Reflection Measurement of the Scattering Mean Free Path at the Onset of Multiple Scattering.

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 ℓ_{s} that provides crucial information on the medium microarchitecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate.

Weight of single and recurrent scattering in the reflection matrix of complex media.

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.

Evaluation of a multiple scattering filter to enhance defect detection in heterogeneous media.

Ultrasonic evaluation of coarse-grain 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 nickel-based alloy with coarse-grain structure.

Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.

Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r.

Anderson Mobility Gap Probed by Dynamic Coherent Backscattering.

We use dynamic coherent backscattering to study one of the Anderson mobility gaps in the vibrational spectrum of strongly disordered three-dimensional mesoglasses. Comparison of experimental results with the self-consistent theory of localization allows us to estimate the localization (correlation) length as a function of frequency in a wide spectral range covering bands of diffuse transport and a mobility gap delimited by two mobility edges. The results are corroborated by transmission measurements on one of our samples.

Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms.

In this paper, ultrasound measurements of 1:1 scale three-dimensional (3D) printed trabecular bone phantoms are reported. The micro-structure of a trabecular horse bone sample was obtained via synchrotron x-ray microtomography, converted to a 3D binary data set, and successfully 3D-printed at scale 1:1. Ultrasound through-transmission experiments were also performed through a highly anisotropic version of this structure, obtained by elongating the digitized structure prior to 3D printing.

Scattering mean free path in continuous complex media: beyond the Helmholtz equation.

We present theoretical calculations of the ensemble-averaged (or effective or coherent) wave field propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that heterogeneity can be accounted for by a random scalar function of the space coordinates, termed the potential. Physically, this amounts to replacing the constant wave speed in Helmholtz' equation by a space-dependent speed.

Measurements of ultrasonic diffusivity and transport speed from coda waves in a resonant multiple scattering medium.

Frequency-resolved experimental measurements of ultrasonic diffusivity in the MHz range are presented. The samples under study are two-dimensional random arrangements of parallel steel rods immersed in water and exhibit high-order multiple scattering. Their physical characteristics, particularly the density and pair-correlation functions of the scatterers, are well controlled.

Full transmission and reflection of waves propagating through a maze of disorder.

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.

Recurrent scattering and memory effect at the Anderson localization transition.

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.

Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot's and multiple scattering models.

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations.

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment.

Comparison between experimental and 2-D numerical studies of multiple scattering in Inconel600 by means of array probes.

Ultrasonic non-destructive testing of polycrystalline structures can be disturbed by scattering at grain boundaries. Understanding and modeling this so-called "structural noise" is crucial for characterization as well as detection purposes. Structural noise can be considered as a fingerprint of the material under investigation, since it contains information about its microstructure.

Simulations of ultrasound propagation in random arrangements of elliptic scatterers: occurrence of two longitudinal waves.

Ultrasound propagation in clusters of elliptic (two-dimensional) or ellipsoidal (three-dimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering.

Multiple scattering of ultrasound in weakly inhomogeneous media: application to human soft tissues.

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 setup uses an array of sources/receivers placed in front of the medium.

Random matrix theory applied to acoustic backscattering and imaging in complex media.

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.

Temperature-dependent diffusing acoustic wave spectroscopy with resonant scatterers.

The influence of a slight temperature change on the correlation of multiply scattered acoustic waves is studied, and experimental results are discussed. The technique presented here, similar to diffusing-acoustic-wave spectroscopy, is based on the sensitivity of a multiply scattering medium to a slight change. Ultrasonic waves around 3 MHz are transmitted through a sample made of steel rods in water and recorded by an array of transducers at different temperatures.

Ultrasonic imaging of highly scattering media from local measurements of the diffusion constant: separation of coherent and incoherent intensities.

As classical imaging fails with diffusive media, one way to image a multiple-scattering 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 multiple-scattering medium. The experimental setup consists in an array of programmable transducers placed in front of the multiple-scattering medium to be imaged.

Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium.

Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the mean-free path deviates from the classical first-order approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements.

Passive retrieval of Rayleigh waves in disordered elastic media.

When averaged over sources or disorder, cross correlation of diffuse fields yields the Green's function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earth's crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab.

Weak localization and time reversal of ultrasound in a rotational flow.

A one-channel time-reversal (TR) experiment is performed inside a rough reverberating cavity in the presence of a rotational flow. The amplitude of the TR wave is plotted versus the distance between the TR channel and the initial source: when they coincide, it exhibits a "time-reversal enhancement" (TRE). With no flow, the TRE is the same as the coherent backscattering enhancement (CBE).

Relation between time reversal focusing and coherent backscattering in multiple scattering media: a diagrammatic approach.

In this paper, we revisit one-channel time reversal (TR) experiments through multiple scattering media in the framework of the multiple scattering theory. The hyperresolution and the self-averaging property are retrieved. The developed formalism leads to a deeper understanding of the role of the ladder and most-crossed diagrams in a TR experiment and also establishes the link between TR and coherent backscattering (CBS).

Time reversal of electromagnetic waves.

We report the first experimental demonstration of time-reversal focusing with electromagnetic waves. An antenna transmits a 1-micros electromagnetic pulse at a central frequency of 2.45 GHz in a high-Q cavity.

Taking advantage of multiple scattering to communicate with time-reversal antennas.

We present an experimental demonstration showing that, contrary to first intuition, the more scattering a mesoscopic medium is, the more information can be conveyed through it. We used a multiple input-multiple output configuration: a multichannel ultrasonic time-reversal antenna is used to transmit random series of bits simultaneously to different receivers which were only a few wavelengths apart. Whereas the transmission is free of error when multiple scattering occurs in the propagation medium, the error rate is huge in a homogeneous medium.