Matrix Approach of Seismic Imaging: Application to the Erebus Volcano, Antarctica. Blondel, T., J. Chaput, A. Derode, M. Campillo, and A. Aubry. Journal of Geophysical Research: Solid Earth 123, no. 12 (2018): 10,936–10,950.
Résumé: ©2018. American Geophysical Union. All Rights Reserved. Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a singlescattering assumption. In heterogeneous areas such as volcanoes, the multiplescattering contribution limits the imagingdepth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof of concept, the case of the Erebus volcano in Antarctica is considered. The Green's functions between a set of geophones placed on top of the volcano are first retrieved by the cross correlation of coda waves induced by multiple icequakes. This set of impulse responses forms a reflection matrix. By combining a matrix discrimination of singly scattered waves with iterative time reversal, we are able to push back the multiple scattering limit beyond 10 scattering mean free paths. The matrix approach reveals the internal structure of the Erebus volcano: A chimneyshaped structure at shallow depths, a magma reservoir at 2,500 m and several cavities at sea level and below it. The matrix approach paves the way toward a greatly improved monitoring of volcanic structures at depth. Beyond this specific case, the matrix approach of seismic imaging can generally be applied to all scales and areas where multiple scattering events undergone by body waves prevent indepth imaging of the Earth's crust.
MotsClés: coda crosscorrelation; iterative time reversal; matrix approach; multiple scattering; seismic imaging; volcano seismology


Dynamic coherent backscattering of ultrasound in threedimensional stronglyscattering media. Cobus, L. A., B. A. Tiggelen, A. Derode, and J. H. Page. European Physical Journal: Special Topics 226, no. 7 (2017): 1549–1561.
Résumé: © 2017, The Author(s).We present measurements of the diffusion coefficient of ultrasound in strongly scattering threedimensional (3D) disordered media using the dynamic coherent backscattering (CBS) effect. Our experiments measure the CBS of ultrasonic waves using a transducer array placed in the farfield of a 3D slab sample of brazed aluminum beads surrounded by vacuum. We extend to 3D media the general microscopic theory of CBS that was developed initially for acoustic waves in 2D. This theory is valid in the strong scattering, but still diffuse, regime that is realized in our sample, and is evaluated in the diffuse far field limit encountered in our experiments. By comparing our theory with the experimental data, we obtain an accurate measurement of the Boltzmann diffusion coefficient of ultrasound in our sample. We find that the value of DB is quite small, 0.74 ± 0.03 mm2/μs, and comment on the implications of this slow transport for the energy velocity.


Evaluation of a multiple scattering filter to enhance defect detection in heterogeneous media. Shahjahan, S., F. Rupin, A. Aubry, and A. Derode. Journal of the Acoustical Society of America 141, no. 1 (2017): 624–640.
Résumé: © 2017 Acoustical Society of America.Ultrasonic evaluation of coarsegrain materials generates multiple scattering at high frequency and large depth. Recent academic experiments with array probes showed the ability of a random matrix method [multiple scattering filter (MSF)] to reduce multiple scattering, hence improving detection. Here, MSF is applied to an industrial nickelbased alloy with coarsegrain structure. Two samples with average grain sizes 90 ± 60 μm and 750 ± 400 μm are inspected with wideband 64element arrays at central frequencies 2, 3, and 5 MHz. They contain cylindrical throughholes (1mm radius) at various depths. The array transfer matrix is recorded and postprocessed both in the flawless area and for eleven positions above each defect, which allows for a statistical analysis. MSF is compared with two conventional imaging techniques: the total focusing method (TFM) and the decomposition of the timereversal operator (DORT). Several parameters to assess the performance of detection techniques are proposed and discussed. The results show the benefit of MSF, especially at high frequencies and for deep defects: at 5 MHz and 70 mm depth, i.e., more than three scattering meanfree paths, the detection rate for MSF ranges between 55% and 100% while it is found to be 0% both for TFM and DORT.


Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation. Baydoun, I., D. Baresch, R. Pierrat, and A. Derode. Physical Review E 94, no. 5 (2016).


Anderson Mobility Gap Probed by Dynamic Coherent Backscattering. Cobus, L. A., S. E. Skipetrov, A. Aubry, B. A. Van Tiggelen, A. Derode, and J. H. Page. Physical Review Letters 116, no. 19 (2016).
Résumé: © 2016 American Physical Society. We use dynamic coherent backscattering to study one of the Anderson mobility gaps in the vibrational spectrum of strongly disordered threedimensional mesoglasses. Comparison of experimental results with the selfconsistent theory of localization allows us to estimate the localization (correlation) length as a function of frequency in a wide spectral range covering bands of diffuse transport and a mobility gap delimited by two mobility edges. The results are corroborated by transmission measurements on one of our samples.


Experimental observation of ultrasound fast and slow waves through threedimensional printed trabecular bone phantoms. Mézière, F., P. Juskova, J. Woittequand, M. Muller, E. Bossy, L. Malaquin, A. Derode, and R. Boistel. Journal of the Acoustical Society of America 139, no. 2 (2016): EL13–EL18.
Résumé: © 2016 Acoustical Society of America. In this paper, ultrasound measurements of 1:1 scale threedimensional (3D) printed trabecular bone phantoms are reported. The microstructure of a trabecular horse bone sample was obtained via synchrotron xray microtomography, converted to a 3D binary data set, and successfully 3Dprinted at scale 1:1. Ultrasound throughtransmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing. As in real anisotropic trabecular bone, both the fast and slow waves were observed. This illustrates the potential of stereolithography and the relevance of such bone phantoms for the study of ultrasound propagation in bone.


Scattering mean free path in continuous complex media: Beyond the Helmholtz equation. Baydoun, I., D. Baresch, R. Pierrat, and A. Derode. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 92, no. 3 (2015).
Résumé: © 2015 American Physical Society. We present theoretical calculations of the ensembleaveraged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a spacedependent speed. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the lowfrequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the selfenergy and mean free path within Bourret's and onshell approximations. They are confirmed by numerical experiments.


Measurements of ultrasonic diffusivity and transport speed from coda waves in a resonant multiple scattering medium. Viard, N., and A. Derode. Journal Of The Acoustical Society Of America 138, no. 1 (2015): 134–145.


