Matrix imaging as a tool for highresolution monitoring of deep volcanic plumbing systems with seismic noise Giraudat, E., A. Burtin, A. Le Ber, M. Fink, J. C. Komorowski, and A. Aubry Communications Earth and Environment 5, no. 1 (2024)
Résumé: Volcanic eruptions necessitate precise monitoring of magma pressure and inflation for improved forecasting. Understanding deep magma storage is crucial for hazard assessment, yet imaging these systems is challenging due to complex heterogeneities that disrupt standard seismic migration techniques. Here we map the magmatic and hydrothermal system of the La Soufrière volcano in Guadeloupe by analyzing seismic noise data from a sparse geophone array under a matrix formalism. Seismic noise interferometry provides a reflection matrix containing the signature of echoes from deep heterogeneities. Using wave correlations resistant to disorder, matrix imaging successfully unscrambles wave distortions, revealing La Soufrière’s internal structure down to 10 km with 100 m resolution. This method surpasses the diffraction limit imposed by geophone array aperture, providing crucial data for modeling and highresolution monitoring. We see matrix imaging as a revolutionary tool for understanding volcanic systems and enhancing observatories’ abilities to monitor dynamics and forecast eruptions. (Figure presented.)


Harnessing forward multiple scattering for optical imaging deep inside an opaque medium Najar, U., V. Barolle, P. Balondrade, M. Fink, C. Boccara, and A. Aubry Nature Communications 15, no. 1 (2024)
Résumé: As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to indepth optical microscopy, as it causes a drastic degradation of contrast, resolution and brightness of the resulting image beyond a few scattering mean free paths. However, the information about the inner reflectivity of the sample is not lost; only scrambled. To recover this information, a matrix approach of optical imaging can be fruitful. Here, we report on a descanned measurement of a highdimension reflection matrix R via low coherence interferometry. Then, we show how a set of independent focusing laws can be extracted for each medium voxel through an iterative multiscale analysis of wave distortions contained in R. It enables an optimal and local compensation of forward multiple scattering paths and provides a threedimensional confocal image of the sample as the latter one had become digitally transparent. The proofofconcept experiment is performed on a human opaque cornea and an extension of the penetration depth by a factor five is demonstrated compared to the stateoftheart.


Imaging the Crustal and Upper Mantle Structure of the North Anatolian Fault: A Transmission Matrix Framework for Local Adaptive Focusing Touma, R., A. Le Ber, M. Campillo, and A. Aubry Journal of Geophysical Research: Solid Earth 128, no. 11 (2023)
Résumé: Imaging the structure of major fault zones is essential for our understanding of crustal deformations and their implications on seismic hazards. Investigating such complex regions presents several issues, including the variation of seismic velocity due to the diversity of geological units and the cumulative damage caused by earthquakes. Conventional migration techniques are in general strongly sensitive to the available velocity model. Here we apply a passive matrix imaging approach which is robust to the mismatch between this model and the real seismic velocity distribution. This method relies on the crosscorrelation of ambient noise recorded by a geophone array. The resulting set of impulse responses form a reflection matrix that contains all the information about the subsurface. In particular, the reflected body waves can be leveraged to: (a) determine the transmission matrix between the Earth's surface and any point in the subsurface; (b) build a confocal image of the subsurface reflectivity with a transverse resolution only limited by diffraction. As a study case, we consider seismic noise (0.1–0.5 Hz) recorded by the Dense Array for Northern Anatolia that consists of 73 stations deployed for 18 months in the region of the 1999 Izmit earthquake. Passive matrix imaging reveals the scattering structure of the crust and upper mantle around the North Anatolian Fault zone over a depth range of 60 km. The results show that most of the scattering is associated with the Northern branch that passes throughout the crust and penetrates into the upper mantle.


