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Transcranial ultrasound imaging is usually limited by skull-induced attenuation and high-order aberrations. By using contrast agents such as microbubbles in combination with ultrafast imaging, not only can the signal-to-noise ratio be improved, but super-resolution images down to the micrometer scale of the brain vessels can be obtained. However, ultrasound localization microscopy (ULM) remains impacted by wave-front distortions that limit the microbubble detection rate and hamper their localization. In this work, we show how matrix imaging, which relies on the prior recording of the reflection matrix, can provide a solution to those fundamental issues. As an experimental proof-of-concept, an in-vivo reconstruction of deep brain microvessels is performed on three anesthetized sheeps. The compensation of wave distortions is shown to drastically enhance the contrast and resolution of ULM. This experimental study thus opens up promising perspectives for a transcranial and non-ionizing observation of human cerebral microvascular pathologies, such as stroke., Comment: 43 pages, 11 figures, 3 tables

High-resolution label-free imaging of oocytes and embryos is essential for in vitro fertilization procedures. Yet conventional microscopy fails in this task because of aberrations and multiple scattering induced by refractive index heterogeneities inside the sample. These detrimental phenomena drastically degrade the images of early embryos particularly in depth. To overcome these fundamental problems without sacrificing the frame rate, optical matrix imaging (OMI) is a suitable tool. Relying on an ultra-fast measurement of the reflection matrix associated with the sample, it can compensate for aberration and forward multiple scattering in post-processing, thereby providing three-dimensional and highly contrasted images of embryos at a confocal resolution. As a first proof-of-concept, bovine oocytes and embryos are imaged at a 300 nm resolution almost in real time. Our system enables visualization of intracellular structures such as lipids and mitochondria in the cytoplasm or the zona pellucida surrounding it. Altogether, we demonstrate that OMI is a promising tool for research in developmental biology and for time-lapse monitoring of oocytes and embryos in assisted reproduction., Comment: 18 pages, 6 figures

Besides controlling wave trajectory inside complex media, wave velocity constitutes a relevant bio-marker for medical imaging. In a transmission configuration, wave-front distortions can be unscrambled to provide a map of the wave velocity landscape $c(\mathbf{r})$. However, most in-vivo applications correspond to a reflection configuration for which only back-scattered echoes generated by short-scale fluctuations of $c(\mathbf{r})$ can be harvested. Under a single scattering assumption, this speckle wave-field cannot provide the long-scale variations of $c(\mathbf{r})$. In this paper, we go beyond the first Born approximation and show how a map of $c(\mathbf{r})$ can be retrieved in epi-detection. To that aim, a reflection matrix approach of wave imaging is adopted. While standard reflection imaging methods generally rely on confocal focusing operations, matrix imaging consists in decoupling the location of the incident and received focal spots. Following this principle, a self-portrait of the focusing process can be obtained around each point of the medium. The Gouy phase shift exhibited by each focal spot is leveraged to finely monitor the wave velocity distribution $c(\mathbf{r})$ inside the medium. Experiment in a tissue-mimicking phantom and numerical simulations are first presented to validate our method. Speed-of-sound tomography is then applied to ultrasound data collected on the liver of a difficult-to-image patient. Beyond paving the way towards quantitative ultrasound, our approach can also be extremely rewarding for standard imaging. Indeed, each echo can be assigned to the actual position of a scatterer. It allows an absolute measurement of distance, an observable often used for diagnosis but generally extremely sensitive to wave velocity fluctuations., Comment: 45 pages, 9 figures, 3 tables

Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path $\ell_s$ that provides crucial information on the medium micro-architecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate. Our method is first validated by an ultrasound experiment on a tissue-mimicking phantom before being applied in-vivo to a human liver. This study opens important perspectives for quantitative imaging of heterogeneous media with waves, whether it be for non-destructive testing, biomedical or geophysical applications., Comment: 29 pages, 7 figures

