Modeling of the exact solution of the inverse scattering problem by functional methods

Relations between different functional algorithms for solving the inverse scattering problem are analyzed. It is shown that the Rose algorithm does not provide a unique solution, but can be used as a means to improve the interference resistance in reconstruction algorithms that provide unique restoration of scatterer characteristics. The possibility of unique reconstruction of refractive-absorbing scatterers by the modified Rose algorithm, which includes the Sokhotsky equation, is illustrated. Results of numeric simulation of the Novikov-Grinevich-Manakov algorithm, which is efficient in reconstructing two-dimensional acoustic refractive-absorbing scatterers of actually arbitrary shape and strength, are presented. The algorithm rigorously allows for multiple scattering effects. It is promising for tomography-like application problems and features a sufficiently high interference resistance.     

Multifrequency generalization of the Novikov algorithm for the two-dimensional inverse scattering problem

The process of reconstruction of two-dimensional refractive-absorbing scatterers by the modified Novikov algorithm is considered. A generalization of this algorithm to the multifrequency mode is proposed. The scattering data obtained at different frequencies are combined in the process of the solution using the a priori known frequency dependence of the scatterer function, which yields the constraint equations that are absent in the single-frequency version. It is shown that the problem of reconstruction instability observed in strong scatterers in the single-frequency mode can be removed by the multifrequency mode. The quality of the scatterer estimate in the multifrequency mode is significantly higher than that of the estimate obtained by straightforwardly averaging the single-frequency solutions. Interference resistance of the algorithm is sufficiently high to allow its application in practice.     

Inverse problem of a statistical estimation of scatterer characteristics and model examples

The inverse scattering problem involving experimental data with errors is considered in its statistical formulation. An algorithm for retrieving regularized estimates of the characteristics of spatially distributed scatterers (the phase velocity and absorption inhomogeneities) is developed. The algorithm takes into account the multiple scattering and generalizes the Wiener filtering to the nonlinear case. For weak scatterers, this nonlinear generalization is reduced to the linear Wiener filtering. The performance of the algorithm is verified by model examples simulating the operation of active acoustic tomography systems against various noise levels. The necessity of taking into account the multiple scattering and the fundamental role of the nonlinear filtering in the regularization procedure is demonstrated. It is remarkable that the noise robustness achieved in the reconstruction of strong scatterers with the optimal regularization algorithm is only slightly inferior to that achieved in the case of weak scatterers.     

Layer homogenization of a 2D periodic array of scatterers

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from an asymptotic theory and an optimization algorithm. Detailed numerical results are given for resonant scatterers and the spatial dispersion is investigated.     

Simulation of a functional solution to the acoustic tomography problem for data from quasi-point transducers

Two variants of a functional-analytical algorithm intended for solving inverse tomography problems are discussed and numerically carried out. The acoustic fields that are transmitted and received by transducers, which are equivalent to point ones, serve as experimental data. These data are used to calculate the classical or generalized scattering amplitude, and the scatterer characteristics are then reconstructed. The algorithm requires neither model linearization, no iterations for refining the estimates of scatterers, thus making it attractive for solving acoustic-tomography problems in different applications. The results of the numerical reconstruction of inhomogeneities in the sound velocity and absorption in a medium are presented.     

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.     

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.     

Inclined focusing method in subsurface radar

An oblique scanning method for subsurface radio tomography is proposed that is aimed at reconstructing the inhomogeneity 3D distribution and discovering out-of-level scatterers under a planar interface. The method is based on synthetic-aperture radar technology and uses data of multiposition sensing by omnidi-rectional antennas elevated over the Earth’s surface. The focusing of the synthetic-aperture radar is based on fast Fourier transformation providing a fast algorithm of 3D reconstruction. The method is verified numerically and in real experiments.     

Reconstruction of the fine structure of an acoustic scatterer against the distorting influence of its large-scale inhomogeneities

In the ultrasonic diagnostics of small-size neoplasms of biological tissues at the earliest stage of their development, an efficient way to eliminate the distorting influence of high-contrast or large inhomogeneities of the biological medium is to apply the iterative technique. A simple approach is proposed, which makes it possible with only two iteration steps to achieve an efficient focusing of the tomograph array. At the first step, the unknown distribution of the large-scale inhomogeneities of sound velocity and absorption over the scatterer is reconstructed, where the large-scale inhomogeneities are those whose size exceeds several wavelengths. At the second step, the fine structure of the scatterer is reconstructed against the large-scale background, which can be performed with a high accuracy owing to the evaluation of the background at the first step. The possibility of simultaneous reconstruction of the large-scale and fine structures by the noniterative Grinevich-Novikov algorithm is considered as an alternative. This algorithm reconstructs in an explicit form two-dimensional refractive-absorbing acoustic scatterers of almost arbitrary shape and strength. Taking into account the effects of multiple scattering, this algorithm provides resolution of the fine structure almost as good as that achieved in reconstructing the same structure against an undistorting homogeneous background. The results of numerical simulations of both algorithms are presented.     

