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

Experimental evidence of isotropic transparency and complete band gap formation for ultrasound propagation in stealthy hyperuniform media

Following on recent experimental characterization of the transport properties of stealthy hyperuniform media for electromagnetic and acoustic waves, we report here measurements at ultrasonic frequencies of the multiple scattering of waves by 2D hyperuniform distributions of steel rods immersed in water. The transparency, for which the effective attenuation of the medium is canceled, is first evidenced by measuring the transmission of a plane wave propagating in a highly correlated and relatively dense medium. It is shown that a band gap occurs in the vicinity of the first Bragg frequency. The isotropy of both transparency and band gap are also evidenced for the case of waves generated by a point source in differently ordered and circular-shaped distributions. In other words, we thus obtain a representation of the Green's function. Our results demonstrate the huge potential of hyperuniform, as well as highly correlated, media for the design of functional materials.

Time reversal of long coda waves: Experiments in the nonlinear regime

A problem that arises when the time-reversal process is applied in a nonlinear regime is related to the generation of harmonics: conventional piezoelectric transducers cannot work properly at the frequency of the second harmonic. Then, the time-reversed wave cannot be completely emitted. Few works provide a solution to this issue. Thus, we study the alternative of performing a cross correlation of the wavefield. In a linear regime, this procedure is an accurate method for estimating real time-reversal properties. To study both procedures in the nonlinear regime in detail, we measure the wavefield of a wave that (1) traverses a multiple scattering medium, composed by a random set of parallel copper rods and (2) propagates inside a reverberant cavity, consisting of an aluminum case immersed in water. Cross correlation yields a virtually focused wavefield, where the focal width at the frequency of the first, second, and third harmonics can be measured. We compare these values with those obtained in a real time-reversal experiment. Results suggest that both time-reversal procedures are equivalent. In addition, we discuss the possibility of amplitude estimation at the focal spot and the limits of this work based on a theoretical model.

Ultrasound Scattering in Cortical Bone

Recent advances in imaging of bone microstructure have led to a growing recognition of the role of cortical microstructure in osteoporosis. It is now accepted that the assessment of the microstructure of cortical porosity is essential to assess bone mechanical competence and predict fracture risk. Cortical porosity affects the propagation of ultrasound waves because pores act as ultrasound scatterers. Scattering by the porosity is an opportunity that should be leveraged to extract quantitative information about cortical microstructure. Scattering by the pores affects a number of ultrasound parameters that should be quantified, including attenuation, backscatter coefficient, ultrasound diffusivity, and their frequency dependence. Measuring these ultrasound parameters and developing models that describe their dependence upon parameters of cortical microstructure is the key to solve inverse problems that will allow the quantitative assessment of cortical porosity and ultimately will improve the non-invasive ultrasound-based evaluation of bone mechanical competence and fracture risk. In this chapter, we present recent advances in measuring and modeling those parameters in cortical bone.

Propagation of scalar waves in dense disordered media exhibiting short- and long-range correlations

Correlated disorder is at the heart of numerous challenging problematics in physics. In this work we focus on the propagation of acoustic coherent waves in two-dimensional dense disordered media exhibiting long- and short-range structural correlations. The media are obtained by inserting elastic cylinders randomly in a stealth hyperuniform medium itself made up of cylinders. The properties of the coherent wave is studied using an original numerical software. In order to understand and discuss the complex physical phenomena occurring in the different media, we also make use of effective media models derived from the quasicrystalline approximation and the theory of Fikioris and Waterman that provides an explicit expression of the effective wave numbers. Our study shows a very good agreement between numerical and homogenization models up to very high concentrations of scatterers. This study shows that media with both short- and long-range correlations are of strong interest to design materials with original properties.

Impact of particle size and multiple scattering on the propagation of waves in stealthy-hyperuniform media

Propagation of waves in materials that exhibit stealthy-hyperuniform long-range correlations is investigated. By using a modal decomposition of the field that takes multiple scattering into account at all orders, we study the impact of the concentration of particles on the transparency of such materials at low frequency. An upper frequency limit for transparency is defined that include both the particle size and the degree of stealthiness. We show that the independent scattering approximation is not relevant to calculate elastic mean free paths when wavelength becomes comparable to the size of particles. We find that transparency is very robust with regard to the degree of heterogeneity of the host random medium and the polydispersity of particles. Finally, it is shown that resonances can be used as the frequency filter.