Threedimensional ultrasound matrix imaging Bureau, F., J. Robin, A. Le Ber, W. Lambert, M. Fink, and A. Aubry Nature Communications 14, no. 1 (2023)
Résumé: Matrix imaging paves the way towards a next revolution in wave physics. Based on the response matrix recorded between a set of sensors, it enables an optimized compensation of aberration phenomena and multiple scattering events that usually drastically hinder the focusing process in heterogeneous media. Although it gave rise to spectacular results in optical microscopy or seismic imaging, the success of matrix imaging has been so far relatively limited with ultrasonic waves because wave control is generally only performed with a linear array of transducers. In this paper, we extend ultrasound matrix imaging to a 3D geometry. Switching from a 1D to a 2D probe enables a much sharper estimation of the transmission matrix that links each transducer and each medium voxel. Here, we first present an experimental proof of concept on a tissuemimicking phantom through exvivo tissues and then, show the potential of 3D matrix imaging for transcranial applications.


Ultrasound Matrix Imaging  Part II: The Distortion Matrix for Aberration Correction Over Multiple Isoplanatic Patches Lambert, W., L. A. Cobus, J. Robin, M. Fink, and A. Aubry IEEE Transactions on Medical Imaging 41, no. 12, 39213938 (2022)
Résumé: This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speedofsound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentallyrecorded matrix of reflected acoustic signals to synthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wavefronts consist of two components: (i) An ideal geometric wavefront linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speedofsound variations. These distortions are stored in a socalled distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even highorder and spatiallydistributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the invivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.


Ultrasound Matrix Imaging  Part I: The Focused Reflection Matrix, the FFactor and the Role of Multiple Scattering Lambert, W., J. Robin, L. A. Cobus, M. Fink, and A. Aubry IEEE Transactions on Medical Imaging 41, no. 12, 39073920 (2022)
Résumé: This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and reception on each point of the medium. Ultrasound matrix imaging (UMI) consists in decoupling the location of these transmitted and received focal spots. The response between those virtual transducers form the socalled focused reflection matrix that actually contains much more information than a confocal ultrasound image. In this paper, a timefrequency analysis of this matrix is performed, which highlights the single and multiple scattering contributions as well as the impact of aberrations in the monochromatic and broadband regimes. Interestingly, this analysis enables the measurement of the incoherent inputoutput point spread function at any pixel of this image. A fitting process enables the quantification of the single scattering, multiple scattering and noise components in the image. From the single scattering contribution, a focusing criterion is defined, and its evolution used to quantify the amount of aberration throughout the ultrasound image. In contrast to the stateoftheart coherence factor, this new indicator is robust to multiple scattering and electronic noise, thereby providing a contrasted map of the focusing quality at a much better transverse resolution. After a validation of the proofofconcept based on timedomain simulations, UMI is applied to the invivo study of a human calf. Beyond this specific example, UMI opens a new route for speedofsound and scattering quantification in ultrasound imaging.


Weight of single and recurrent scattering in the reflection matrix of complex media Brütt, C., A. Aubry, B. Gérardin, A. Derode, and C. Prada Physical Review E 106, no. 2 (2022)
Résumé: In a heterogeneous medium, the wave field can be decomposed as an infinite series known as the Born expansion. Each term of the Born expansion corresponds to a scattering order, it is thus theoretically possible to discriminate single and multiple scattering contribution to the field. Experimentally, what is actually measured is the total field in which all scattering orders interfere. Conventional imaging methods usually rely on the assumption that the multiple scattering contribution can be disregarded. In a backscattering configuration, this assumption is valid for small depths, and begins to fail for depths larger than the scattering meanfree path s. It is therefore a key issue to estimate the relative amount of single and multiple scattering in experimental data. To this end, a singlescattering estimator ρ computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wave field. In this paper, the meaning of this estimator is investigated and a particular attention is given to recurrent scattering. In a diffractionlimited experiment, a multiple scattering sequence is said to be recurrent if the first and last scattering events occur in the same resolution cell. Recurrent scattering is shown to be responsible for correlations between single scattering and higher scattering orders of the Born expansion, inducing a bias to the estimator ρ that should rather be termed confocal scattering ratio. Interestingly, a more robust estimator is built by projecting the reflection matrix in a focused basis. The argument is sustained by numerical simulations as well as ultrasonic data obtained around 1.5 MHz in a model medium made of nylon rods immersed in water. From a more general perspective, this work raises fundamental questions about the impact of recurrent scattering on wave imaging.