In geophysics, volcanoes are particularly difficult to image because of the multi-scale heterogeneities of fluids and rocks that compose them and their complex non-linear dynamics. By exploiting seismic noise recorded by a sparse array of geophones, we are able to reveal the magmatic and hydrothermal plumbing system of La Soufri\`ere volcano in Guadeloupe. Spatio-temporal cross-correlation of seismic noise actually provides the impulse responses between virtual geophones located inside the volcano. The resulting reflection matrix can be exploited to numerically perform an auto-focus of seismic waves on any reflector of the underground. An unprecedented view on the volcano's inner structure is obtained at a half-wavelength resolution. This innovative observable provides fundamental information for the conceptual modeling and high-resolution monitoring of volcanoes., Comment: 32 pages, 9 figures

Label-free microscopy exploits light scattering to obtain a three-dimensional image of biological tissues. However, light propagation is affected by aberrations and multiple scattering, which drastically degrade the image quality and limit the penetration depth. Multi-conjugate adaptive optics and time-gated matrix approaches have been developed to compensate for aberrations but the associated frame rate is extremely limited for 3D imaging. Here we develop a multi-spectral matrix approach to solve these fundamental problems. Based on a sparse illumination scheme and an interferometric measurement of the reflected wave-field at multiple wavelengths, the focusing process can be optimized in post-processing for any voxel by addressing independently each frequency component of the reflection matrix. A proof-of-concept experiment demonstrates the three-dimensional image of an opaque human cornea over a 0.1 mm$^3$-field-of-view at a 290 nm-resolution and a 1 Hz-frame rate. This work paves the way towards a fully-digital microscope allowing real-time, in-vivo, quantitative and deep inspection of tissues., Comment: 55 pages, 9 figures

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 tissue-mimicking phantom through ex-vivo tissues and then, show the potential of 3D matrix imaging for transcranial applications., Comment: 60 pages, 14 figures

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 cross-correlation 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: (i) determine the transmission matrix between the Earth's surface and any point in the subsurface; (ii) 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 (DANA) 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 NAFZ 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., Comment: 44 pages, 9 figures

As light travels through a disordered medium such as biological tissues, it undergoes multiple scattering events. This phenomenon is detrimental to in-depth 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 de-scanned measurement of a high-dimension 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 multi-scale analysis of wave distortions contained in R. It enables an optimal and local compensation of forward multiple scattering paths and provides a three-dimensional confocal image of the sample as the latter one had become digitally transparent. The proof-of-concept experiment is performed on a human opaque cornea and an extension of the penetration depth by a factor five is demonstrated compared to the state-of-the-art., Comment: 78 pages, 29 figures, 1 table

In a heterogeneous medium, the wavefield 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 field components. 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 back-scattering configuration, this assumption is valid for small depths, and begins to fail for depths larger than the scattering mean-free path $\ell_s$. It is therefore a key issue to estimate the relative amount of single and multiple scattering in experimental data. To this end, a single scattering estimator $\hat{\rho}$ computed from the reflection matrix has been introduced in order to assess the weight of single scattering in the backscattered wavefield. In this article, the meaning of this estimator is investigated and a particular attention is given to recurrent scattering. In a diffraction-limited 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 $\hat{\rho}$ 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., Comment: 17 pages, 11 figures

The last decade has seen the development of a wide set of tools, such as wavefront shaping, computational or fundamental methods, that allow 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 on this field, that has revolutionized the prospect of diffraction-limited imaging at depth in tissues. This roadmap highlights several key aspects of this fast developing field, and some of the challenges and opportunities ahead., Comment: submitted to J.Phys Photonics (IOP), 116 pages, 23 sections

We report on anomalous light transport in the strong scattering regime. Using low-coherence interferometry, we measure the reflection matrix of titanium dioxide powders, revealing crucial features of strong optical scattering which can not 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 near-field coupling between scatterers prohibits Anderson localization of light in three-dimensional disordered media., Comment: 13 pages, 7 figures

