Determining the geometric parameters of diffuse scattering objects

A spectral-correlation diagnostic method has been used for determining the linear dimensions of inhomogeneities with diffuse scattering surfaces in optical media. Experimental data are in good agreement with the results of numerical simulations and are consistent with theoretical notions. It is shown that the proposed method can be implemented on a simple technical basis and used is practice.     

水下刚硬体声散射场计算及分析

针对水下任意形状刚硬体,建立了其声散射T矩阵法计算模型。利用物体的几何对称性,提出了各种简化计算Q矩阵的方法。以两端有半椭球顶的有限长圆柱体为例,分别计算了具有不同长宽比或者是不同端部几何形状的有限长圆柱体的反向散射和前向散射函数。深入讨论了有限长圆柱体的镜反射波和Franz波的干涉物理模型,以及其圆柱体中段长度对散射场的影响,并对得到的计算结果给出了合理的物理解释。计算结果同时也表明T矩阵法是一种很简便实用的计算水下物体远场散射的方法。     

Partial-differential-equation-constrained amplitude-based shape detection in inverse acoustic scattering

In this article we discuss a formal framework for casting the inverse problem of detecting the location and shape of an insonified scatterer embedded within a two-dimensional homogeneous acoustic host, in terms of a partial-differential-equation-constrained optimization approach. We seek to satisfy the ensuing Karush–Kuhn–Tucker first-order optimality conditions using boundary integral equations. The treatment of evolving boundary shapes, which arise naturally during the search for the true shape, resides on the use of total derivatives, borrowing from recent work by Bonnet and Guzina [1–4] in elastodynamics. We consider incomplete information collected at stations sparsely spaced at the assumed obstacle’s backscattered region. To improve on the ability of the optimizer to arrive at the global optimum we: (a) favor an amplitude-based misfit functional; and (b) iterate over both the frequency- and wave-direction spaces through a sequence of problems. We report numerical results for sound-hard objects with shapes ranging from circles, to penny- and kite-shaped, including obstacles with arbitrarily shaped non-convex boundaries. Partial support for this work was provided by the US National Science Foundation under grant award CMS-0348484.     

A three-dimensional shape optimization for transient acoustic scattering problems using the time-domain boundary element method

We develop a three-dimensional shape optimization (SO) framework for the wave equation with taking the unsteadiness into account. Resorting to the adjoint variable method, we derive the shape derivative (SD) with respect to a deformation (perturbation) of an arbitrary point on the target surface of acoustic scatterers. Successively, we represent the target surface with non-uniform rational B-spline patches and then discretize the SD in term of the associated control points (CPs), which are useful for manipulating a surface. To solve both the primary and adjoint problems, we apply the time-domain boundary element method (TDBEM) because it is the most appropriate when the analysis domain is the ambient air and thus infinitely large. The issues of the severe computational cost and instability of the TDBEM are resolved by exploiting the fast and stable TDBEM proposed by the present authors. Instead, since the TDBEM is mesh-based and employs the piecewise-constant element for space, we introduce some approximations in evaluating the discretized SD from the two solutions of TDBEM. By regarding the evaluation scheme as the computation of the gradient of the objective functional, given as the summation of the absolute value of the sound pressure over the predefined observation points, we can solve SO problems with a gradient-based non-linear optimization solver. To assess the developed SO system, we performed several numerical experiments from the perspective of verification and application with satisfactory results.     

Multichannel television method for measuring geometric parameters of objects

The use of television devices for measuring geometric parameters of pipes using several television cameras set up at fixed distances in space is considered. The method provided is based on automatic calibration and processing algorithms providing independence of measurement results from the distance to an object and its movement in space. __________ Translated from Metrologiya, No. 1, pp. 13–18, January, 2008.     

A BEM sensitivity and shape identification analysis for acoustic scattering in fluid–solid problems

In this paper a boundary element formulation for the sensitivity analysis of structures immersed in an inviscide fluid and illuminated by harmonic incident plane waves is presented. Also presented is the sensitivity analysis coupled with an optimization procedure for analyses of flaw identification problems. The formulation developed utilizes the boundary integral equation of the Helmholtz equation for the external problem and the Cauchy–Navier equation for the internal elastic problem. The sensitivities are obtained by the implicit differentiation technique. Examples are presented to demonstrate the accuracy of the proposed formulations. © 1998 John Wiley & Sons, Ltd.     