Comparison between experimental and 2D numerical studies of multiple scattering in Inconel600® by means of array probes. Shahjahan, S., F. Rupin, A. Aubry, B. Chassignole, F. Fouquet, and A. Derode. Ultrasonics 54 (2014): 358–367.


A random matrix approach to detect defects in a strongly scattering polycrystal : how the memory effect can help overcome multiple scattering. Shahjahan, S., A. Aubry, F. Rupin, B. Chassignole, and A. Derode. Applied Physics Letters 104 (2014): 234105.


Full Transmission and Reflection of Waves Propagating through a Maze of Disorder. Gerardin, B., J. Laurent, A. Derode, C. Prada, and A. Aubry. Physical Review Letters 113, no. 17 (2014).


Recurrent Scattering and Memory Effect at the Anderson Localization Transition. Aubry, A., L. A. Cobus, S. E. Skipetrov, B. A. Van Tiggelen, A. Derode, and J. H. Page. Physical Review Letters 112, no. 4 (2014).


Frequencyresolved measurements of the diffusion constant for ultrasonic waves in resonant multiple scattering media. Viard, N., and A. Derode. The Journal of the Acoustical Society of America 133, no. 5 (2013): 3374.


Coherent transmission of an ultrasonic shock wave through a multiple scattering medium. Viard, N., B. Giammarinaro, A. Derode, and C. Barrière. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 88, no. 2 (2013).
Résumé: We report measurements of the transmitted coherent (ensembleaveraged) wave resulting from the interaction of an ultrasonic shock wave with a twodimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (215 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled. © 2013 American Physical Society.
MotsClés: Broad frequency range; Coherent transmission; Coherent waveforms; Multiplescattering medium; Nonlinear harmonic generation; Spatial correlations; Theoretical modeling; Ultrasonic shock waves; Harmonic generation; Shock waves; Multiple scattering


Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot's and multiple scattering models. Mézière, F., M. Muller, E. Bossy, and A. Derode. Ultrasonics 54, no. 5 (2014): 1146–1154.
Résumé: This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finitedifference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensembleaveraged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the microstructure. The results are confronted with two standard theoretical approaches: Biot's theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical firstorder approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot's theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study twowave propagation, unlike Biot's model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot's theory. Finally we investigate the phaseshift between waves in the fluid and the solid structure, and compare them to Biot's predictions of inphase and outofphase motions. © 2013 Elsevier B.V. All rights reserved.
MotsClés: Biot's theory; Cancellous bone; Fast and slow waves; Multiple scattering; Porous media


Characterisation of ultrasonic structural noise in multiple scattering media using phased arrays. Bedetti, T., V. Dorval, F. Jenson, and A. Derode. Journal of Physics: Conference Series 457 (2013).
Résumé: The ultrasonic inspection of multiple scattering media gives rise to structural noise which makes it difficult to detect potential damage or crack inside the component. In order to predict the performances of ultrasonic inspection over such complex media, scattering models can be used. Such models rely on specific key parameters describing the multiple scattering process, which can be determined by specific measurements and postprocessing techniques. Such experiments were carried out on stainless steel plates using linear phasedarrays. They consist in recording the response matrix constituted by impulse responses between all the elements of the array. By conducting postprocessing on this matrix, we measure the elastic mean free path le and the correlation distance dc of the recorded noise. Additionally, the dynamic behaviour of the coherent backscattering effect was studied in order to measure the diffusion constant D. Planewave beamforming has been applied to the response matrix to improve the angular resolution and the signaltonoise ratio of the backscattered intensity. Details of postprocessing techniques will be shown. © Published under licence by IOP Publishing Ltd.


Simulations of ultrasound propagation in random arrangements of elliptic scatterers: Occurrence of two longitudinal waves. Mézière, F., M. Muller, B. Dobigny, E. Bossy, and A. Derode. Journal of the Acoustical Society of America 133, no. 2 (2013): 643–652.
Résumé: Ultrasound propagation in clusters of elliptic (twodimensional) or ellipsoidal (threedimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering. Some phenomena remain partially unexplained, such as the propagation of two longitudinal waves. The objective of this study was to shed more light on the occurrence of these two waves, using finitedifference simulations on a model medium simpler than bone. Slabs of anisotropic, scattering media were randomly generated. The coherent wave was obtained through spatial and ensembleaveraging of the transmitted wavefields. When varying relevant medium parameters, four of them appeared to play a significant role for the observation of two waves: (i) the solid fraction, (ii) the direction of propagation relatively to the scatterers orientation, (iii) the ability of scatterers to support shear waves, and (iv) a continuity of the solid matrix along the propagation. These observations are consistent with the hypothesis that fast waves are guided by the locally plate/barlike solid matrix. If confirmed, this interpretation could significantly help developing approaches for a better understanding of trabecular bone microarchitecture using ultrasound. © 2013 Acoustical Society of America.
MotsClés: Bone microstructure; Coherent waves; Fast waves; Finite difference; Longitudinal waves; Multiple waves; Randomly distributed; Scattering media; Solid fraction; Solid matrixes; Structural anisotropy; Trabecular bones; Ultrasound propagation; Wavefields; Anisotropy; Bone; Computer simulation; Ultrasonic propagation; Scattering; animal; anisotropy; article; bone; computer simulation; echography; human; mathematical computing; Monte Carlo method; motion; pressure; radiation scattering; reproducibility; sound; theoretical model; time; ultrasound; Animals; Anisotropy; Bone and Bones; Computer Simulation; Humans; Models, Theoretical; Monte Carlo Method; Motion; Numerical Analysis, ComputerAssisted; Pressure; Reproducibility of Results; Scattering, Radiation; Sound; Time Factors; Ultrasonics