Roadmap on wavefront shaping and deep imaging in complex media Gigan, S., O. Katz, H. B. De Aguiar, E. R. Andresen, A. Aubry, J. Bertolotti, E. Bossy, D. Bouchet, J. Brake, S. Brasselet, Y. Bromberg, H. Cao, T. Chaigne, Z. Cheng, W. Choi, T. čižmár, M. Cui, V. R. Curtis, H. Defienne, M. Hofer, R. Horisaki, R. Horstmeyer, N. Ji, A. K. Laviolette, J. Mertz, C. Moser, A. P. Mosk, N. C. Pégard, R. Piestun, S. Popoff, D. B. Phillips, D. Psaltis, B. Rahmani, H. Rigneault, S. Rotter, L. Tian, I. M. Vellekoop, L. Waller, and Wan Journal of Physics: Photonics 4, no. 4, 042501 (2022)
Résumé: The last decade has seen the development of a wide set of tools, such as wavefront shaping, computational or fundamental methods, that allow us to understand and control light propagation in a complex medium, such as biological tissues or multimode fibers. A vibrant and diverse community is now working in this field, which has revolutionized the prospect of diffractionlimited imaging at depth in tissues. This roadmap highlights several key aspects of this fast developing field, and some of the challenges and opportunities ahead.


Crossover from renormalized to conventional diffusion near the threedimensional Anderson localization transition for light Cobus, L. A., G. Maret, and A. Aubry Physical Review B 106, no. 1 (2022)
Résumé: We report on anomalous light transport in the strong scattering regime. Using lowcoherence interferometry, we measure the reflection matrix of titanium dioxide powders, revealing crucial features of strong optical scattering which cannot be observed with transmission measurements: (i) a subdiffusive regime of transport at early times of flight that is a direct consequence of predominant recurrent scattering loops and (ii) a crossover to a conventional, but extremely slow, diffusive regime at long times. These observations support previous predictions that nearfield coupling between scatterers prohibits Anderson localization of light in threedimensional disordered media.


FreezeDried Microfluidic Monodisperse Microbubbles as a New Generation of Ultrasound Contrast Agents Soysal, U., P. N. Azevedo, F. Bureau, A. Aubry, M. S. Carvalho, A. C. S. N. Pessoa, L. G. D. L. Torre, O. Couture, A. Tourin, M. Fink, and P. Tabeling Ultrasound in Medicine and Biology (2022)
Résumé: We succeeded in freezedrying monodisperse microbubbles without degrading their performance, that is, their monodispersity in size and echogenicity. We used microfluidic technology to generate cryoprotected highly monodisperse microbubbles (coefficient of variation [CV] <5%). By using a novel retrieval technique, we were able to freezedry the microbubbles and resuspend them without degradation, that is, keeping their size distribution narrow (CV <6%). Acoustic characterization performed in two geometries (a centimetric cell and a millichannel) revealed that the resuspended bubbles conserved the sharpness of the backscattered resonance peak, leading to CVs ranging between 5% and 10%, depending on the geometry. As currently observed with monodisperse bubbles, the peak amplitudes are one order of magnitude higher than those of commercial ultrasound contrast agents. Our work thus solves the question of storage and transportation of highly monodisperse bubbles. This work might open pathways toward novel clinical noninvasive measurements, such as local pressure, impossible to carry out with the existing commercial ultrasound contrast agents.


Cloaking, trapping and superlensing of lamb waves with negative refraction Legrand, F., B. Gérardin, F. Bruno, J. Laurent, F. Lemoult, C. Prada, and A. Aubry Scientific Reports 11, no. 1 (2021)
Résumé: We report on experimental and numerical implementations of devices based on the negative refraction of elastic guided waves, the socalled Lamb waves. Consisting in plates of varying thickness, these devices rely on the concept of complementary media, where a particular layout of negative index media can cloak an object with its antiobject or trap waves around a negative corner. The diffraction cancellation operated by negative refraction is investigated by means of laser ultrasound experiments. However, unlike original theoretical predictions, these intriguing wave phenomena remain, nevertheless, limited to the propagating component of the wavefield. To go beyond the diffraction limit, negative refraction is combined with the concept of metalens, a device converting the evanescent components of an object into propagating waves. The transport of an evanescent wavefield is then possible from an object plane to a farfield imaging plane. Twenty years after Pendry’s initial proposal, this work thus paves the way towards an elastic superlens.


