Selective focusing through inhomogeneous media: the DORT method

Ultra wide-band (UWB) radar imaging systems are a promising field of research as they cover a variety of applications. Among all UWB radar imaging methods, the time-reversal (TR) method enables high-resolution imaging in a multi-path environment. Conventional TR methods have been applied to antenna array systems while our previous work proposed a type of TR method, namely the frequency-domain D'ecomposition de Op'erateur de Retournement Temporel (DORT) method, designed for a low-cost single antenna-based system. Because the frequency-domain DORT method was developed assuming a point-like target, the performance of the method for a finite-sized target is unknown. In this study, we investigate numerically the performance of the frequency-domain DORT method by applying it to finite-sized targets and evaluating the quality of the resultant images.

Among structural health monitoring techniques, Lamb waves is frequently used as diagnostic tools to detect damage in plate-like structures. Lamb waves usually excited by piezoelectric transducers essentially involve exciting the structure with high frequency guided-waves and processing the difference in structural response with respect to a baseline signal for the pristine condition to detect damage. As a kind of baseline free method, time reversal (TR) method applied to ultrasonic detection and focusing with arrays of transducers has been proposed. The decomposition of the time reversal operator (DORT) method is a selective detection and focusing technique using an array of transmit-receive transducers. Unlike body waves, the propagation of Lamb waves is complicated due to their dispersive and multimode characteristics. So Lamb wave is hard to locate different scatterers on the plate using DORT method because of the asymmetry of the time reversal transfer matrix. In this paper, a proposed approach based on the DORT method is developed to distinguish and locate two simulated damages on the aluminum plate using Lamb wave through finite element simulation on the commercial finite element code ANSYS platform. The behavior of reflected waves is analyzed by studying the eigenvalues and eigenvectors of the time reversal transfer matrix, showing that the number of significant eigenvalues is not exactly the number of damage targets and two significant eigenvalues correspond to one target. This method, which uses PZT array and operates under multi-modes pulse-echo mode, can estimate the position of the damaged zone in 2D image by numerically backpropagating selective eigenvector using the S0 and/or A0 Lamb wave propagation analytical solution.

We consider the scattering of time-dependent acoustic waves by some bounded obstacles located in a homogeneous and non-dissipative medium. We propose a far-field model of time reversal mirror that reverses the asymptotic wave profile of a scattered wave. Following the idea developed for time-harmonic waves in the so-called decomposition of the time reversal operator in French (DORT) method, we define a time reversal operator (TRO) in the time domain, which is related to the scattering operator involved in scattering theory. We show how this operator is related to the family of single frequency TROs involved in the DORT method, which clarifies the link between time-dependent and time-harmonic waves in the time reversal process. As an application of this relation, we prove that iterative time reversal generally converges to a single frequency time-harmonic wave.

For a few years, adaptive time delay focusing techniques have been extensively studied in order to focus through inhomogeneous media. However, these techniques can only correct the effects of a thin aberrator located near the array. Time reversal of ultrasonic fields allows another approach to focus in the transmit mode through inhomogeneous media. Compared to the adaptive time delay focusing technique, time reversal requires the transmission of different waveforms from each individual element of an array. Focusing via time reversal is shown to be optimal in comparison with time delay focusing since it realizes the spatio-temporally matched filter to the inhomogeneous propagation transfer function between the array and the focal point. In previous papers [Fink et al., Proc. IEEE Ultrasonics Symposium, Montreal (1989)], focusing by time reversal has been described in the transmit mode only. A complete focusing in inhomogeneous medium requires the extension of this technique in the receive mode. This paper describes the extension of the matched filter approach in the receive mode and it is shown that optimal focusing in this mode can be achieved using adaptive convolution beamforming techniques instead of simple time delay lines. Theoretical and experimental results are presented to show the efficiency of this technique compared to adaptive delay line focusing.