Multiple scattering of ultrasound in weakly inhomogeneous media: Application to human soft tissues. Aubry, A., and A. Derode. Journal of the Acoustical Society of America 129, no. 1 (2011): 225–233.
Résumé: Waves scattered by a weakly inhomogeneous random medium contain a predominant singlescattering contribution as well as a multiplescattering contribution which is usually neglected, especially for imaging purposes. A method based on random matrix theory is proposed to separate the single and multiplescattering contributions. The experimental setup uses an array of sources/receivers placed in front of the medium. The impulse responses between every couple of transducers are measured and form a matrix. Singlescattering contributions are shown to exhibit a deterministic coherence along the antidiagonals of the array response matrix, whatever the distribution of inhomogeneities. This property is taken advantage of to discriminate single from multiplescattered waves. This allows one to evaluate the absorption losses and the scattering losses separately, by comparing the multiplescattering intensity with a radiative transfer model. Moreover, the relative contribution of multiple scattering in the backscattered wave can be estimated, which serves as a validity test for the Born approximation. Experimental results are presented with ultrasonic waves in the megahertz range, on a synthetic sample (agargelatine gel) as well as on breast tissues. Interestingly, the multiplescattering contribution is found to be far from negligible in the breast around 4.3 MHz. © 2011 Acoustical Society of America.
MotsClés: Absorption loss; Array response; Backscattered; Breast tissues; Experimental setup; Inhomogeneities; Inhomogeneous media; matrix; Radiative transfer model; Random matrix theory; Random medium; Relative contribution; Scattered waves; Scattering intensity; Scattering loss; Single scattering; Soft tissue; Validity tests; Born approximation; Histology; Multiple scattering; Radiative transfer; Ultrasonics; Coherent scattering; agar; gelatin; absorption; article; biological model; echomammography; female; human; image quality; instrumentation; motion; reproducibility; signal processing; time; transducer; ultrasound; Absorption; Agar; Female; Gelatin; Humans; Models, Biological; Motion; Phantoms, Imaging; Reproducibility of Results; Signal Processing, ComputerAssisted; Time Factors; Transducers; Ultrasonics; Ultrasonography, Mammary


Singular value distribution of the propagation matrix in random scattering media. Aubry, A., and A. Derode. Waves in Random and Complex Media 20, no. 3 (2010): 333–363.
Résumé: The distribution of singular values of the propagation operator in a random medium is investigated, in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of 64 programmable transducers placed in front of a random scattering medium. The impulse responses between each pair of transducers are measured and form the response matrix. The evolution of its singular values with time and frequency is computed by means of a shorttime Fourier analysis. The mean distribution of singular values exhibits a very different behaviour in the single and multiple scattering regimes. The results are compared with random matrix theory. Once the experimental matrix coefficients are renormalized, experimental results and theoretical predictions are found to be in a very good agreement. Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. Finally, the possibility of detecting a target embedded in a random scattering medium based on the statistical properties of the strongest singular value is discussed. © 2010 Taylor & Francis.
MotsClés: Key parameters; Matrix coefficients; Matrix elements; Propagation matrix; Propagation operators; Pulsed ultrasonic wave; Random matrix theory; Random media; Random medium; Random scattering media; Random scattering medium; Residual correlation; Response matrices; Scattering medium; Singular values; Statistical properties; Theoretical prediction; Fourier analysis; Multiple scattering; Transducers; Ultrasonics


Detection and imaging in a random medium: A matrix method to overcome multiple scattering and aberration. Aubry, A., and A. Derode. Journal of Applied Physics 106, no. 4 (2009).
Résumé: We present an imaging technique particularly suited to the detection of a target embedded in a strongly scattering medium. Classical imaging techniques based on the Born approximation fail in this kind of configuration because of multiply scattered echoes and aberration distortions. The experimental setup we consider uses an array of programmable transmitters/receivers. A target is placed behind a scattering medium. The impulse responses between all array elements are measured and form a matrix. The core of the method is to separate the single scattered echo of the target from the multiple scattering background. This is possible because of a deterministic coherence along the antidiagonals of the array response matrix, which is typical of single scattering. Once this operation is performed, target detection is achieved by applying the DORT method (French acronym for decomposition of the time reversal operator). Experimental results are presented in the case of wideband ultrasonic waves around 3 MHz. A 125element array is placed in front of a collection of randomly distributed steel rods (diameter of 0.8 mm). The slab thickness is three times the scattering mean free path. The target is a larger steel cylinder (diameter of 15 mm) that we try to detect and localize. The quality of detection is assessed theoretically based on random matrix theory and is shown to be significantly better than what is obtained with classical imaging methods. Aside from multiple scattering, the technique is also shown to reduce the aberrations induced by a heterogeneous layer. © 2009 American Institute of Physics.
MotsClés: Array elements; Array response; Classical imaging; Decomposition of the time reversal operator; Element array; Experimental setup; matrix; Matrix methods; Mean free path; Random matrix theory; Random medium; Randomly distributed; Scattering medium; Single scattering; Slab thickness; Steel cylinders; Steel rod; Target detection; Wideband; Aberrations; Approximation theory; Born approximation; Imaging techniques; Multiple scattering; Quantum theory; Steel; Targets; Ultrasonic imaging; Ultrasonics; Ultrasonic applications


Random matrix theory applied to acoustic backscattering and imaging in complex media. Aubry, A., and A. Derode. Physical Review Letters 102, no. 8 (2009).
Résumé: The singular values distribution of the propagation operator in a random medium is investigated in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of transducers. Coherent backscattering and field correlations are taken into account. Interestingly, the distribution of singular values shows a dramatically different behavior in the single and multiplescattering regimes. Based on a matrix separation of single and multiplescattered waves, an experimental illustration of imaging through a highly scattering slab is presented. © 2009 The American Physical Society.
MotsClés: Backscattering; Ultrasonics; Acoustic backscatterings; Coherent backscatterings; Complex medias; Matrix separations; Multiplescattering; Propagation operators; Pulsed ultrasonic waves; Random matrix theories; Random mediums; Scattered waves; Singular values; Ultrasonic imaging