Scattering by acoustic boundary scatterers with small wave sizes and their reconstruction

The scattering efficiencies of hard and soft cylindrical scatterers are compared using the Novikov-Grinevich-Manakov functional algorithm designed to reconstruct two-dimensional scatterers. The existence of a rigid relationship between the amplitude and phase of the wave scattered by a quasi- point-like scatterer and by scatterers with small wave sizes in the form of a soft cylinder, a soft sphere, and an air bubble in a liquid is confirmed by numerical simulations.     

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.     

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 the Disperse Composition of a PbO Suspension Containing Aggregates of Particles of Lamellar Shape by the Laser-Polarimetry Method

The results of measurements of the scattering matrix at a wavelength of 0.63 μm in the range of scattering angles of 10°–155° are presented for an aqueous suspension of lead oxide containing particles of plate form and their aggregates of monomers with dimensions of ~5 nm. The results of the measurements are compared with the results of calculations for axially symmetric scatterers (ellipsoids of rotation, cylinders). It is shown that the presence of aggregates affects the scattering properties of such a medium. The results of reconstructing the distribution of particles of a disperse medium in sizes from the measurements data of the scattering matrix are presented. The reconstruction of the distributions was carried out by solving the problem of optimizing the sum of the squared deviations of the experimental and calculated values of matrix elements in the framework of the model of axially symmetric scatterers. It is shown that the distribution of particles by sizes is more accurately reconstructed by minimizing the sum of the squares of the deviations for the sum of the diagonal elements. The obtained distribution is compared with the distribution measured by the method of dynamic light scattering.     

A Polydisperse Sphere Model Describing the Propagation of Light in Biological Tissue

A polydisperse sphere model with the complex refractive index is employed to describe the propagation of light in biological tissue. The scattering coefficient, absorption coefficient and scattering phase function are calculated. At the same time, the inverse problem on retrieving the particles size distribution, imaginary part of the refractive index and number density of scatterers is investigated. The result shows that the retrieval scheme together with the Chahine algorithm is effective in dealing with such an inverse problem. It is also clarified that a group of parameters including the scattering coefficient, absorption coefficient and phase function are associated with another group including the refractive index, particle size distribution and number density of scatterers, which is a problem described in two different ways and the anisotropy factor is not an independent variable, but is determined by the phase function.     

Solution of problem of electromagnetic waves scattering on inhomogeneously layered scatterers using pattern equation method

In this paper, the pattern equation method (PEM) is used to solve the problems of electromagnetic waves scattering by inhomogeneously layered scatterers. The numerical algorithm based on PEM for multilayered scatterers of arbitrary geometry is developed. The numerical results are presented for magneto-dielectric objects coated with magneto-dielectric materials to demonstrate the stability, accuracy, and efficiency of the proposed method. A comparison of the results obtained by the present method and by the other methods are shown and the limits of applicability of method are outlined.     

中红外散射的基质折射率效应研究

本文利用Mie散射理论对中红外波段三种不同类型散射体的散射和消光进行了研究,发现基质在三种不同类型散射体的散射和消光中所起作用完全不同。对于无吸收的高折射率散射体,基质折射率越大面积散射比(或面积消光比)越低;对于反常色散散射体,基质折射率越大面积散射比和面积肖光比越高;而对于金属散射体,基质折射率的大小对于散射和消光影响极小。     

压缩感知的远场亚波长声成像仿真

压缩感知算法可以利用信号的稀疏性较好地分辨出两个相距较远的目标,但是当两个目标相距较近时仅利用压缩感知算法,分辨性能较差;另外,当分辨目标为硬散射体时,由于偶极散射的影响,分辨性能也会变得较差。考虑到上述两个问题,该文提出了以下解决方案：针对第一个问题,该文将声学超透镜和压缩感知算法进行结合;针对第二个问题,该文提出在压缩感知算法中考虑偶极散射分量的影响。根据上述方案进行仿真,仿真结果证明了在加入声超透镜并考虑偶极散射以后,硬散射体目标在相距较近时实现了较好的分辨率。     

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.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.