Acoustic time reversal is a promising technique for spatial and temporal focusing of sound in unknown environments. Acoustic time reversal can be implemented with an array of transducers that listens to a remote sound source and then transmits a time-reversed version of what was heard. In a noisy environment, the performance of such a time-reversing array (TRA) will be degraded because the array will receive and transmit noise, and the intended signal may be masked by ambient noise at the retrofocus location. This article presents formal results for the signal-to-noise ratio at the intended focus (SNRf) for TRAs that receive and send finite-duration broadband signals in noisy environments. When the noise is homogeneous and uncorrelated, and a broadcast power limitation sets the TRA's electronic amplification, the formal results can be simplified to an algebraic formula that includes the characteristics of the signal, the remote source, the TRA, and the noisy environment. Here, SNRf is found to be proportional to the product of the signal bandwidth and the duration of the signal pulse after propagation through the environment. Using parabolic-equation propagation simulations, the formal results for SNRf are illustrated for a shallow water environment at source-array ranges of 1 to 40 km and bandwidths from several tens of Hz to more than 500 Hz for a signal center frequency of 500 Hz. Shallow-water TRA noise rejection is predicted to be superior to that possible in free space because TRAs successfully exploit multipath-propagation.

Active acoustic time reversal is a technique for focusing sounds recorded in complex unknown environments back to their remote point(s) of origin. It can be accomplished with a transducer array—a time-reversing array (TRA)—that sends and receives sound. Nearly all prior work on TRA performance has involved stationary arrays. This letter describes how random array deformation influences TRA retrofocusing in shallow ocean environments. For harmonic signals, randomly drifting array elements degrade TRA performance by ∼20% when the average horizontal wavenumber times the root-mean-square horizontal element displacement approaches 0.5. TRA focusing should be less sensitive to vertical element drift.

This paper concerns a ground penetrating radar system (GPR) presenting beam forming ability. This ability is due to a great flexibility in the emission of wavefronts. The innovative concept is to use an array of antennas which can reconfigure itself dynamically, in order to focus on a desired target. This antennas system can act as a new microwave sensor to detect and characterize buried targets in an inhomogeneous medium which is the case study in various application fields such as geophysics, medical, planetology,... Its electronics are in development with the DORT (Time reversal technique) method integration for optimizing the localization of buried target. This paper aims are to present the antenna optimization used in the GPR applications. Typical antennas used in GPR are generally Vivaldi ones directly on the ground. Especially, in the context of the space mission ExoMars 2020, the radar antenna is set on a mobile station at a distance of about 30 cm from the ground to avoid any contact. However, they are limited by their important size, due to the lowest frequency of their bandwidth. Results of this work concern an increase of the antenna bandwidth by shifting the lower-band limit, making it a UWB type [500 MHz–4 GHz] without changing its size. As low frequency waves can spread deeper into probed medium, this optimization can improve the radar data inversion performances.

Publication in the conference proceedings of EUSIPCO, Glasgow, Scotland, 2009

The self-adaptive focusing of the time reversal in anisotropic media isstudied theoretically and experimentally. It is conducted for thecompressional wave field in the cubic crystal silicon. The experimentalresult is in agreement with our theoretical analysis. The focusing gainand the displacement distributions of the time reversal field areanalysed in detail. It is shown that the waves from different elementsof the transducer array arrive at the original place of the sourcesimultaneously after the time reversal operation. The waveformdistortions caused by the velocity anisotropy can automatically becompensated for after the time reversal processing.

Time reversal processes have been used to improve communication performance in the severe underwater communication environment characterized by significant multipath channels by reducing inter-symbol interference and increasing signal-to-noise ratio. In general, the performance of the time reversal is strongly related to the behavior of the q -function, which is estimated by a sum of the autocorrelation of the channel impulse response for each channel in the receiver array. The q -function depends on the complexity of the communication channel, the number of channel elements and their spacing. A q -function with a high side-lobe level and a main-lobe width wider than the symbol duration creates a residual ISI (inter-symbol interference), which makes communication difficult even after time reversal is applied. In this paper, we propose a new parameter, E q , to describe the performance of time reversal communication. E q is an estimate of how much of the q -function lies within one symbol duration. The values of E q were estimated using communication data acquired at two different sites: one in which the sound speed ratio of sediment to water was less than unity and one where the ratio was higher than unity. Finally, the parameter E q was compared to the bit error rate and the output signal-to-noise ratio obtained after the time reversal operation. The results show that these parameters are strongly correlated to the parameter E q .

In ultrasonic testing of dissimilar metal welds, application of phased array technique in terms of incident beam focusing is not easy because of complicated material structures formed during the multi-pass welding process. Time reversal (TR) techniques can overcome some limitations of phased array since they are self-focusing that does not depend on the geometrical and physical properties of testing components. In this paper, we test the possibility of TR focusing on a defect within anisotropic, heterogeneous austenitic welds. A commercial simulation software is employed for TR focusing and imaging of a side-drilled hole. The performance of time reversed adaptive focal law is compared with those of calculated focal laws for both anisotropic and isotropic welds.