Fluctuations of correlations and Green's function reconstruction: Role of scattering. Larose, E., P. Roux, M. Campillo, and A. Derode. Journal of Applied Physics 103, no. 11 (2008).
Résumé: Correlations of ambient seismic or acoustic vibrations are now widely used to reconstruct the impulse response between two passive receivers as if a source was placed at one of them. This provides the opportunity to do imaging without a source, or passive imaging. Applications include terrestrial and solar seismology, underwater acoustics, and structural health monitoring, to cite only a few. Nevertheless, for a given set of data, correlations do not only yield Green's function between the sensors. They also contain residual fluctuations that result from an imperfect time or source averaging that might eventually blur the images. In this article, we propose a heuristic model to describe the level of fluctuations of the correlations in the case of nonstationary wavefields, and more particularly in the case of scattering media. The work includes theoretical derivations and numerical simulations. The role of multiple scattering is quantitatively evaluated. The level of fluctuations decreases when the duration and intensity of the diffuse waves increase. The role of absorption is also discussed: absorption is properly retrieved by correlation, but the level of fluctuations is greater, thus degrading Green's function reconstruction. Discrepancies of our simple model in the case of strong multiple scattering (k * ≤18) are discussed. © 2008 American Institute of Physics.
MotsClés: Absorption; Acoustic receivers; Acoustics; Computer simulation; Correlation methods; Differential equations; Functions; Health; Impulse response; Mathematical models; Multiple scattering; Photoacoustic effect; Repair; Restoration; Scattering; Seismology; Set theory; Structural health monitoring; Underwater acoustics; Underwater audition; Acoustic vibrations; American Institute of Physics (AIP); Diffuse waves; Function reconstruction; Healthmonitoring; Heuristic models; Non stationary; Numerical simulations; passive imaging; Passive receivers; Residual fluctuations; Scattering medium; Simple modeling; Wavefields; Green's function


Temperaturedependent diffusing acoustic wave spectroscopy with resonant scatterers. Leroy, V., and A. Derode. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 77, no. 3 (2008).
Résumé: The influence of a slight temperature change on the correlation of multiply scattered acoustic waves is studied, and experimental results are discussed. The technique presented here, similar to diffusingacousticwave spectroscopy, is based on the sensitivity of a multiply scattering medium to a slight change. Ultrasonic waves around 3 MHz are transmitted through a sample made of steel rods in water and recorded by an array of transducers at different temperatures. The cross correlations between highly scattered signals are computed. The main effect of the temperature change is a simple dilation of the times of arrival, due to a change of the sound velocity in water. But the scatterers also play a role in the progressive decorrelation of wave forms. An analysis resolved in both time and frequency shows that at some particular frequencies, the resonant behavior of the scatterers is responsible for a significantly larger decorrelation. Interestingly, the experimental results allow one to detect the presence of a small resonance that was not detected earlier on the same scatterers with classical measurement of the scattering mean free path. A simple model is proposed to interpret the experimental results. © 2008 The American Physical Society.
MotsClés: Acoustic spectroscopy; Scattering; Ultrasonic waves; Acoustic wave spectroscopy; Resonant scatterers; Steel rods; Acoustic wave effects


Ultrasonic imaging of highly scattering media from local measurements of the diffusion constant: Separation of coherent and incoherent intensities. Aubry, A., and A. Derode. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 75, no. 2 (2007).
Résumé: As classical imaging fails with diffusive media, one way to image a multiplescattering medium is to achieve local measurements of the dynamic transport properties of a wave undergoing diffusion. This paper presents a method to obtain local measurements of the diffusion constant D in a multiplescattering medium. The experimental setup consists in an array of programmable transducers placed in front of the multiplescattering medium to be imaged. By achieving Gaussian beamforming both at emission and reception, an array of virtual sources and receivers located in the near field is constructed. The time evolution of the incoherent component of the intensity backscattered on this virtual array is shown to represent directly the growth of the diffusive halo as Dt. A matrix treatment is proposed to separate the incoherent intensity from the coherent backscattering peak. Once the incoherent contribution is isolated, a local measurement of the diffusion constant is possible. The technique is applied to image the longscale variations of D in a randomscattering sample made of two parts with a different concentration of cylindrical scatterers. This experimental result is obtained with ultrasonic waves around 3 MHz. It illustrates the possibility of imaging diffusive media from local measurements of the diffusion constant, based on coherent Gaussian beamforming and a matrix “antisymmetrization,” which creates a virtual antireciprocity. © 2007 The American Physical Society.
MotsClés: Backscattering; Light scattering; Transducers; Transport properties; Ultrasonic waves; Diffusion constants; Multiple scattering medium; Programmable transducers; Scattering media; Ultrasonic imaging


Coherent backscattering and farfield beamforming in acoustics. Aubry, A., A. Derode, P. Roux, and A. Tourin. Journal of the Acoustical Society of America 121, no. 1 (2007): 70–77.
Résumé: Coherent backscattering of waves by a random medium is spectacular evidence of interference effects despite disorder and multiple scattering. It manifests itself as a doubling of the wave intensity reflected exactly in the backward direction. This phenomenon has been observed experimentally in optics, acoustics, or seismology. While optical measurements are realized in farfield conditions with a plane wave illumination and a beamwidth much larger than the wavelength, ultrasonic experiments are carried out with wideband controllable arrays of (nearly) pointlike transducers that directly record the wave field, in amplitude and phase. Therefore it is possible to perform beamforming of the incoming and outgoing wave fields before computing the average backscattered intensity. In this paper, the advantages of plane wave beamforming applied to the study of the coherent backscattering effect are shown. Particularly, the angular resolution, the signaltonoise ratio, as well as the estimation of the enhancement factor can be improved by beamforming. Experimental results are presented with ultrasonic pulses, in the 2.53.5 MHz range, propagating in random collections of scatterers. Since the coherent backscattering effect can be taken advantage of to measure diffusive parameters (transport mean free path, diffusion constant), planewave beamforming can be applied to the characterization of highly scattering media. © 2007 Acoustical Society of America.
MotsClés: Signal interference; Signal to noise ratio; Transducers; Ultrasonics; Beamforming; Coherent backscattering effects; Plane wave beamforming; Acoustic wave backscattering; acoustics; article; beamforming; coherent backscattering; measurement; priority journal; signal noise ratio; transducer


Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium. Derode, A., V. Mamou, and A. Tourin. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 74, no. 3 (2006).
Résumé: Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the meanfree path deviates from the classical firstorder approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements. The best agreement is obtained with the secondorder diagrammatic expansion of the selfenergy. © 2006 The American Physical Society.
MotsClés: Approximation theory; Electromagnetic wave propagation; Optical correlation; Random processes; Ultrasonic waves; Coherent waves; Diagrammatic expansion; Random medium; Ultrasonic wave propagation; Coherent light


