基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

Constructing ultrasonic images of soft spherical scatterers

The paper considers specific features of ultrasonic visualization of gas bubbles in a liquid or a medium of like soft biological tissue type under conditions when the size of scatterers is comparable to the acoustic wavelength. It was proposed to use styrofoam specimens as the experimental model of stationary gas bubbles. Patterns of ultrasound scattering by a styrofoam sphere in water were obtained experimentally. It was shown that the measurement results agree well with the prediction of the classical theoretical model of scattering of a plane wave by a perfectly soft sphere. Several experiments were performed illustrating the specific features of visualizing millimeter-sized bubbles. A Terason commercial ultrasonic scanner was used; gelatin specimens with embedded styrofoam spheres served as the objects of study. The simulation and experimental results showed that when bubbles with diameters of <1 mm are visualized, it is impossible to measure the diameter of scatterers because bubbles of different diameters are imaged as bright spots of identical diameter, which is equal to the scanner resolution. To eliminate this difficulty, it is recommended to use the results of theoretical simulation performed in this study, which revealed a monotonic increase in the backscattered signal intensity with an increase in bubble radius. An ultrasonic visualization mode is proposed in which the brightness of scattered signals is used to differentiate between bubbles of different size.     

Scattering of a spherical wave by a small sphere: an elementary solution

Wave scattering by objects that are small compared to the wavelength (Rayleigh scattering) is usually studied for plane incident waves. However, knowledge of the full Green's function of the problem becomes necessary when the separation of scatterers from either an interface or each other is comparable to the scatterers' dimensions. Here, an elementary analytic solution is derived for diffraction of a spherical sound wave by a small, soft sphere. The approximate solution is obtained from asymptotic expansions of an exact solution, holds everywhere outside the sphere, and reduces to classical results due to Kelvin and Rayleigh in appropriate special cases.     

Wave propagation in a disordered array of monopole scatterers

We study scalar wave propagation in a disordered static array of spherical scatterers. Due to a hard core repulsion the scatterers do not overlap. The wave is scattered by a δ-function potential at the center of each of the spheres. To this monopole model we apply the previously developed cluster expansion for the self-energy. We find the root of the dispersion equation for the coherent wave for a range of volume fraction⁵. It turns out that the monopole model develops an instability when the scattering is too strong.     

Condensation of interacting bosons in a random potential

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval.     

Ultrasonic properties of random media under uniaxial loading.

Acoustic properties of two types of soft tissue-like media were measured as a function of compressive strain. Samples were subjected to uniaxial strains up to 40% along the axis of the transducer beam. Measurements were analyzed to test a common assumption made when using pulse-echo waveforms to track motion in soft tissues--that local properties of wave propagation and scattering are invariant under deformation. Violations of this assumption have implications for elasticity imaging procedures and could provide new opportunities for identifying the sources of backscatter in biological media such as breast parenchyma. We measured speeds of sound, attenuation coefficients, and echo spectra in compressed phantoms containing randomly positioned scatterers either stiffer or softer than the surrounding gelatin. Only the echo spectra of gel media with soft scatterers varied significantly during compression. Centroids of the echo spectra were found to be shifted to higher frequencies in proportion to the applied strain up to 10%, and increased monotonically up to 40% at a rate depending on the scatterer size. Centroid measurements were accurately modeled by assuming incoherent scattering from oblate spheroids with an eccentricity that increases with strain. While spectral shifts can be accurately modeled, recovery of lost echo coherence does not seem possible. Consequently, spectral variance during compression may ultimately limit the amount of strain that can be applied between two data fields in heterogeneous media such as lipid-filled tissues. It also appears to partially explain why strain images often produce greater echo decorrelation in tissues than in commonly used graphite-gelatin test phantoms.     

Reconstruction of acoustic boundary scatterers using the Novikov-Grinevich-Manakov algorithm

Models of perfectly rigid and perfectly soft acoustic scatterers of different dimensions are used to study the applicability limits of the Novikov-Grinevich-Manakov functional algorithm intended for reconstructing two-dimensional scatterers. Particular scattering features intrinsic to boundary scatterers are revealed.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).     

On the utilization of acoustic diffraction in monitoring cetaceans

An active acoustic technique for monitoring the whales is proposed. The technique allows one to monitor the whales’ crossing of a conventional borderline extending for several tens of kilometers in a shallow-water area. The potentialities of the technique are demonstrated in the framework of a numerical experiment by solving the problem of diffraction by model scatterers in an acoustic waveguide. The scatterers are selected in the form of soft spheroids with dimensions characteristic of various kinds of cetaceans.     

Generalized Foldy-Lax formulation

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the Foldy-Lax formulation. This formulation forms the basis for our numerical procedure.     