Acoustic density estimation of dense fish shoals

Multiple scattering of acoustic waves offers a noninvasive method for density estimation of a dense shoal of fish where traditional techniques such as echo-counting or echo-integration fail. Through acoustic experiments with a multi-beam sonar system in open sea cages, multiple scattering of sound in a fish shoal, and, in particular, the coherent backscattering effect, can be observed and interpreted quantitatively. Furthermore, a volumetric scan of the fish shoal allows isolation of a few individual fish from which target strength estimations are possible. The combination of those two methods allows for fish density estimation in the challenging case of dense shoals.

Quantitative assessment of media concentration using the Homodyned K distribution

The Homodyned K distribution has been used successfully as a tool in the ultrasound characterization of sparse media, where the scatterer clustering parameter α accurately discriminates between media with different numbers of scatterers per resolution cell. However, as the number of scatterers increases and the corresponding amplitude statistics become Rician, the reliability of the α estimates decreases rapidly. In the present study, we assess the usefulness of α for the characterization of both sparse and concentrated media, using simulated independent and identically distributed (i.i.d.) samples from Homodyned K distributions, ultrasound images of media with up to 68 scatterers per resolution cell and ultrasound signals acquired from particle phantoms with up to 101 scatterers per resolution cell. All parameter estimates are obtained using the XU estimator (Destrempes et al., 2013). Results suggest that the parameter α can be used to distinguish between media with up to 40 scatterers per resolution cell at 22 MHz, provided that parameter estimation can be performed on very large sample sizes (i.e., >10,000 i.i.d. samples).

Influence of the microstructure of two-dimensional random heterogeneous media on propagation of acoustic coherent waves

Multiple scattering of waves arises in all fields of physics in either periodic or random media. For random media the organization of the microstructure (uniform or nonuniform statistical distribution of scatterers) has effects on the propagation of coherent waves. Using a recent exact resolution method and different homogenization theories, the effects of the microstructure on the effective wave number are investigated over a large frequency range (ka between 0.1 and 13.4) and high concentrations. For uniform random media, increasing the configurational constraint makes the media more transparent for low frequencies and less for high frequencies. As a side but important result, we show that two of the homogenization models considered here appear to be very efficient at high frequency up to a concentration of 60% in the case of uniform media. For nonuniform media, for which clustered and periodic aggregates appear, the main effect is to reduce the magnitude of resonances and to make network effects appear. In this case, homogenization theories are not relevant to make a detailed analysis.

Low frequency propagation through random polydisperse assemblies of cylindrical or spherical poroelastic obstacles

The effective wavenumbers, moduli, and mass densities are found for polydisperse assemblies of poroelastic obstacles (considering fluid flow and solid deformation in the porous medium). The obstacles are infinite length cylinders and spheres. To achieve this, recent formulas for the effective wavenumbers, given by Linton and Martin [SIAM J. Appl. Math. 66(5), 1649-1668 (2006)] and Norris and Conoir [J. Acoust. Soc. Am. 129(1), 104-113 (2011)] in the dilute monodisperse case (obstacles of identical sizes in a fluid matrix), have been modified. Given the uncertainty in predicting the distribution in size of the obstacles, three quite different probability density functions are studied and compared: uniform, Schulz, and lognormal. Specifically, the Rayleigh approximation (low frequency regime) is considered, in which the wavelengths can be assumed very large compared to the size of the obstacles. Within this limit, simplified formulas are provided for the concentrations depending on the parameter characterizing the size dispersion.

Modeling ultrasound attenuation in porous structures with mono-disperse random pore distributions using the independent scattering approximation: a 2D simulation study

The validity of the independent scattering approximation (ISA) to predict the frequency dependent attenuation in 2D models of simplified structures of cortical bone is studied. Attenuation of plane waves at central frequencies ranging from 1 to 8 MHz propagating in structures with mono-disperse random pore distributions with pore diameter and pore density in the range of those of cortical bone are evaluated by finite difference time domain numerical simulations. An approach to assess the multiple scattering of waves in random media is discussed to determine the pore diameter ranges at which the ISA is applicable. A modified version of the ISA is proposed to more accurately predict the attenuation in porosity ranges where it would traditionally fail. The results show that the modified ISA can model the frequency-dependent attenuation of ultrasonic wave with pore diameter and density ranges comparable to those of cortical bone.