Time reversal telecommunications in complex environments. Tourin, A., G. Lerosey, J. de Rosny, A. Derode, and M. Fink. Comptes Rendus Physique 7, no. 7 (2006): 816–822.
Résumé: The time reversal technique is well known in acoustics and has lead to remarkable applications in ultrasound and underwater acoustics. Here we propose to apply it to MIMO (Multiple Input – Multiple Output) UWB (Ultra Wide Band) communication: in a first 'training' step, the intended user transmits an electromagnetic pulse that propagates in a medium, where it undergoes multiple reflections. The resulting signals are recorded at the base station by one or more antennas, time reversed and used to precode the transmitted symbols. The resulting sequences are sent back by the antennas. The timereversed wave retraces its former paths and leads to a focus of the message in space and time at the receiver. The equalization step is thus simplified since TR compensates for the reverberation caused by the channel. Furthermore, TR takes advantage of the multipaths to increase the signal strength at the receiver and to improve spatial focusing. To cite this article: A. Tourin et al., C. R. Physique 7 (2006). © 2006 Académie des sciences.
MotsClés: MIMO; Multiple scattering; Reverberation; Time reversal; UWB


Time reversal of wideband microwaves. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, and M. Fink. Applied Physics Letters 88, no. 15 (2006).
Résumé: In this letter, time reversal is applied to wideband electromagnetic waves in a reverberant room. To that end a multiantenna time reversal mirror (TRM) has been built. A 150 MHz bandwidth pulse at a central frequency of 2.45 GHz is radiated by a monopolar antenna, spread in time due to reverberation, recorded at the TRM, time reversed, and retransmitted. The timereversed wave converges back to its source and focus in both time and space. The time compression is studied versus the number of antennas in the TRM and its bandwidth. The focal spot is also measured thanks to an eightchannel receiving array. © 2006 American Institute of Physics.
MotsClés: Arrays; Bandwidth; Microwave antennas; Mirrors; Reverberation; Monopolar antenna; Receiving array; Time reversal mirror (TRM); Microwaves


Time reversal of electromagnetic waves and telecommunication. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink. Radio Science 40, no. 6 (2005).
Résumé: [1] Time reversal (TR) communication in various configurations (single input, single output (SISO); multiple inputs, single output (MISO); or multiple inputs, multiple outputs (MIMO)) is studied. In particular, we report an experimental demonstration of time reversal focusing with electromagnetic waves in a SISO scheme. An antenna transmits a 1 μs electromagnetic pulse at a central frequency of 2.45 GHz in a highQ cavity. Another antenna records the strongly reverberated signal. The timereversed wave is built and transmitted back by the same antenna acting now as a time reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity. A spatial focusing of the compressed pulse is also shown. This experiment is the first step for a communication scheme based on time reversal. It would be very interesting for ultrawideband communication in complex media since TR would permit compensation for delay spreading. MISO and MIMO TR communications are discussed on the basis of smallscale experiments with ultrasound. In particular, the binary error rate of the method is studied as a function of both data rate and external noise. A simple theoretical approach explains the results. Copyright 2005 by the American Geophysical Union.
MotsClés: Antennas; Bandwidth; Error analysis; Functions; Telecommunication systems; Binary error rate; Complex media; Ultrawideband communication; Electromagnetic waves


Weak localization and time reversal of ultrasound in a rotational flow. De Rosny, J., A. Tourin, A. Derode, P. Roux, and M. Fink. Physical Review Letters 95, no. 7 (2005).
Résumé: A onechannel timereversal (TR) experiment is performed inside a rough reverberating cavity in the presence of a rotational flow. The amplitude of the TR wave is plotted versus the distance between the TR channel and the initial source: when they coincide, it exhibits a “timereversal enhancement” (TRE). With no flow, the TRE is the same as the coherent backscattering enhancement (CBE). But contrary to CBE, the TRE peak is shown to be insensitive to the breaking down of reciprocity due to the flow. This new effect of weak localization is sustained by a diagrammatic approach. © 2005 The American Physical Society.
MotsClés: Coherent backscattering enhancement (CBE); Weak localization; Backscattering; Coherent light; Light sources; Rotational flow; Ultrasonics


Relation between time reversal focusing and coherent backscattering in multiple scattering media: A diagrammatic approach. De Rosny, J., A. Tourin, A. Derode, B. Van Tiggelen, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 70, no. 4 2 (2004): 04660104660112.
Résumé: Onechannel time reversal (TR) experiments through multiple scattering media were discussed. The hyperresolution and the selfaveraging property was described. It was found that the developed formalism leads to a deeper understanding of the role of the ladder and mostcrossed diagrams in a TR experiment. Results show that when the initial source and the time reversal point are at the same location, the timereversed amplitude is twice higher.
MotsClés: Approximation theory; Diffusion; Green's function; Mathematical models; Random processes; Spectroscopy; Statistical methods; Ultrasonic propagation; Paraxial approximation; Spatial focusing; Spatiotemporal focusing; Time reversal (TR); Acoustic wave backscattering


Telecommunication in a disordered environment with iterative time reversal. Montaldo, G., G. Lerosey, A. Derode, A. Tourin, J. de Rosny, and M. Fink. Waves Random Media 14, no. 3 (2004): 287–302.
Résumé: We present a method to transmit digital information through a highly scattering medium in a MIMOMU (multiple input multiple output multiple users) context. It is based on iterations of a timereversal process, and permits us to focus short pulses, both spatially and temporally, from a base antenna to different users. This iterative technique is shown to be more efficient (lower intersymbol interference and lower error rate) than classical timereversal communication, while being computationally light and stable. Experiments are presented: digital information is conveyed from 15 transmitters to 15 receivers by ultrasonic waves propagating through a highly scattering slab. From a theoretical point of view, the iterative technique achieves the inverse filter of propagation in the subspace of nonnull singular values of the timereversal operator. We also investigate the influence of external additive noise, and show that the number of iterations can be optimized to give the lowest error rate. © 2004 IOP Publishing Ltd.
MotsClés: Antenna lobes; Antennas; Digital communication systems; Eigenvalues and eigenfunctions; Iterative methods; Matrix algebra; Signal receivers; Transmitters; Ultrasonic propagation; Multiple input multiple output multiple users; Short pulses; Time reversal method; Electromagnetic wave scattering


