analysis of the coupling term is performed and yields the introduction of a very near field region in which its amplitude behaves as 1/r. To address the calculation of impulse responses, a simplified Greens function is proposed for semi-infinite media and compared to exact solutions. Impulse response calculations are successfully compared with experimental measurements obtained for circular radiators of different diameters using transient elastography. Results presented in this paper provide a better understanding of the role of the coupling term in elastography and should be used to compensate diffraction and coupling effects observed in transient elastography.

Theory of the time-reversal process in solids

In this paper, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves. A plane time-reversal mirror (TRM) is used, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM. The basic approach is similar to the case of a plane fluid–fluid interface [D. Cassereau and M. Fink, J. Acoust. Soc. Am. 96, 3145–3154 (1994)]; it is extended to take into account the different wave types. It is shown that the TRM is able to recreate properly in time and space the reversed fields of the longitudinal wave and the vertical polarization SV of the transverse waves, but not the horizontal polarization SH. The focusing quality of the backpropagating waves is limited by their respective wavelengths, so the slower SV wave can be better focused. Additional, unwanted wavefronts are created in the solid, too, but they are of weak amplitude and they are not focused. Numerical simulations ...

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.

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.

Focusing with plane time‐reversal mirrors: An efficient alternative to closed cavities

In this paper, a theoretical foundation is proposed and numerical results are provided for focusing by plane, time‐reversal mirrors of finite dimensions in a homogeneous fluid. The basic ideas are the same as those used in the closed time‐reversal cavity (CTRC) system [Cassereau et al., Proc. IEEE Ultrason. Symp., 1613–1618 (1990); D. Cassereau and M. Fink, IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 579–592 (1992)], except that the most unrealistic assumptions made in this theoretical approach are dropped. Plane mirrors are considered that do not surround the object source, and different kinds of radiation conditions are introduced on the surface of these mirrors, in order to obtain more realistic situations from an experimental point of view. The results are compared with those of the CTRC system and it is shown how the focal pattern is changed in comparison with the pattern of the theoretical (and ideal) model. The differences between several radiation conditions on the surface of the mirror are...

Optimal focusing through aberrating media: a comparison between time reversal mirror and time delay correction techniques

The problem of focusing an ultrasonic beam through an inhomogeneous medium was investigated experimentally for conventional time delay focusing, adaptive time delay focusing, and time reversal focusing. It is shown that neither time delay based technique gives a properly focused beam for all aberrator locations. Only time reversal focusing allows a robust focusing regardless of the aberrator location. The matched filter theory of signal processing allows an interpretation of this result: time reversal focusing provides the optimal input to the linear system consisting of the acousto-electric and diffraction impulse response.<<ETX>>

Time deconvolution of diffraction effects—Application to calibration and prediction of transducer waveforms

The concept of a radiation coupling function is used to write a transducer response that includes the diffraction losses. This concept leads to easy interpretations of experimental observations. In a second part a method is proposed for removing the diffraction effects from the observed transducer response. A linear system approach is taken to define the transducer output signal in terms of successive convolutions. The proposed method, based on a numerical deconvolution of the radiation filter, leads to an absolute calibration of the transducer impulse response. Deconvolved waveforms are presented for circular and annular arrays. Once the intrinsic transducer response is known, a direct convolution enables the prediction of the output signal for any distance transducer/reflector. Comparisons between predicted and observed transient waveforms are given for circular and annular arrays.