Numerical simulation of two-dimensional multiple scattering of sound by a large number of circular cylinders

The purpose of this article is to present an innovative resolution method for investigating problems of sound scattering by infinite cylinders immersed in a fluid medium. The study is based on the analytical solution of multiple scattering, where incident and scattered waves are expressed in cylindrical harmonics. This modeling leads to dense linear systems, which are made sparse by introducing a cutoff radius around each particle. This cutoff radius is deeply studied and quantified. Numerical resolution is performed using parallel computing methods designed to solve very large sparse linear systems. Comparisons with direct calculations made with another numerical software and homogenization techniques follow and show good agreement with the implemented method. The last part is dedicated to a comparison between the propagation of waves in a circular cluster made of a random distribution of cylinders and the propagation in the corresponding homogenized cluster where the multiple scattering formalism is combined with a statistical analysis to provide an effective medium.

Bubbly flow velocity measurement in multiple scattering regime

We propose a technique to measure the velocity of a bubble cloud based on the coda correlation. The method is founded on successive recordings of multiple scattered waves from a bubble cloud. Our model predicts the dependence between the correlation coefficient of these coda waves and the velocity of the bubble cloud under diffusion approximation. The Acoustic experiments are validated by simultaneous optical measurements in a water tank, with a good agreement between the acoustical and the optical methods (relative difference smaller than 7%). This technique can be transposed to any particle flow velocity problems involving multiple scattering effects in acoustics.

Influence of bubble distributions on the propagation of linear waves in polydisperse bubbly liquids

The influence of the spatial distributions of bubbles on the propagation of linear acoustic waves in polydisperse bubbly liquids is studied. Using the diagrammatic approach, the effective wavenumber, which includes both spatial information and higher orders of multiple scattering, is presented. The phase speed and attenuation coefficient of acoustic waves in bubbly liquids are calculated from the effective wavenumber. A three-dimensional random model, the Generalized Matérn's hard-core point process, is used to close the model. Numerical simulations reveal that as the bubble volume fraction becomes larger so does the effect of the bubble distributions on the attenuation and phase speed. The irregular discrepancy between previously reported experimental results and the classical theory is attributed to the influence of bubble clustering on the propagation of linear waves. The comparison between the present model and the experimental measurements [Leroy, Strybulevych, Page, and Scanlon. (2011). Phys. Rev. E 83, 046605] reveals that the proposed correction term significantly improves the theoretical predictions.

Multiple scattering of an ultrasonic shock wave in bubbly media

This experimental study deals with the propagation of an ultrasonic shock wave in a random heterogeneous medium, constituted of identical 75μm radius bubbles, trapped in a yield-stress fluid. The fundamental frequency of the incident wave (in the MHz range) was much larger than the resonance frequency of bubbles (38kHz). A well-expanded coda, resulting from the multiple scattering of the incident shock wave through the heterogeneous medium, was experimentally measured in transmission. Despite the significant amplitude of the shock wave (90kPa), no sign of nonlinear response of the bubbles was detected. Both the coherent and incoherent fields were successfully described by linear theories. Using a shock wave presents the advantage of characterizing the medium over a large frequency range (1.5-15MHz).

Sound propagation over the ground with a random spatially-varying surface admittance

Sound propagation over the ground with a random spatially-varying surface admittance is investigated. Starting from the Green's theorem, a Dyson equation is derived for the coherent acoustic pressure. Under the Bourret approximation, an explicit expression is deduced and an effective admittance that depends on the correlation function of the admittance fluctuations is exhibited. An asymptotic expression at long range is then obtained. Influence of the randomness on the amplitude of the reflection coefficient and on the wavenumbers of the surface wave component is analyzed. Afterwards, numerical simulations of the linearized Euler equations are carried out and the coherent pressure obtained by an ensemble-averaging over 200 realizations of the admittance is found to be in good agreement with the analytical solution. In the considered examples of grounds, the mean intensity is shown to be similar to the intensity in the non-random case, except near interferences that are smoothened out due to randomness. It is however exemplified that the intensity fluctuations can be large, especially near destructive interferences.

Photoacoustic imaging in scattering media by combining a correlation matrix filter with a time reversal operator

Acoustic scattering medium is a fundamental challenge for photoacoustic imaging. In this study, we reveal the different coherent properties of the scattering photoacoustic waves and the direct photoacoustic waves in a matrix form. Direct waves show a particular coherence on the antidiagonals of the matrix, whereas scattering waves do not. Based on this property, a correlation matrix filter combining with a time reversal operator is proposed to preserve the direct waves and recover the image behind a scattering layer. Both numerical simulations and photoacoustic imaging experiments demonstrate that the proposed approach effectively increases the image contrast and decreases the background speckles in a scattering medium. This study might improve the quality of photoacoustic imaging in an acoustic scattering environment and extend its applications.