Distribution of seismic scatterers in the San Jacinto Fault Zone, southeast of Anza, California, based on passive matrix imaging Touma, R., A. Aubry, Y. BenZion, and M. Campillo Earth and Planetary Science Letters 578 (2022)
Résumé: Fault zones are associated with multiscale heterogeneities of rock properties. Large scale variations may be imaged with conventional seismic reflection methods that detect offsets in geological units, and tomographic techniques that provide average seismic velocities in resolved volumes. However, characterizing elementary localized inhomogeneities of fault zones, such as cracks and fractures, constitutes a challenge for conventional techniques. Resolving these smallscale heterogeneities can provide detailed information for structural and mechanical models of fault zones. Recently, the reflection matrix approach utilizing body wave reflections in ambient noise crosscorrelations was extended with the introduction of aberration corrections to handle the actual lateral velocity variations in the fault zone (Touma et al., 2021). Here this method is applied further to analyze the distribution of scatterers in the first few kilometers of the crust in the San Jacinto Fault Zone at the Sage Brush Flat (SGB) site, southeast of Anza, California. The matrix approach allows us to image not only specular reflectors but also to resolve the presence, location and reflectivity of scatterers for seismic waves starting with a simple homogeneous background velocity model of the medium. The derived threedimensional image of the fault zone resolves lateral variations of scattering properties in the region within and around the surface fault traces, as well as differences between the Northwest (NW) and the Southeast (SE) parts of the study area. A localized intense damage zone at depth is observed in the SE section, suggesting that a geometrical complexity of the fault zone at depth induces ongoing generation of rock damage.


Manifestation of aberrations in fullfield optical coherence tomography Barolle, V., J. Scholler, P. Mecê, J. M. Chassot, K. Groux, M. Fink, A. C. Boccara, and A. Aubry Optics Express 29, no. 14, 2204422065 (2021)
Résumé: We report on a theoretical model for image formation in fullfield optical coherence tomography (FFOCT). Because the spatial incoherence of the illumination acts as a virtual confocal pinhole in FFOCT, its imaging performance is equivalent to a scanning timegated coherent confocal microscope. In agreement with optical experiments enabling a precise control of aberrations, FFOCT is shown to have nearly twice the resolution of standard imaging at moderate aberration level. Beyond a rigorous study on the sensitivity of FFOCT with respect to aberrations, this theoretical model paves the way towards an optimized design of adaptive optics and computational tools for highresolution and deep imaging of biological tissues.


A distortion matrix framework for highresolution passive seismic 3D imaging: Application to the San Jacinto fault zone, California Touma, R., T. Blondel, A. Derode, M. Campillo, and A. Aubry Geophysical Journal International 226, no. 2, 780794 (2021)
Résumé: Reflection seismic imaging usually suffers from a loss of resolution and contrast because of the fluctuations of the wave velocities in the Earth's crust. In the literature, phase distortion issues are generally circumvented by means of a background wave velocity model. However, it requires a prior tomography of the wave velocity distribution in the medium, which is often not possible, especially in depth. In this paper, a matrix approach of seismic imaging is developed to retrieve a 3D image of the subsoil, despite a rough knowledge of the background wave velocity. To do so, passive noise crosscorrelations between geophones of a seismic array are investigated under a matrix formalism. They form a reflection matrix that contains all the information available on the medium. A set of matrix operations can then be applied in order to extract the relevant information as a function of the problem considered. On the one hand, the background seismic wave velocity can be estimated and its fluctuations quantified by projecting the reflection matrix in a focused basis. It consists in investigating the response between virtual sources and detectors synthesized at any point in the medium. The minimization of their crosstalk can then be used as a guide star for approaching the actual wave velocity distribution. On the other hand, the detrimental effect of wave velocity fluctuations on imaging is overcome by introducing a novel mathematical object: The distortion matrix. This operator essentially connects any virtual source inside the medium with the distortion that a wavefront, emitted from that point, experiences due to heterogeneities. A time reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each real geophone at the surface and each virtual geophone in depth. Phase distortions can then be compensated for any point of the underground. Applied to passive seismic data recorded along the Clark branch of the San Jacinto fault zone (SJFZ), the present method is shown to provide an image of the fault until a depth of 4 km over the frequency range 1020Hz with an horizontal resolution of 80 m. Strikingly, this resolution is almost one eighth below the diffraction limit imposed by the geophone array aperture. The heterogeneities of the subsoil play the role of a scattering lens and of a transverse waveguide which increase drastically the array aperture. The contrast is also optimized since most of the incoherent noise is eliminated by the iterative time reversal process. Beyond the specific case of the SJFZ, the reported approach can be applied to any scales and areas for which a reflection matrix is available at a spatial sampling satisfying the Nyquist criterion.