In the paper, we succeeded to freeze-dry monodisperse microbubbles without degrading their size and acoustic properties. We used microfluidic technology to generate highly monodisperse (coefficient of variation, CV<5%) microbubbles and optimized their formulation along with a cryoprotectant. By using a specific technique of retrieval of the bubble, we showed that freeze-drying the microbubbles does not alter their size distribution. To compare the fundamental resonance properties of the bubbles, we performed backscattered acoustic characterization measurements. Our experimental results revealed that the freeze-drying process conserved the acoustic properties of the bubbles. The maximum backscattering power amplitude of fresh and freeze-dried monodisperse PVA bubbles was around ten eight times higher than that of SonoVue at a similar concentration in vitro. By solving the question of storage and transportation of monodisperse bubbles, our work facilitates their penetration in the domain of UCAs, for performing new tasks and developing novel non-invasive measurements, such as pressure, unaccessible to the existing commercialized bubbles., Comment: Preprint submitted to Ultrasound in Medicine and Biology. Preprint consists of 14 pages and 5 figures. Ugur Soysal and Pedro N. Azevedo contributed equally to the work. Corresponding author: email ugur.soysal@espci.fr

Fault zones are associated with multi-scale 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 small-scale 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 cross-correlations was extended with the introduction of aberration corrections to handle the actual lateral velocity variations in the fault zone [Touma et al., Geophys. J. Int. 226, 780-794, 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 intensity of scatterers of seismic waves starting with a simple homogeneous background velocity model of the medium. The derived three-dimensional 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., Comment: 15 pages, 8 figures

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 speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals tosynthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called 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 high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo 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., Comment: 20 pages, 11 figures

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 so-called focused reflection matrix that actually contains much more information than a confocal ultrasound image. In this paper, a time-frequency 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 input-output 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 state-of-the-art 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 proof-of-concept based on time-domain simulations, UMI is applied to the in-vivo study of a human calf. Beyond this specific example, UMI opens a new route for speed-of-sound and scattering quantification in ultrasound imaging., Comment: 15 pages, 7 figures

We report on experimental and numerical implementations of devices based on the negative refraction of elastic guided waves, the so-called 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 anti-object 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 wave-field. 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 wave-field is then possible from an object plane to a far-field imaging plane. Twenty years after Pendry's initial proposal, this work thus paves the way towards an elastic superlens., Comment: 16 pages, 9 figures

We report on a theoretical model for image formation in full-field 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 time-gated 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 \rev{computational tools} for high-resolution and deep imaging of biological tissues., Comment: 23 pages, 10 figures

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 three-dimensional image of the subsoil, despite a rough knowledge of the background wave velocity. To do so, passive noise cross-correlations between geophones of a seismic array are investigated under a matrix formalism. More precisely, 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 seismic data recorded along the Clark branch of the San Jacinto fault zone, the present method is shown to provide an image of the fault until a depth of 4 km with a transverse 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 wave guide which increase drastically the array aperture., Comment: 24 pages, 12 figures

Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wavefronts 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 full-field 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 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 sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a full-field image of the medium with diffraction-limited 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 tissue mimicking 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., Comment: 24 pages, 11 figures

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 multi-element technology is available. The concept is that focused beamforming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The inter-element 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) an 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., Comment: 18 pages, 6 figures

In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. Based on a dynamic correction of the incident and/or reflected wave-fronts, adaptive optics has been employed to compensate for those aberrations. However, it only applies to spatially-invariant aberrations or to thin aberrating layers. Here, we propose a global and non-invasive approach based on the distortion matrix concept. This matrix basically connects any focusing point of the image with the distorted part of its wave-front in reflection. A singular value decomposition of the distortion matrix allows to correct for high-order aberrations and forward multiple scattering over multiple isoplanatic modes. Proof-of-concept experiments are performed through biological tissues including a turbid cornea. We demonstrate a Strehl ratio enhancement up to 2500 and recover a diffraction-limited resolution until a depth of ten scattering mean free paths., Comment: 61 pages, 10 figures, 2 tables

Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single scattering assumption. In heterogeneous areas such as volcanoes, the multiple scattering contribution limits the imaging-depth 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 chimney-shaped structure at shallow depths, a magma reservoir at 2500 m and several cavities at sea level and below it. The matrix approach paves the way towards 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 in-depth imaging of the Earth's crust., Comment: 14 pages, 7 figures

This paper provides a theoretical investigation of negative refraction and focusing of elastic guided waves in a free-standing plate with a step-like 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 semi-analytical model is developed in order to study the influence of various parameters such as the material Poisson's coefficient, the step-like thickness, the frequency and the incidence angle. To this end, all the Lamb and shear horizontal propagating modes, but also a large number of their inhomogeneous and evanescent counterpart,s are taken into account. The boundary conditions applied to the stress-displacement fields at the thickness step yields an equation system. Its inversion provides the transmission and reflection coefficients between each mode at the interface. The step-like 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. Theoretical results are confirmed by a numerical FDTD simulation and experimental measurements made on an optimized Duralumin flat lens by means of laser interferometry. This theoretical study paves the way towards the optimization of elastic devices based on negative refraction, in particular for cloaking or super-focusing purposes., Comment: 8 pages, 6 figures

The propagation of waves in complex media can be harnessed either by taming the incident wave-field 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 super-focusing 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 zero-gap 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., Comment: 9 pages, 6 figures

Optical microscopy offers a unique insight of biological structures with a sub-micrometer 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 single-to-multiple 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., Comment: 18 pages, 7 figures

Imaging the propagation of light in time and space is crucial in optics, notably for the study of complex media. We here demonstrate the passive measurement of time-dependent Green's functions between every point at the surface of a strongly scattering medium by means of low coherence interferometry. The experimental access to this Green's matrix is essential since it contains all the information about the complex trajectories of light within the medium. In particular, the spatio-temporal spreading of the diffusive halo and the coherent backscattering effect can be locally investigated in the vicinity of each point acting as a virtual source. On the one hand, this approach allows a quantitative imaging of the diffusion constant in the scattering medium with a spatial resolution of the order of a few transport mean free paths. On the other hand, our approach is able to reveal and quantify the anisotropy of light diffusion, which can be of great interest for optical characterization purposes. This study opens important perspectives both in optical diffuse tomography with potential applications to biomedical imaging and in fundamental physics for the experimental investigation of Anderson localization., Comment: 11 pages, 8 figures

The paper studies the interaction of Lamb waves with the free edge of a plate. The reflection coefficients of a Lamb mode at a plate free edge are calculated using a semi-analytical method, as a function of frequency and angle of incidence. The conversion between forward and backward Lamb modes is thoroughly investigated. It is shown that, at the zero-group velocity (ZGV) frequency, the forward $S_1$ Lamb mode fully converts into the backward $S_{2b}$ Lamb mode at normal incidence. Besides, this conversion is very efficient over most of the angular spectrum and remains dominant at frequencies just above the ZGV-point. This effect is observed experimentally on a Duralumin plate. Firstly, the $S_1$ Lamb mode is selectively generated using a transducer array, secondly the $S_{2b}$ mode is excited using a single circular transducer. The normal displacement field is probed with an interferometer. The free edge is shown to retro-focus the incident wave at different depths depending on the wave number mismatch between the forward and backward propagating modes. In the vicinity of the ZGV-point, wave numbers coincide and the wave is retro-reflected on the source. In this frequency range, the free edge acts as a perfect phase conjugating mirror., Comment: 12 pages, 10 figures

A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes. Controlling wave propagation through complex systems is thus of fundamental interest in many areas, ranging from optics or acoustics to medical imaging or telecommunications. Here, we study the propagation of elastic waves in a cavity and a disordered waveguide by means of laser interferometry. From the direct experimental access to the time-delay matrix of these systems, we demonstrate the existence of particle-like wave packets that remain focused in time and space throughout their complex trajectory. Due to their limited dispersion, their selective excitation will be crucially relevant for all applications involving selective wave focusing and efficient information transfer through complex media., Comment: 12 pages, 9 figures