A semi-analytical model of a time reversal cavity for high-amplitude focused ultrasound applications

Time reversal cavities (TRC) have been proposed as an efficient approach for 3D ultrasound therapy. They allow the precise spatio-temporal focusing of high-power ultrasound pulses within a large region of interest with a low number of transducers. Leaky TRCs are usually built by placing a multiple scattering medium, such as a random rod forest, in a reverberating cavity, and the final peak pressure gain of the device only depends on the temporal length of its impulse response. Such multiple scattering in a reverberating cavity is a complex phenomenon, and optimisation of the device's gain is usually a cumbersome process, mostly empirical, and requiring numerical simulations with extremely long computation times. In this paper, we present a semi-analytical model for the fast optimisation of a TRC. This model decouples ultrasound propagation in an empty cavity and multiple scattering in a multiple scattering medium. It was validated numerically and experimentally using a 2D-TRC and numerically using a 3D-TRC. Finally, the model was used to determine rapidly the optimal parameters of the 3D-TRC which had been confirmed by numerical simulations.

Multiple scattering in random dispersions of spherical scatterers: Effects of shear-acoustic interactions

The propagation of acoustic waves through a suspension of spherical particles in a viscous liquid is investigated, through application of a multiple scattering model. The model is based on the multiple scattering formulation of Luppé, Conoir, and Norris [J. Acoust. Soc. Am. 131, 1113-1120 (2012)] which incorporated the effects of thermal and shear wave modes on propagation of the acoustic wave mode. Here, the model is simplified for the case of solid particles in a liquid, in which shear waves make a significant contribution to the effective properties. The relevant scattering coefficients and effective wavenumber are derived in analytical form. The results of calculations are presented for a system of silica particles in water, illustrating the dependence of the scattering coefficients, effective wavenumber, speed, attenuation on particle size and frequency. The results demonstrate what has already been shown experimentally; that the shear-mediated processes have a very significant effect on the effective attenuation of acoustic waves, especially as the concentration of particles increases.

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. In the case of acoustic waves, we show that this approach leads to incorrect results for the scattering mean free path, no matter how weak the fluctuations. The detailed calculation of the coherent wave field must take into account both a scalar and an operator part in the random potential. When both terms have identical amplitudes, the correct value for the scattering mean free paths is shown to be more than 4 times smaller (13/3, precisely) in the low-frequency limit, whatever the shape of the correlation function. Based on the diagrammatic approach of multiple scattering, theoretical results are obtained for the self-energy and mean free path within Bourret's and on-shell approximations. They are confirmed by numerical experiments.

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. These synthetic samples are used as phantoms for actual inhomogeneous materials. The resonant nature of the scatterers has a strong effect on diffusivity, which is shown to vary significantly with frequency. This may affect the result of broadband measurements of apparent diffusivity, which can be expected to depend on time and sample thickness, whereas diffusivity is intrinsically an intensive parameter. Moreover, the transport speed is shown to vary drastically with frequency, sometimes by more than 50%, due to a very narrow resonance that slows down transport. Interestingly, this sharp resonance could only be revealed by experiments performed with coda waves, and not with ballistic or coherent waves whose frequency resolution is intrinsically limited from an experimental point of view.

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. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot's theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot's theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot's model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot's theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot's predictions of in-phase and out-of-phase motions.

Multiple scattering in porous media: comparison with water saturated double porosity media

Multiple scattering in a poroelastic medium obeying Biot's theory is studied; the scatterers are parallel identical cylindrical holes pierced at random in the medium. The paper focuses first on the influence, on the effective wavenumbers, of the mode conversions that occur at each scattering event. The effect of the holes on the dispersion curves is then examined for two different values of the ratio of their radius to the pores mean radius. Depending on the latter, the dispersion curves of the pierced material are compared, for the fast and shear waves, with those of either a more porous medium or a double porosity medium.