Reflection Matrix Approach for Quantitative Imaging of Scattering Media Lambert, W., L. A. Cobus, M. Couade, M. Fink, and A. Aubry Physical Review X 10, no. 2 (2020)
Résumé: © 2020 authors. Published by the American Physical Society. We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof of concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics for which multielement technology is available. The concept is that focused beam forming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The interelement responses of this virtual array form a focused reflection matrix from which spatial maps of various characteristics of the propagating wave can be retrieved. Here we demonstrate (i) a local focusing criterion that enables the image quality and the wave velocity to be evaluated everywhere inside the medium, including in random speckle, and (ii) a highly resolved spatial mapping of the prevalence of multiple scattering, which constitutes a new and unique contrast for ultrasonic imaging. The approach is demonstrated for a controllable phantom system and for in vivo imaging of the human abdomen. More generally, this matrix approach opens an original and powerful route for quantitative imaging in wave physics.


Distortion matrix concept for deep optical imaging in scattering media Badon, A., V. Barolle, K. Irsch, A. Claude Boccara, M. Fink, and A. Aubry Science Advances 6, no. 30 (2020)
Résumé: © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BYNC). In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sampleinduced aberrations and multiple scattering can strongly degrade the image resolution and contrast. On the basis of a dynamic correction of the incident and/or reflected wavefronts, adaptive optics has been used to compensate for those aberrations. However, it only applies to spatially invariant aberrations or to thin aberrating layers. Here, we propose a global and noninvasive approach based on the distortion matrix concept. This matrix basically connects any focusing point of the image with the distorted part of its wavefront in reflection. A singular value decomposition of the distortion matrix allows to correct for highorder aberrations and forward multiple scattering over multiple isoplanatic modes. Proofofconcept experiments are performed through biological tissues including a turbid cornea. We demonstrate a Strehl ratio enhancement up to 2500 and recover a diffractionlimited resolution until a depth of 10 scattering mean free paths.


Distortion matrix approach for ultrasound imaging of random scattering media Lambert, W., L. A. Cobus, T. Frappart, M. Fink, and A. Aubry Proceedings of the National Academy of Sciences of the United States of America 117, no. 26, 1464514656 (2020)
Résumé: Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wave fronts and degrade image quality. Adaptive focusing can compensate for such aberration but is only effective over a restricted field of view. Here, we introduce a fullfield approach to wave imaging based on the concept of the distortion matrix. This operator essentially connects any focal point inside the medium with the distortion that a wave front, emitted from that point, experiences due to heterogeneities. A timereversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a fullfield image of the medium with diffractionlimited resolution. Importantly, this process is particularly efficient in random scattering media, where traditional approaches such as adaptive focusing fail. Here, we first present an experimental proof of concept on a tissuemimicking phantom and then, apply the method to in vivo imaging of human soft tissues. While introduced here in the context of acoustics, this approach can also be extended to optical microscopy, radar, or seismic imaging.
Motsclés: acoustic speckle; complex media; sampleinduced aberrations; transmission matrix imaging; waves