Multiple scattering of waves in disordered media is a nightmare whether it be for detection or imaging purposes. The best approach so far to get rid of multiple scattering is optical coherence tomography. It basically combines confocal microscopy and coherence time-gating to discriminate ballistic photons from a predominant multiple scattering background. Nevertheless, the imaging depth range remains limited to 1 mm at best in human soft tissues. Here we propose a matrix approach of optical imaging to push back this fundamental limit. By combining a matrix discrimination of ballistic waves and iterative time-reversal, we show both theoretically and experimentally an extension of the imaging-depth limit by at least a factor two compared to optical coherence tomography. In particular, the reported experiment demonstrates imaging through a strongly scattering layer from which only one reflected photon over 1000 billion is ballistic. This approach opens a new route towards ultra-deep tissue imaging., Comment: 14 pages, 9 figures

We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence 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., Comment: 5 pages, 4 figures

We report on ultrasonic imaging in a random heterogeneous medium. The goal is to detect flaws embedded deeply into a polycrystalline material. A 64-element array of piezoelectric transmitters/receivers at a central frequency of 5 MHz is used to capture the Green's matrix in a backscattering configuration. Because of multiple scattering, conventional imaging completely fails to detect the deepest flaws. We utilize a random matrix approach, taking advantage of the deterministic coherence of the backscattered wave-field which is characteristic of single scattering and related to the memory effect. This allows us to separate single and multiple scattering contributions. As a consequence, we show that flaws are detected beyond the conventional limit, as if multiple scattering had been overcome., Comment: 11 pages, 4 figures

Thirty years ago, theorists showed that a properly designed combination of incident waves could be fully transmitted through (or reflected by) a disordered medium, based on the existence of propagation channels which are essentially either closed or open (bimodal law). In this Letter, we study elastic waves in a disordered waveguide and present direct experimental evidence of the bimodal law. Full transmission and reflection are achieved. The wave field is monitored by laser interferometry and highlights the interference effects that take place within the scattering medium., Comment: 5 pages, 3 figures

We report on ultrasonic measurements of the propagation operator in a strongly scattering mesoglass. The backscattered field is shown to display a deterministic spatial coherence due to a remarkably large memory effect induced by long recurrent trajectories. Investigation of the recurrent scattering contribution directly yields the probability for a wave to come back close to its starting spot. The decay of this quantity with time is shown to change dramatically near the Anderson localization transition. The singular value decomposition of the propagation operator reveals the dominance of very intense recurrent scattering paths near the mobility edge., Comment: 5 pages, 4 figures

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 DORT method (Decomposition of the Time Reversal 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., Comment: 10 pages

Waves scattered by a weakly inhomogeneous random medium contain a predominant single scattering contribution as well as a multiple scattering contribution which is usually neglected, especially for imaging purposes. A method based on random matrix theory is proposed to separate the single and multiple scattering contributions. The experimental set up 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. Single-scattering 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 multiple-scattered waves. This allows one to evaluate the absorption losses and the scattering losses separately, by comparing the multiple scattering 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 MHz range, on a synthetic sample (agar-gelatine gel) as well as on breast tissues. Interestingly, the multiple scattering contribution is found to be far from negligible in the breast around 4.3 MHz., Comment: 35 pages, 11 figures, final version, contains the appendix of the original article

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 set up 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 wide-band ultrasonic waves around 3 MHz. A 125-element array is placed in front of a collection of randomly distributed steel rods (diameter 0.8mm). The slab thickness is three times the scattering mean free path. The target is a larger steel cylinder (diameter 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 an heterogeneous layer., Comment: 48 pages, 18 figures, corrected typos, v2

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 short-time Fourier analysis. The mean distribution of singular values exhibits very different behaviours 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., Comment: 41 pages, 10 figures, definitive version