To reduce time and cost of damage inspection, on-line impact monitoring of aircraft composite structures is needed. A digital monitor based on an array of piezoelectric transducers (PZTs) is developed to record the impact region of impacts on-line. It is small in size, lightweight and has low power consumption, but there are two problems with the impact alarm region localization method of the digital monitor at the current stage. The first one is that the accuracy rate of the impact alarm region localization is low, especially on complex composite structures. The second problem is that the area of impact alarm region is large when a large scale structure is monitored and the number of PZTs is limited which increases the time and cost of damage inspections. To solve the two problems, an impact alarm region imaging and localization method based on digital sequences and time reversal is proposed. In this method, the frequency band of impact response signals is estimated based on the digital sequences first. Then, characteristic signals of impact response signals are constructed by sinusoidal modulation signals. Finally, the phase synthesis time reversal impact imaging method is adopted to obtain the impact region image. Depending on the image, an error ellipse is generated to give out the final impact alarm region. A validation experiment is implemented on a complex composite wing box of a real aircraft. The validation results show that the accuracy rate of impact alarm region localization is approximately 100%. The area of impact alarm region can be reduced and the number of PZTs needed to cover the same impact monitoring region is reduced by more than a half.

The problem of focusing a field into inhomogeneous media is a canonic open problem relevant in many engineering areas. Several approaches have been developed, for example, Time Reversal, Inverse Filter, and Eigenvalues approach, but they suffer from several drawbacks which are counteracted by Optimal Constrained Power Focusing (OCPF) technique. OCPF was first introduced to deal with scalar fields and, recently, it has been extended to tackle the problem of focusing vector fields. In particular, the proposed approach allows reducing the focusing problem, which is NP-hard in case of vector fields, to a series of convex programming (CP) ones. In this paper, an alternative OCPF formulation is presented, which consists in the research of the most suitable polarization of the field into the target point and relies on the convexity of the problem when fixing this polarization. Such a result allows the development of two different solution procedures: an enumerative one that can take advantage of parallel programming in order to explore all possible polarizations and hybrid one which relies on the exploitation of global search algorithm just to solve the nonconvex part of the problem at hand.

A new echo-to-reverberation enhancement method with reverberation nulling constrains based on waveguide invariant is proposed to solve the problems of direct time reversal processing and the time reversal reverberation nulling method. Firstly, a 2-dimensional signal subspace for the range containing a target potentially is obtained by decomposition of time reversal operator at central frequency. And the bottom focusing weight vector for the target range is obtained by the decomposition of time reversal operator at another range near the target with a frequency-shift, according to the waveguide invariant. Then, combined the optimal array signal processing theory, a constrained optimal excitation weight vector of source receiver array is deduced from the signal subspace and the bottom focusing weight vector, so as to focus sound energy on target while null the sound energy on the seafloor below the target, resulting in echo-to-reverberation enhancement. This method not only remedies the shortages of conventional time reversal processing and the time reversal reverberation nulling, but also obtains an improved performance for echo-to- reverberation enhancement, because of the bottom reverberation nulling constrains at the target range. Numerical simulations in typical shallow water environments illustrate the effectiveness of the proposed method.

To focus ultrasonic waves in an unknown inhomogeneous medium using a phased array, one has to calculate the optimal set of signals to be applied on the transducers of the array. In the case of time-reversal mirrors, one assumes that a source is available at the focus, providing the Green's function of this point. In this paper, the robustness of this time-reversal method is investigated when loss of information breaks the time-reversal invariance. It arises in dissipative media or when the field radiated by the source is not entirely measured by the limited aperture of a time-reversal mirror. However, in both cases, linearity and reciprocity relations ensure time reversal to achieve a spatiotemporal matched filtering. Nevertheless, though it provides robustness to this method, no constraints are imposed on the field out of the focus and sidelobes may appear. Another approach consists of measuring the Green's functions associated to the focus but also to neighboring points. Thus, the whole information characterizing the medium is known and the inverse source problem can be solved. A matrix formalism of the propagation operator is introduced to compare the time-reversal and inverse filter techniques. Moreover, experiments investigated in various media are presented to illustrate this comparison.