Negative reflection of elastic guided waves in chaotic and random scattering media Gérardin, B., J. Laurent, F. Legrand, C. Prada, and A. Aubry Scientific reports 9, no. 1, 2135 (2019)
Résumé: The propagation of waves in complex media can be harnessed either by taming the incident wavefield impinging on the medium or by forcing waves along desired paths through its careful design. These two alternative strategies have given rise to fascinating concepts such as time reversal or negative refraction. Here, we show how these two processes are intimately linked through the negative reflection phenomenon. A negative reflecting mirror converts a wave of positive phase velocity into its negative counterpart and vice versa. In this article, we experimentally demonstrate this phenomenon with elastic waves in a 2D billiard and in a disordered plate by means of laser interferometry. Despite the complexity of such configurations, the negatively reflected wave field focuses back towards the initial source location, thereby mimicking a phase conjugation operation while being a fully passive process. The superfocusing capability of negative reflection is also highlighted in a monochromatic regime. The negative reflection phenomenon is not restricted to guided elastic waves since it can occur in zerogap systems such as photonic crystals, chiral metamaterials or graphene. Negative reflection can thus become a tool of choice for the control of waves in all fields of wave physics.


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, 10,93610,950 (2018)
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


Negative refraction of Lamb modes: A theoretical study Legrand, F., B. Gérardin, J. Laurent, C. Prada, and A. Aubry Physical Review B 98, no. 21 (2018)
Résumé: © 2018 American Physical Society. This paper provides a theoretical investigation of negative refraction and focusing of elastic guided waves in a freestanding plate with a steplike thickness change. Under certain conditions, a positive phase velocity (forward) Lamb mode can be converted into a negative phase velocity (backward) mode at such interface, giving rise to negative refraction. A semianalytical model is developed to study the influence of various parameters such as the material Poisson's coefficient, the steplike thickness, the frequency, and the incidence angle. To this end, all the Lamb and shear horizontal propagating modes and also a large number of their inhomogeneous and evanescent counterparts are taken into account. The boundary conditions applied to the stressdisplacement fields at the thickness step yields an equation system. Its inversion provides the transmission and reflection coefficients between each mode at the interface. The steplike thickness and Poisson's ratio are shown to be key parameters to optimize the negative refraction process. In terms of material, Duralumin is found to be optimal as it leads to a nearly perfect conversion between forward and backward modes over broad frequency and angular ranges. An excellent focusing ability is thus predicted for a flat lens made of two symmetric thickness steps. A laser ultrasonic experiment quantitatively confirms those theoretical predictions. This study paves the way toward the optimization of elastic devices based on negative refraction, in particular for cloaking or superfocusing purposes.


Multiple scattering limit in optical microscopy Badon, A., A. C. Boccara, G. Lerosey, M. Fink, and A. Aubry Optics Express 25, no. 23, 2891428934 (2017)
Résumé: © 2017 Optical Society of America. Optical microscopy offers a unique insight of biological structures with a submicrometer resolution and a minimum invasiveness. However, the inhomogeneities of the specimen itself can induce multiple scattering of light and optical aberrations which limit the observation to depths close to the surface. To predict quantitatively the penetration depth in microscopy, we theoretically derive the singletomultiple scattering ratio in reflection. From this key quantity, the multiple scattering limit is deduced for various microscopic imaging techniques such as confocal microscopy, optical coherence tomography and related methods.


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, 624640 (2017)
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.


Smart optical coherence tomography for ultradeep imaging through highly scattering media Badon, A., D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry Science Advances 2, no. 11 (2016)


Spatiotemporal imaging of light transport in highly scattering media under white light illumination Badon, A., D. Li, G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry Optica 3, no. 11, 11601166 (2016)


Particlelike wave packets in complex scattering systems Gerardin, B., J. Laurent, P. Ambichl, C. Prada, S. Rotter, and A. Aubry Physical Review B 94, no. 1 (2016)


Negative reflection of Lamb waves at a free edge: Tunable focusing and mimicking phase conjugation. Gerardin, B., J. Laurent, C. Prada, and A. Aubry The Journal of the Acoustical Society of America 140, no. 1, 591 (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.


Retrieving timedependent green's functions in optics with lowcoherence interferometry Badon, A., G. Lerosey, A. C. Boccara, M. Fink, and A. Aubry Physical Review Letters 114, no. 2 (2015)
Résumé: © 2015 American Physical Society. We report on the passive measurement of timedependent Green's functions in the optical frequency domain with lowcoherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a broadband and incoherent wave field can directly yield the Green's functions between scatterers of a complex medium. Both the ballistic and multiple scattering components of the Green's function are retrieved. This approach opens important perspectives for optical imaging and characterization in complex scattering media.