Tuning Mie scattering resonances in soft materials with magnetic fields

An original approach is proposed here to reversibly tune Mie scattering resonances occurring in random media by means of external low induction magnetic fields. This approach is valid for both electromagnetic and acoustic waves. The experimental demonstration is supported by ultrasound experiments performed on emulsions made of fluorinated ferrofluid spherical droplets dispersed in a Bingham fluid. We show that the electromagnet-induced change of droplet shape into prolate spheroids, with a moderate aspect ratio of 2.5, drastically affects the effective properties of the disordered medium. Its effective acoustic attenuation coefficient is shown to vary by a factor of 5, by controlling both the flux density and orientation of the applied magnetic field.

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. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

On the estimation of dynamic mass density of random composites

The dynamic effective mass density and bulk modulus of an inhomogeneous medium at low frequency limit are discussed. Random configurations in a variety of two-dimensional physical contexts are considered. In each case, effective dynamic mass density and bulk modulus are calculated based on eigenmode matching theory. The results agree with those provided by Martin et al. [J. Acoust. Soc. Am. 128, 571-577 (2010)] obtained from effective wavenumber method.

Coherent acoustic wave propagation in media with pair-correlated spheres

Propagation of plane compressional waves in a non-viscous fluid with a dense distribution of identical spherical scatterers is investigated. The analysis is based on the multiple scattering approach proposed by Fikioris and Waterman, and is generalized to include arbitrary choice of the pair-correlation functions used to represent the distribution of the scatterers. A closed form solution for the effective wavenumber as a function of the concentration of pair-correlated finite-size spheres is derived up to the second order. In the limit of uncorrelated point-scatterers, this solution is identical to that obtained by Lloyd and Berry. Different pair-correlation functions are exemplified and compared, and the resulting differences discussed.

Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low-frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wavenumber of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the independent scattering approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA.

Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions

In a previous paper, Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] obtained two formulas for the effective wavenumber in a dilute random array of circular scatterers. They emerged from a study of the problem of the reflection of a plane wave at oblique incidence to a half-space containing the scatterers. Here, their study is extended to obtain formulas for the reflection and transmission coefficients and to investigate the average fields near the boundary of the half-space. Comparisons with previous work are made.

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. 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 megahertz 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.

Multiple scattering by cylinders immersed in fluid: high order approximations for the effective wavenumbers

Acoustic wave propagation in a fluid with a random assortment of identical cylindrical scatterers is considered. While the leading order correction to the effective wavenumber of the coherent wave is well established at dilute areal density (n0) of scatterers, in this paper the higher order dependence of the coherent wavenumber on n0 is developed in several directions. Starting from the quasi-crystalline approximation (QCA) a consistent method is described for continuing the Linton and Martin formula, which is second order in n0, to higher orders. Explicit formulas are provided for corrections to the effective wavenumber up to O (n0(4)). Then, using the QCA theory as a basis, generalized self-consistent schemes are developed and compared with self-consistent schemes using other dynamic effective medium theories. It is shown that the Linton and Martin formula provides a closed self-consistent scheme, unlike other approaches.

Estimating the dynamic effective mass density of random composites

The effective mass density of an inhomogeneous medium is discussed. Random configurations of circular cylindrical scatterers are considered, in various physical contexts: fluid cylinders in another fluid, elastic cylinders in a fluid or in another solid, and movable rigid cylinders in a fluid. In each case, time-harmonic waves are scattered, and an expression for the effective wavenumber due to Linton and Martin [J. Acoust. Soc. Am. 117, 3413-3423 (2005)] is used to derive the effective density in the low frequency limit, correct to second order in the area fraction occupied by the scatterers. Expressions are recovered that agree with either the Ament formula or the effective static mass density, depending upon the physical context.

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. Interestingly, the distribution of singular values shows a dramatically different behavior in the single and multiple-scattering regimes. Based on a matrix separation of single and multiple-scattered waves, an experimental illustration of imaging through a highly scattering slab is presented.

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. The cross correlations between highly scattered signals are computed. The main effect of the temperature change is a simple dilation of the times of arrival, due to a change of the sound velocity in water. But the scatterers also play a role in the progressive decorrelation of wave forms. An analysis resolved in both time and frequency shows that at some particular frequencies, the resonant behavior of the scatterers is responsible for a significantly larger decorrelation. Interestingly, the experimental results allow one to detect the presence of a small resonance that was not detected earlier on the same scatterers with classical measurement of the scattering mean free path. A simple model is proposed to interpret the experimental results.

Localized modes in a finite-size open disordered microwave cavity

We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths, and we successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensional open random media.

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. 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 sqrt[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 long-scale variations of D in a random-scattering 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.