Imaging from onebit correlations of wideband diffuse wave fields. Larose, E., A. Derode, M. Campillo, and M. Fink. Journal of Applied Physics 95, no. 12 (2004): 8393–8399.
Résumé: An imaging technique based on onebit correlations of wideband diffuse wave fields was discussed. The first step of the imaging process was to retrive the Green's function between two passive sensors from the correlation of the scattered wave fields generated by distant source. It was found that a short ultrasonic pulse, sent through a highly scattering slab, generates a randomly scattered field. The results show that the soundspeed profile of the layered medium can be precisely imaged.
MotsClés: Acoustic waves; Electromagnetic wave scattering; Green's function; Quantum theory; Seismology; Spectroscopic analysis; Spurious signal noise; Ultrasonic waves; Wave propagation; Waveform analysis; Radiative transfer; Random noise; Thermal fluctuations; Timereversal invariance; Imaging techniques


Time reversal of electromagnetic waves. Lerosey, G., J. De Rosny, A. Tourin, A. Derode, G. Montaldo, and M. Fink. Physical Review Letters 92, no. 19 (2004): 193904–1.
Résumé: A onechannel electromagnetic timereversal mirror (TRM) was used for investigating the feasibility of time reversal focusing with electromagnetic waves in the GHz range. Two omnidirectional antennas with a frequency of 2.45 GHz and two transceiver circuit boards were also used for the investigations. The baseband signals were time reversed and the wave carriers were phase conjugated in order to avoid digitizing the radio signals at GHz frequencies. The circuit boards demodulated the radio frequency signal back to the baseband. The frequency bandwidth and the spectral correlations determined the quality of focusing.
MotsClés: Analog to digital conversion; Bandwidth; Correlation methods; Demodulation; Light scattering; Light transmission; Low pass filters; Mirrors; Monochromators; Signal receivers; Signal to noise ratio; Transceivers; Ultrasonic effects; Wireless telecommunication systems; Phase conjugation; Quasimonochromatic signals; Spectral correlations; Time reversal mirrors (TRM); Antenna radiation


Taking advantage of multiple scattering to communicate with timereversal antennas. Derode, A., A. Tourin, J. De Rosny, M. Tanter, S. Yon, and M. Fink. Physical Review Letters 90, no. 1 (2003): 014301/1–014301/4.
Résumé: An overview is given of the experimental demonstration that highorder scattering in a disordered medium can help by increasing the information transfer rate, especially if the timereversal technique is used to naturally focus the different bistreams onto the receivers. The first key parameter in the experiment is the number of independent focal spots that can be created by the transmitting array in the receiving plane. The second key parameter is the number of uncorrelated frequencies within the bandwidth, which governs the peaktonoise ratio on each receiver.
MotsClés: Antenna arrays; Communication channels (information theory); Data communication systems; Decoding; Eigenvalues and eigenfunctions; Electromagnetic wave propagation; Fourier transforms; Matrix algebra; Signal receivers; Ultrasonic devices; Vectors; Wireless telecommunication systems; Time reversal antennas; Ultrasonic antennas; Electromagnetic wave scattering


Time reversal versus phase conjugation in a multiple scattering environment. Derode, A., A. Tourin, and M. Fink. Ultrasonics 40, no. 18 (2002): 275–280.
Résumé: We present experimental results on the reversibility of ultrasound in a multiple scattering medium. An ultrasonic pulsed wave is transmitted from a point source to a 128element receiving array through 2D samples with various thickness. The samples consist of random collections of parallel steel rods immersed in water. The scattered waves are recorded, time reversed and sent back into the medium. The timereversed waves are converging back to their source and the quality of spatial and temporal focusing on the source is related to the secondorder moments of the scattered wave (correlation) in time and in space. Experimental results show that it is possible to obtain a robust estimation of the correlations on a single realisation of disorder, taking advantage of the wide frequency bandwidth. The spatial resolution of the system is only limited by the correlation length of the scattered field, and no longer by diffraction. Moreover, successful timereversal focusing using a single element instead of an array is possible, whereas a onechannel monochromatic phase conjugation fails. The efficiency of broadband time reversal compared to monochromatic phase conjugation lies in the number of 'information grains' in the frequency bandwidth. © 2002 Elsevier Science B.V. All rights reserved.
MotsClés: Multiple scattering; Phase conjugation; Time reversal; Bandwidth; Focusing; Monochromators; Natural frequencies; Optical correlation; Optical phase conjugation; Optical resolving power; Robustness (control systems); Ultrasonic waves; Multiple scattering; Ultrasonic scattering


Ultrasound shock wave generator with onebit time reversal in a dispersive medium, application to lithotripsy. Montaldo, G., P. Roux, A. Derode, C. Negreira, and M. Fink. Applied Physics Letters 80, no. 5 (2002): 897–899.
Résumé: The building of highpower ultrasonic sources from piezoelectric ceramics is limited by the maximum voltage that the ceramics can endure. We have conceived a device that uses a small number of piezoelectric transducers fastened to a cylindrical metallic waveguide. A onebit time reversal operation transforms the longlasting lowlevel dispersed wave forms into a sharp pulse, thus taking advantage of dispersion to generate highpower ultrasound. The pressure amplitude that is generated at the focus is found to be 15 times greater than that achieved with comparable standard techniques. Applications to lithotripsy are discussed and the destructive efficiency of the system is demonstrated on pieces of chalk. © 2002 American Institute of Physics.
MotsClés: Dispersive medium; High power ultrasound; Highpower ultrasonics; Lithotripsy; Long lasting; Metallic waveguide; Pressure amplitudes; Shock wave generator; Time reversal; Wave forms; Building materials; Ceramic materials; Piezoelectric ceramics; Piezoelectricity; Ultrasonics; Dispersion (waves)


Sensitivity to perturbations of a timereversed acoustic wave in a multiple scattering medium. Tourin, A., A. Derode, and M. Fink. Physical Review Letters 87, no. 27 I (2001): 2743011–2743014.
Résumé: Analysis of experimental results on the robustness of acoustic focusing in a multiple scattering medium undergoing perturbations was presented. A time reversal experiment was performed to follow its timedependent evolution in a perturbed random medium. The method was found to be analogous to the diffusive acoustic wave spectroscopy developed to study fluidized suspensions of particles.
MotsClés: Optical correlation; Perturbation techniques; Scattering; Sensitivity analysis; Spectroscopic analysis; Transducers; Diffusive wave spectroscopy; Multiple scattering; Ultrasonic waves