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, 358367 (2014)


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, 234105 (2014)


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)


Transformation optics and subwavelength control of light Pendry, J. B., A. Aubry, D. R. Smith, and S. A. Maier Science 337, no. 6094, 549552 (2012)
Résumé: Our intuitive understanding of light has its foundation in the ray approximation and is intimately connected with our vision. As far as our eyes are concerned, light behaves like a stream of particles. We look inside the wavelength and study the properties of plasmonic structures with dimensions of just a few nanometers, where at a tenth or even a hundredth of the wavelength of visible light the ray picture fails. We review the concept of transformation optics that manipulates electric and magnetic field lines, rather than rays; can provide an equally intuitive understanding of subwavelength phenomena; and at the same time can be an exact description at the level of Maxwell's equations.
Motsclés: electric field; magnetic field; optimization; transformation; visible spectrum; wavelength; electric field; light; magnetic field; optics; priority journal; review; spectral sensitivity


Exploiting the timereversal operator for adaptive optics, selective focusing, and scattering pattern analysis Popoff, S. M., A. Aubry, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan Physical Review Letters 107, no. 26 (2011)
Résumé: We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the timereversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles. © 2011 American Physical Society.
Motsclés: Backscattering matrix; Experimental measurements; matrix; Nanobeads; Optical imaging; Scattering medium; Scattering pattern; Selective excitations; Single nanoparticle; Timereversal operator; Nanoparticles; Scattering


Plasmonic hybridization between nanowires and a metallic surface: A transformation optics approach Aubry, A., D. Y. Lei, S. A. Maier, and J. B. Pendry ACS Nano 5, no. 4, 32933308 (2011)
Résumé: The interaction between metallic nanowires and a metal substrate is investigated by means of transformation optics. This plasmonic system is of particular interest for single molecule detection or nanolasers. By mapping such a plasmonic device onto a metalinsulatormetal infinite structure, its optical response can be fully derived analytically. In this article, the absorption crosssection of a nanowire placed close to a metallic surface is derived within and beyond the quasistatic limit. The system is shown to support several modes characterized by a different angular momentum and whose resonance redshifts when the nanoparticle approaches the metal substrate. These resonances give rise to a drastic field enhancement (>10 2) within the narrow gap separating the nanoparticle from the metal surface. The case of a nanowire dimer is also investigated and is closely related to the previous configuration. More physical insights are provided especially with respect to the invisibility dips appearing in the radiative spectrum. Numerical simulations have also been performed to confirm our analytical predictions and determine their range of validity. © 2011 American Chemical Society.
Motsclés: field enhancement; hybridization; invisibility dips; metal surface; nanoparticles; plasmonics; transformation optics; Field enhancement; hybridization; invisibility dips; metal surface; plasmonics; transformation optics; Dimers; Metal insulator boundaries; Nanoparticles; Nanowires; Plasmons; Resonance; Surface measurement; Metals


Electromagnetic contribution to surfaceenhanced Raman scattering from rough metal surfaces: A transformation optics approach Luo, Y., A. Aubry, and J. B. Pendry Physical Review B  Condensed Matter and Materials Physics 83, no. 15 (2011)
Résumé: The propagation of surface plasmons along rough metal surfaces is investigated with transformation optics. The roughness is modeled on a nanometer scale either by partly embedding a cylinder of metal into the surface (convex rough surface) or by excavating a cylindrical cavity from it (concave rough surface). These two structures can be treated analytically by means of conformal transformation. The interaction of surface plasmons with the singularities of these structures is shown to induce extreme field enhancements. These modes dominate the surfaceenhanced Ramanscattering response and enhancement factors of the order of 107 are predicted. Interestingly, concave rough surfaces are shown to be the best candidates for surfaceenhanced Raman scattering due to a stronger field enhancement and a lower sensitivity to the incident light polarization. Our analytical approach also points out the influence of the contact angle between the asperities and the metal surface on the bandwidth and the efficiency of the lightharvesting process. © 2011 American Physical Society.


