Time reversal for a single spherical scatterer.

We show that the time reversal operator for a planar time reversal mirror (TRM) can have up to four distinct eigenvalues with a small spherical acoustic scatterer. Each eigenstate represents a resonance between the TRM and an induced scattering moment of the sphere. Their amplitude distributions on the TRM are orthogonal superpositions of the radiation patterns from a monopole and up to three orthogonal dipoles. The induced monopole moment is associated with the compressibility contrast between the sphere and the medium, while the dipole moments are associated with density contrast. The number of eigenstates is related to the number of orthogonal orientations of each induced multipole. For hard spheres (glass, metals) the contribution of the monopole moment to the eigenvalues is much greater than that of the dipole moments, leading to a single dominant eigenvalue. The other eigenvalues are much smaller, making it unlikely multiple eigenvalues could have been observed in previous experiments using hard materials. However, for soft materials such as wood, plastic, or air bubbles the eigenvalues are comparable in magnitude and should be observable. The presence of multiple eigenstates breaks the one-to-one correspondence between eigenstates and distinguishable scatterers discussed previously by Prada and Fink [Wave Motion 20, 151-163 (1994)]. However, eigenfunctions from separate scatterers would have different phases for their eigenfunctions, potentially restoring the ability to distinguish separate scatterers. Since relative magnitudes of the eigenvalues for a single scatterer are governed by the ratio of the compressibility contrast to the density contrast, measurement of the eigenvalue spectrum would provide information on the composition of the scatterer.     

Comment on "Analysis of the time-reversal operator for scatterers of finite size," by D. H. Chambers [J. Acoust. Soc. Am. 112, 411-419 (2002)

This letter concerns the paper "Analysis of the time-reversal operator for scatterers of finite size" [J. Acoust. Soc. Am. 112, 411-419 (2002)]. The number of possible eigenvalues and eigenfunctions of the time reversal operator for a finite sphere given in the paper is much more than the correct number, which is proven to be the total number of multipole moments induced inside the finite sphere.     

The reflection of ultrasound from partially contacting rough surfaces

Ultrasound is commonly used to detect and size cracks in a range of engineering components. Modeling techniques are well established for smooth and open cracks. However, real cracks are often rough (relative to the ultrasonic wavelength) and closed due to compressive stress. This paper describes an investigation into the combined effects of crack face roughness and closure on ultrasonic detectability. A contact model has been used to estimate the size and shape of scatterers (voids) at the interface of these rough surfaces when loaded. The response of such interfaces to excitation with a longitudinal ultrasonic pulse over a wide range of frequencies has been investigated. The interaction of ultrasound with this scattering interface is predicted using a finite-element model and good agreement with experiments on rough surfaces is shown. Results are shown for arrays of equi-sized scatterers and a distribution of scatterer sizes. It is shown that the response at high frequencies is dependent on the size, shape, and distribution of the scatterers. It is also shown that the finite-element results depart from the mass-spring model predictions when the product of wave number and scatterer half-width is greater than 0.4.     

Time-reversal multiple signal classification in case of noise: a phase-coherent approach

The problem of locating point-like targets beyond the classical resolution limit is revisited. Although time-reversal MUltiple SIgnal Classification (MUSIC) is known for its super-resolution ability in localization of point scatterers, in the presence of noise this super-resolution property will easily break down. In this paper a phase-coherent version of time-reversal MUSIC is proposed, which can overcome this fundamental limit. The algorithm has been tested employing synthetic multiple scattering data based on the Foldy-Lax model, as well as experimental ultrasound data acquired in a water tank. Using a limited frequency band, it was demonstrated that the phase-coherent MUSIC algorithm has the potential of giving significantly better resolved scatterer locations than standard time-reversal MUSIC.     

Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: theory and experiment

The decomposition of the time-reversal operator provides information on the scattering medium. It has been shown [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)] that a small spherical scatterer is in general associated with four eigenvalues and eigenvectors of the time-reversal operator. In this paper, the 2D problem of scattering by an elastic cylinder, imbedded in water, measured by a linear array of transducers is considered. In this case, the array response matrix has three nonzero singular values. Experimental results are obtained with linear arrays of transducers and for wires of different diameters smaller that the wavelength. It is shown how the singular value distribution and the singular vectors depend on the elastic velocities cL, cT, the density rho of each wire, and on the density rho0 and velocity c0 of the surrounding fluid. These results offer a new perspective towards solution of the inverse problem by determining more than scattering contrast using conventional array processing like that used in medical ultrasonic imaging.     

The 2D Kramers–Dirac oscillator

The Dirac oscillator was initially introduced as a Dirac operator which is linear in momentum and coordinate variables. In contrast to the usual 2D Dirac oscillator, the 2D Kramers–Dirac oscillator admits the time-reversal symmetry, which is a reason for the present nomenclature. It is shown that there exists a family of eigenstates associated with an eigenvalue linear in the control parameter, and the eigenvalue in question goes down from positive values to negative values as the parameter varies in the positive direction. The other eigenvalues are broken up into two bands, positive and negative. The 2D Dirac and the 2D Kramers–Dirac oscillators are compared in their physical grounds and in their spectral structure from the viewpoint of the time-reversal symmetry.     