Determination of Tiny Scatterer#x0027;s Shape by Light Scattering Tomography

We have developed a new method of recognizing the shape of tiny light scatterers by matrix calculation (conjugate gradient method) using the wave field on the objective lens. We describe simulation results for scatterers of about 100 nm and show that they accurately produce the scatterer shape.     

Superfocusing of a spherical wave: Theory and experiment

The possibility of focusing a spherical wave within a region considerably smaller than the wavelength is studied theoretically and experimentally. The coefficient of reflection of a spherical wave from a small rigid or soft sphere is-1. Consequently, the total field near such scatterers remains finite as the radius of the sphere tends to zero. The power of the acoustic field concentrates in this case in a region whose radius is proportional to the acoustic wavelength. The field can be enhanced by choosing an appropriate reflection coefficient. For example, if the reflection coefficient is made equal to 0, the sound pressure will be created by the converging wave alone. As the observation point approaches the center, this field increases without limit as 1/r, where r is the distance from the center. Structures that provide the absorption of the converging wave are analyzed. The experimental setup is described, and the experimental results demonstrating a strong absorption (the reflection coefficient does not exceed 0.2) of the converging wave are presented. The main result of the study is that it experimentally corroborates the possibility of focusing the wave in a region whose dimensions are much smaller than the wavelength.     

3D analysis of in-filled trench as passive barriers for ground vibration isolation

The three-dimensional (3D) problem of the ground vibration isolation by an in-filled trench as a passive barrier is studied theoretically. Integral equations governing Rayleigh wave scattering are derived based on the Green’s solution of Lamb problem. The integral equations are solved accurately and efficiently with an iteration technique. They are used to evaluate the complicated Rayleigh wave field generated by irregular scatterers embedded in an elastic half-space solid. The passive isolation effectiveness of ground vibration by the in-filled trench for screening Rayleigh wave is further studied in detail. Effects of relevant parameters on the effectiveness of vibration isolation are investigated and presented. The results show that a trench filled with stiff backfill material gets a better isolation effect than a soft one, and increasing the depth or width of the in-filled trench also improves its screening effectiveness. The effectiveness and the area of the screened zone are surging with the increase in the length of the in-filled trench. Supported by the National Natural Science Foundation of China (Grant Nos. 50678128 and 50538010) and the Research Fund for PhD Student of Chinese College (Grant No. 20050247030)     

A unified optical theorem for scalar and vectorial wave fields

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.     

Acoustic anechoic layers with singly periodic array of scatterers: Computational methods,absorption mechanisms,and optimal design

The acoustic properties of anechoic layers with a singly periodic array of cylindrical scatterers are investigated. A method combined plane wave expansion and finite element analysis is extended for out-of-plane incidence. The reflection characteristics of the anechoic layers with cavities and locally resonant scatterers are discussed. The backing is a steel plate followed by an air half space. Under this approximate zero transmission backing condition, the reflection reduction is induced by the absorption enhancement. The absorption mechanism is explained by the scattering/absorption cross section of the isolated scatterer. Three types of resonant modes which can induce efficient absorption are revealed. Due to the fact that the frequencies of the resonant modes are related to the size of the scatterers, anechoic layers with scatterers of mixed size can broaden the absorption band. A genetic optimization algorithm is adopted to design the anechoic layer with scatterers of mixed size at a desired frequency band from 2 kHz to l0 kHz for normal incidence, and the influence of the incident angle is also discussed.     

Application of the mutual-interaction method to a class of two-scatterer systems: I. Two discrete scatterers

In a recent paper we developed a formalism that fully accommodates the mutual interactions among scatterers separable by parallel planes. The total fields propagating away from these planes are the unknowns of a system of difference equations. Each scatterer is characterized by a scattering function that expresses the scattered wave amplitude as a function of the incident and scattered wavevectors for a unit-amplitude plane wave scattered from the object in isolation. This function can be derived completely from the scattered far field with the help of analytic continuation. For a two-scatterer system the mutual-interaction equations reduce to a single Fredholm integral equation of the second kind. It turns out that analytic solutions are tractable for those scattering functions that are Dirac deltas or a sum of products of separable functions of the incident and scattered wavevectors. Scattering functions for planes and isotropic scatterers, as well as electric and magnetic dipoles all possess this property and are considered. The exact scattering functions agree with results obtained by analytic continuation. This paper consists of two parts. Part I derives analytic solutions for two discrete scatterers (isotropic scatterers. electric dipoles, magnetic dipoles). Part II is devoted to scattering from an object (isotropic or dipole scatterer) near an interface separating two semi-infinite uniforn-media. Because the results in this paper are exact, the effects of near-field interactions can be assessed. The forms of the scattering solutions can be adapted to objects that are both radiating and scattering.