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, 225233 (2011)
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; fe


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, 333363 (2010)
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


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


Experimental detection and focusing in shallow water by decomposition of the time reversal operator Prada, C., J. De Rosny, D. Clorennec, J.G. Minonzio, A. Aubry, M. Fink, L. Berniere, P. Billand, S. Hibral, and T. Folegot Journal of the Acoustical Society of America 122, no. 2, 761768 (2007)
Résumé: A rigid 24element sourcereceiver array in the 1015 kHz frequency band, connected to a programmable electronic system, was deployed in the Bay of Brest during spring 2005. In this 10 to 18m deep environment, backscattered data from submerged targets were recorded. Successful detection and focusing experiments in very shallow water using the decomposition of the time reversal operator (DORT method) are shown. The ability of the DORT method to separate the echo of a target from reverberation as well as the echo from two different targets at 250 m is shown. An example of active focusing within the waveguide using the first invariant of the time reversal operator is presented, showing the enhanced focusing capability. Furthermore, the localization of the scatterers in the water column is obtained using a rangedependent acoustic model. © 2007 Acoustical Society of America.
Motsclés: Backscattering; Data acquisition; Frequency bands; Signal receivers; Waveguide components; Acoustic model; Time reversal operator (DORT method); Water column; Water; article; decomposition; echolocation; electronics; frequency modulation; priority journal; receiver operating characteristic; sound detection; sound intensity; water content; Kinetics; Models, Theoretical; Sound; Sound Localization; Time; Water


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, 7077 (2007)
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


Gaussian beams and Legendre polynomials as invariants of the time reversal operator for a large rigid cylinder Aubry, A., J. De Rosny, J.G. Minonzio, C. Prada, and M. Fink Journal of the Acoustical Society of America 120, no. 5, 27462754 (2006)
Résumé: The DORT method (French acronym for decomposition of the time reversal operator) is an active remote sensing technique using an array of antennas for the detection and localization of scatterers. This method is based on the singular value decomposition of the interelement response matrix. In this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided. Depending on the array aperture, two asymptotic regimes are described. It is shown that the singular vectors correspond to HermiteGaussian modes for large apertures and Legendre polynomials for small ones. Using perturbation theory, the corresponding singular values are deduced. Theoretical predictions are in good agreement with experimental results. © 2006 Acoustical Society of America.
Motsclés: Acoustic fields; Antenna arrays; Polynomials; Remote sensing; Vectors; DORT method; Gaussian modes; Rigid cylinder; Singular value decomposition; Gaussian noise (electronic); acoustics; article; decomposition; mathematical analysis; mathematical computing; model; normal distribution; priority journal; remote sensing; technique; transducer


Multiple scattering between two elastic cylinders and invariants of the timereversal operator: Theory and experiment Minonzio, J.G., C. Prada, A. Aubry, and M. Fink Journal of the Acoustical Society of America 120, no. 2, 875883 (2006)
Résumé: The decompositionofthetimereversaloperator method is an ultrasonic method based on the analysis of the array response matrix used for detection and characterization. The eigenvalues and the eigenvectors of the timereversal operator (equivalent to the singular values and the singular vectors of the array response matrix) provide information on the localization and nature of scatterers in the insonified medium. Here, the eigenmodes of the timereversal operator are studied for two elastic cylinders: The effects of multiple scattering and anisotropic scattering are considered. Analytical expressions for the singular values are established within the isotropic scattering approximation. Then, the comparison with a complete model is presented, putting in evidence the importance of the anisotropy of the scattering. Experiments, carried out at central frequency 1.5 MHz on 0.25 mm diameter nylon and copper cylinders embedded in water, confirm the theory. In particular, the small cylinder limit and the effect of the dominant quadrupolar normal mode of nylon are discussed. © 2006 Acoustical Society of America.
Motsclés: Anisotropy; Approximation theory; Cylinders (shapes); Eigenvalues and eigenfunctions; Mathematical operators; Vectors; Elastic cylinders; Insonified medium; Isotropic scattering approximation; Quadrupolar normal mode; Acoustic wave scattering; acoustics; analytic method; anisotropy; article; decomposition; electromagnetic radiation; imaging system; model; priority journal; sound transmission; stimulus response; theory; ultrasound