Generation of very high pressure pulses with 1bit time reversal in a solid waveguide. Montaldo, G., P. Roux, A. Derode, C. Negreira, and M. Fink. Journal of the Acoustical Society of America 110, no. 6 (2001): 2849–2857.
Résumé: The use of piezoelectric transducer arrays has opened up the possibility of electronic steering and focusing of acoustic beams to track kidney stones. However, owing to the limited pressure delivered by each transducer (typically 10 bar), the number of transducers needed to reach an amplitude at the focus on the order of 1000 bars is typically of some hundreds of elements. We present here a new solution based on 1bit time reversal in a solid waveguide to obtain, with a small number of transducers, a very high amplitude pulse in tissues located in front of the waveguide. The idea is to take advantage of the temporal dispersion in the waveguide to create, after time reversal, a temporally recompressed pulse with a stronger amplitude. The aim of this work is threefold: first, we experimentally demonstrate 1bit time reversal between a point source in water and several transducers fastened to one section of a finitelength cylindrical waveguide. Second, we numerically and experimentally study the temporal and spatial focusing at the source as a function of the characteristics of the “solid waveguidetime reversal mirror (TRM)” system: length and diameter of the guide, number of transducers of the TRM. Last, we show that the instantaneous power delivered in water at the focus of the solid waveguide is much higher than the power directly transmitted into water from a classically focused transducer. The combination of 1bit time reversal and a solid waveguide leads to shock wave lithotripsy with lowpower electronics. © 2001 Acoustical Society of America.
MotsClés: Arrays; Piezoelectric transducers; Shock waves; Steering; Waveguides; High pressure pulses; Lithotripsies; Acoustics; acoustic technique; pulse generator; acoustics; amplitude modulation; article; electronics; hyperbarism; lithotripsy; nephrolithiasis; pressure; priority journal; pulse generator; transducer; waveform


Numerical and experimental timereversal of acoustic waves in random media. Derode, A., M. Tanter, A. Tourin, L. Sandrin, and M. Fink. Journal of Computational Acoustics 9, no. 3 (2001): 993–1003.
Résumé: In classical mechanics, a timereversal experiment with a large number of particles is impossible. Because of the high sensitivity to initial conditions, one would need to resolve the positions and velocities of each particle with infinite accuracy. Thus, it would require an infinite amount of information, which is of course out of reach. In wave physics however, the amount of information required to describe a wave field is limited and depends on the shortest wavelength of the field. Thus we can propose an acoustic equivalent of the experiment we mentioned above. We start with a coherent transient pulse, let it propagate through a disordered highly scattering medium, then record the scattered field and timereverse it: surprisingly, it travels back to its initial source, which is not predictable by usual theories for random media. Indeed, to study waves propagation in disordered media theoreticians, who find it difficult to deal with one realization of disorder, use concepts defined as an average over the realizations, which naturally leads to the diffusion approximation. But the corresponding equation is not timereversal invariant and thus fails in describing our experiment. Then, to understand our experimental results and try to predict new ones, we have developed a finite elements simulation based on the real microscopic timeinvariant equation of propagation. The experimental and numerical results are found to be in very good agreement.


Random multiple scattering of ultrasound. II. Is time reversal a selfaveraging process? Derode, A., A. Tourin, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 64, no. 3 II (2001): 366061–366113.
Résumé: The statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering were investigated. An ultrasonic pulsed wave was transmitted from a point source to a 128element receiving array through twodimensional samples with various thickness. The results show that a robust estimation on a single realization of disorder is obtained using wide frequency bandwidth.
MotsClés: Acoustic wave propagation; Backscattering; Bandwidth; Integral equations; Interfaces (computer); Mathematical models; Piezoelectric devices; Steel; Ultrasonic scattering; Ultrasonic pulsed waves; Ultrasonic waves


Random multiple scattering of ultrasound. I. Coherent and ballistic waves. Derode, A., A. Tourin, and M. Fink. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics 64, no. 3 II (2001): 366051–366057.
Résumé: Random multiple scattering of ultrasound was analyzed using statistical approach techniques. An ultrasonic pulsed wave transmitted from a point source to a 128element receiving array was studied through two dimensional samples with various thickness. It is found that the transmitted wave forms exhibits a timedependent frequency spectrum. The results show that the secondary wave forms on the coherent wave form is produced due to the presence of elastic resonance in the given frequency bandwidth.
MotsClés: Backscattering; Ballistics; Coherent light; Integral equations; Mathematical models; Ultrasonic scattering; Ballistic waves; Resonant multiple scattering; Ultrasonic waves


Multiple scattering of sound. Tourin, A., M. Fink, and A. Derode. Waves Random Media 10, no. 4 (2000): R31–R60.
Résumé: We present a topical review which summarizes the main contributions to `multiple scattering of acoustic and elastic waves' including the most recent advances.The review is divided into five main parts.In the first part, the effects of multiple scattering on ultrasonic propagation are illustrated on the basis of three experimental examples.In the second and third parts, we present the two possible descriptions for the propagation of an acoustic wave in a random medium. The first one is based on the study of the coherent wave, i.e. the wave amplitude averaged over disorder, whereas the second one deals with the propagation of the incoherent intensity, i.e. the intensity averaged over disorder. We especially insist on the microscopic basis for the phenomenological radiative transfer equation and show how it can be solved in the diffusion approximation. The theory is illustrated with experimental results obtained on a twodimensional multiplescattering prototype made of thousands of steel rods randomly distributed and immersed in water. In the fourth part, we present experimental evidence that the diffusion equation fails in describing all the aspects of the propagation of an acoustic wave in a random medium: e.g. the coherent backscattering effect recently observed for ultrasonic waves. We show that this effect arises as a consequence of reciprocity. Finally, in the fifth part, we discuss another property which is not taken into account in the radiative transfer theory: the reversibility of an acoustic wave propagating in a disordered medium.
MotsClés: Acoustic wave backscattering; Approximation theory; Diffusion; Mathematical models; Ultrasonic propagation; Coherent backscattering effects; Radiative transfer equation; Acoustic wave scattering