Time-reversal analysis for scatterer characterization

A new application of time-reversal processing of wave scattering data permits characterization of scatterers by analyzing the number and nature of the singular functions (or eigenfunctions) associated with individual scatterers when they have multiple contributions from monopole, dipole, and/or quadrupole scattering terms. We discuss acoustic, elastic, and electromagnetic scattering problems for low frequencies. Specific examples for electromagnetic scattering from one of a number of small conducting spheres show that each sphere can have up to six distinct time-reversal eigenfunctions associated with it.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Multiple small-angle neutron scattering in media with a high concentration of inhomogeneities

Multiple small-angle neutron scattering (MSANS) on a polydisperse system of scatterers was considered taking into account interparticle interference. The effect of the scatterer’s size distribution on the MSANS spectrum was studied. The exponential and log-normal distributions were analyzed. It was shown that the MSANS linewidth decreases at high scatterer concentrations due to the contribution of interparticle interference. The dependence of this effect on the scattering multiplicity and scatterer’s size dispersion was studied in detail.     

Longitudinal Optical Fields in Light Scattering from Dielectric Spheres and Anderson Localization of Light

Recent research has shown that coupling between point scatterers in a disordered medium by longitudinal electromagnetic fields is harmful for Anderson localization of light. However, it has been unclear if this feature is generic or specific for point scatterers. The present work demonstrates that the intensity of longitudinal field outside a spherical dielectric scatterer illuminated by monochromatic light exhibits a complicated, nonmonotonous dependence on the scatterer size. Moreover, the intensity is reduced for a hollow sphere, whereas one can adjust the parameters of a coated sphere to obtain a relatively low longitudinal field together with a strong resonant scattering efficiency. Therefore, random arrangements of structured (hollow or coated) spheres may be promising three‐dimensional disordered materials for reaching Anderson localization of light.     

Statistics of Wave Functions for a Point Scatterer on the Torus

Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is concentration of eigenfunctions on invariant structures in phase space. In this paper we study eigenfunction statistics for the Laplacian perturbed by a delta-potential (also known as a point scatterer) on a flat torus, a popular model used to study the transition between integrability and chaos in quantum mechanics. The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer, and new, or perturbed, eigenfunctions. We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space.     

Transmission mode time-reversal super-resolution imaging

The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, "Super-resolution imaging using time-reversal and MUSIC," J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, "The iterative time reversal process: Analysis of the convergence," J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., "Decomposition of the time reversal operator: Detection and selective focusing on two scatterers," J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth's surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with "classical" backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.     

Phase-space correlations of chaotic eigenstates

It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in configuration space, they persist in the semiclassical limit. A quantitative theory is developed on the basis of Gaussian wave packet dynamics and random-matrix arguments. The role of symmetries is discussed for the example of time-reversal invariance.     

一种描述散射体系中散射颗粒消光能力的新方法

提出了一种新的衡量散射体系中散射颗粒消光能力、散射能力和吸收能力的方法并与传统方法进行了比较。在此基础上 ,讨论了散射颗粒折射率和颗粒大小对其散射能力的影响。运用此方法可以为各种散射体系 ,尤其是强散射体系选择恰当的散射颗粒 ,其结果优于用传统方法所得的结果     

Solution of the three-dimensional acoustic inverse scattering problem. The modified Novikov algorithm

For the first time, three-dimensional model scatterers of various strengths and size are numerically reconstructed on the basis of the monochromatic functional-analytical Novikov algorithm. The algorithm allows for the multiple scattering processes and does not impose stringent constraints on the scatterer strength. The resulting scatterer estimate approaches the true value after the width of the scatterer’s spatial spectrum is restricted to a region with a radius of about 2k ₀. The noise robustness of the algorithm, i.e., the robustness to random errors in experimental data, is sufficiently high for diagnostic applications. However, the amount of numerical operations required by the algorithm is great.     

Analysis of sound propagation in a fluid through a screen of scatterers

A multiple scattering analysis in a nonviscous fluid is developed in detail in order to predict the coherent sound motion in the presence of disordered heterogeneities, such as particles, fibers, bubbles, or contrast agents. Scatterers can be homogeneous, layered, shell-like with encapsulated liquids or gas, nonabsorbing, or absorbing, and can take a wide variety of shapes. A priori imposed limitations or physical assumptions are absent in the derivation, whether they concern the expected response of the fluid-scatterer mixture, the scatterer size relative to wavelength, or the scatterer concentration or the screen thickness. However, as in any multiple scattering formulation, a closure assumption is invoked. Closed-form results for the backscattered and forward-scattered wave motions on either side of the screen of scatterers are obtained. The fluid-scatterer mixture is shown to behave as an effective dissipative medium from the standpoint of the coherent motion. It is found that the effective medium is fully described once two parameters are determined: the effective wave number and the reflection coefficient for the associated half-space screen. Remarkably, both parameters depend only on the far-field scattering properties of a single scatterer.     

Free Path Lengths in Quasi Crystals

The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann–Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law.     

Electromagnetic radiation from filamentary sources in the presence of axially magnetized cylindrical plasma scatterers

Electromagnetic radiation from filamentary electric-dipole and magnetic-current sources of infinite length in the presence of gyrotropic cylindrical scatterers in the surrounding free space is studied. The scatterers are assumed to be infinitely long, axially magnetized circular plasma columns parallel to the axis of the filamentary source. The field and the radiation pattern of each source are calculated in the case where the source frequency is equal to one of the surface plasmon resonance frequencies of the cylindrical scatterers. It is shown that the presence of even a single resonant magnetized plasma scatterer of small electrical radius or a few such scatterers significantly affects the total fields of the filamentary sources, so that their radiation patterns become essentially different from those in the absence of scatterers or the presence of isotropic scatterers of the same shape and size. It is concluded that the radiation characteristics of the considered sources can efficiently be controlled using their resonance interaction with the neighboring gyrotropic scatterers.