Transport parameters for an ultrasonic pulsed wave propagating in a multiple scattering medium. Tourin, A., A. Derode, A. Peyre, and M. Fink. Journal of the Acoustical Society of America 108, no. 2 (2000): 503–512.
Résumé: A set of ultrasonic experimental methods was developed to characterize a multiple scattering medium in terms of l(s), l*, l(a), respectively, the elastic, transport, and absorption mean free paths and D the diffusion constant. Actually, these quantities are the key parameters for a wave propagating in a disordered medium. Although they are widely used in optics, they are less common in acoustics. The underlying model is based on the expansion of the average solution for the heterogeneous Green's function equation. To validate this theoretical approach, a sample made of randomly located steel rods was used as a prototype. Through timeresolved measurements of the transmitted amplitude, the difference between the ballistic and the coherent wave is highlighted. In varying the sample thickness, l(s) is determined, the coherent and diffusive regime are distinguished, and the transition from one to the other is followed. Furthermore, as a limit to a description of the average intensity based on the diffusion approximation, the existence of a coherent backscattering effect is shown. This latter gives a method to estimate D and l*. These quantities being determined, it becomes possible to infer l(a) using average timeresolved intensity measurements. Finally, some applications to coarsegrain stainless steels are discussed. (C) 2000 Acoustical Society of America.
MotsClés: acoustics; article; calculation; mathematical analysis; priority journal; sound; theory; ultrasound


Limits of timereversal focusing through multiple scattering: Longrange correlation. Derode, A., A. Tourin, and M. Fink. Journal of the Acoustical Society of America 107, no. 6 (2000): 2987–2998.
Résumé: Experimental results of timereversal focusing in a highorder multiple scattering medium are presented and compared to theoretical predictions based on a statistical model. The medium consists of a random collection of parallel steel rods. An ultrasonic source (3.2 MHz) transmits a pulse that undergoes multiple scattering and is recorded on an array. The timereversed waves are sent by the array back to the source through the scattering medium. The quality of temporal focusing is very well predicted by a simple statistical model. However, for thicker samples, persistent temporal side lobes appear. We interpret these sidelobes as a consequence of the growing number of crossing paths in the sample due to highorder multiple scattering. As to spatial focusing, the resolution is practically independent from the array's aperture. With a 16element array, the resolution was found to be 30 times finer than in a homogeneous medium. Resolutions of the order of the wavelength (0.5 mm) were attained. These results are discussed in relation with the statistical properties of timereversal mirrors in a random medium. (C) 2000 Acoustical Society of America.
MotsClés: acoustics; article; priority journal; signal noise ratio; signal transduction; sound transmission; statistical analysis; thickness


Dynamic time reversal of randomly backscattered acoustic waves. Tourin, A., A. Derode, and M. Fink. Europhysics Letters 47, no. 2 (1999): 175–181.
Résumé: We report the first experiments using the reversibility of a transient acoustic wave in a multiplescattering medium to simulate either a stationary or a dynamic acoustic lens. The method is based on time reversal experiments performed in a backscattering configuration. In the stationary case, we show that we take advantage of multiple scattering to focus better than with a perfect reflecting interface. In the dynamic case, we explain the refocused spot time evolution by a simple model based on the timedependent ability to recover the angular spectrum thanks to both single and multiplescattering paths.


Time reversal in multiply scattering media. Derode, A., A. Tourin, and M. Fink. Ultrasonics 36, no. 15 (1998): 443–447.
Résumé: The application of timereversal mirrors (TRM) to media with very highorder multiple scattering is presented. Random sets of up to 2500 steel rods are considered. When a pulsed wave traverses such a medium, it undergoes many scatterings before reaching the TRM. The resulting pressure field spreads in time, up to 300 times the initial pulse duration; it is recorded, timereversed and retransmitted through the same disordered medium. Surprisingly, the timereversed waves are found to converge to their source and recover their original waveform and duration, unlike one could have expected given the high order of multiple scattering involved and the usual sensitivity to initial conditions of timereversal processes. In addition to this, the observed resolution of the timereversed waves was greatly increased, and found to be smaller than the theoretical limit for the array's aperture. Theoretical limits of timereversed experiments are discussed. © 1998 Elsevier Science B.V.
MotsClés: Multiple scattering; Time reversal; Steel; Ultrasonic transmission; Ultrasonics; Time reversal mirrors (TRM); Ultrasonic scattering


Correlation length of ultrasonic speckle in anisotropic random media: Application to coherent echo detection. Derode, A., and M. Fink. Journal of the Acoustical Society of America 103, no. 1 (1998): 73–82.
Résumé: In a recent paper [Derode and Fink, J. Acoust. Soc. Am. 101, 690704 (1997)], a technique for studying spatial coherence properties of backscattered speckle noise by means of a transducers array was described. In this paper another approach is presented. Here, a single transducer, focusing inside a scattering medium, is moved in a plane; correlation is studied between signals acquired in two different positions. A study investigates how the correlation function of the medium determines that of the speckle noise This is applied to fully or partially incoherent media, and media with anisotropic scatterer distribution such as unidirectional and crossply composites; we show that it is possible to extract information about the medium from a measurement of the backscattered field correlation length. The influence of correlation length on defect detection is discussed. Experimental as well as theoretical results are presented, they are found in good agreement.
MotsClés: anisotropy; article; correlation function; echography; fourier transformation; noise; priority journal; sound detection; sound transmission; ultrasound; ultrasound transducer


Partial coherence of transient ultrasonic fields in anisotropic random media: Application to coherent echo detection. Derode, A., and M. Fink. Journal of the Acoustical Society of America 101, no. 2 (1997): 690–704.
Résumé: In this paper the spatial coherence properties of the speckle noise backscattered from random media insonified by a broadband pulse are studied. The approach presented is an adaptation of the optical notion of coherence introduced by Zernike. How the statistical parameters (particularly the secondorder moment) of the medium determine those of the speckle noise is studied. This is applied to fully or partially incoherent media, and media with anisotropic scatterer distribution such as unidirectional and crossply composites; also investigated is the possibility of detecting a coherent reflector among speckle noise through measurements of coherence length. Experimental as well as theoretical results are presented. Measurements were carried out with a linear array of 128 programmable transmitters/receivers.
MotsClés: acoustics; anisotropy; article; fourier transformation; noise; priority journal; statistical parameters; transducer; ultrasound