掩埋物体的小掠角散射声场与回波信混比

探测掩埋物体的水声系统,通常是在一定距离之外以小掠角声波扫描海底的方式工作,现有的射线声学模型已不能进行系统性能预报。采用波数积分模型和等效源建模方法,将声波在介质中的传播和掩埋物体的散射场计算融为一体,可以高精度地进行各种形状物体、不同声波束和任意掩埋状态下的三维散射场计算。利用开发的声场模型,计算出了典型球壳的等效目标强度和信号混响比随频率、掠射角及掩埋深度的关系曲线。在此基础上,提出一种基于时反聚焦发射、水下移动平台接收的双基地探测设想,并采用开发的声场模型验证了其正确性。     

Multilevel Green's function interpolation method for scattering from composite metallic and dielectric objects

A multilevel Green's function interpolation method based on two kinds of multilevel partitioning schemes--the quasi-2D and the hybrid partitioning scheme--is proposed for analyzing electromagnetic scattering from objects comprising both conducting and dielectric parts. The problem is formulated using the surface integral equation for homogeneous dielectric and conducting bodies. A quasi-2D multilevel partitioning scheme is devised to improve the efficiency of the Green's function interpolation. In contrast to previous multilevel partitioning schemes, noncubic groups are introduced to discretize the whole EM structure in this quasi-2D multilevel partitioning scheme. Based on the detailed analysis of the dimension of the group in this partitioning scheme, a hybrid quasi-2D/3D multilevel partitioning scheme is proposed to effectively handle objects with fine local structures. Selection criteria for some key parameters relating to the interpolation technique are given. The proposed algorithm is ideal for the solution of problems involving objects such as missiles, microstrip antenna arrays, photonic bandgap structures, etc. Numerical examples are presented to show that CPU time is between O(N) and O(N log N) while the computer memory requirement is O(N).     

Fast spectral-domain method for acoustic scattering problems

This paper presents the application of the conjugate-gradient (CG) fast Fourier transform (FFT) (CG-FFT) method and the CG nonuniform FFT (CG-NUFFT) method for the integral equation arising from acoustic scattering problems. In the conventional method of moments (MoM) for integral equations, the CPU and memory requirements are O(N³) and O(N²), respectively, where N is the number of unknowns in the problem. The CG-FFT method, which combines the iterative conjugate-gradient method with FFT, reduces these requirements to O(KN log₂N) and O(N), respectively, where K is the number of CG iterations. The CG-NUFFT method differs from the CG-FFT method in that it makes use of nonuniform FFT algorithms instead of FFT to allow a nonuniform discretization. Therefore, the CG-NUFFT method can solve the integral equation with both uniform and nonuniform grid while retaining the efficiency of the CG-FFT method. These two methods are applied to solve for two-dimensional constant density acoustic scattering problems. Numerical. results demonstrate that they can solve much larger problems than the MoM     

用时域有限差分法计算透声目标的散射场

在透声界面附近运用声学基本方程可导出边界条件的时域有限差分（ＦＤＴＤ）表达式。本文用ＦＤＴＤ计算透声物体的反射、透射和散射，并讨论全内反射和完全透射现象，所得到的结果与理论解相符合，从而验证了这一边界条件差分表达式的适用性。基于此边界条件的ＦＤＴＤ基本框架可望在解决各种非弹性体的散射问题中有广泛的应用。本文还给出一个有效的吸收边界条件     

Characteristics of acoustic scattering from a double-layered micro shell for encapsulated drug delivery

This work examines the characteristic differences in acoustic scattering between air-filled double-layered encapsulating (DLE) shells and air-filled single-layered encapsulating (SLE) shells. The analysis shows that the presence of an outer layer softer than the inner layer results in a shift of the first monopole of the reflectivity-frequency response to a higher frequency and a reduction in the monopole peak; and it leads to a frequency-separation of the two dipoles that trace the monopole. The frequency shift and the peak reduction of the monopole and the frequency separation of the two dipoles all increase with the increasing thickness of the softer outer layer. The numerical results reveal that variations in the Lame constant of the model material for the protein albumin have little effect on the low-frequency scattering characteristics, while they affect the high-frequency scattering characteristics significantly. The authors have shown that this phenomenon is due to the fact that the model material for the protein albumin has a Lame constant substantially larger than its shear modulus. Their further numerical studies conclude that, for each DLE shell, one can construct an equivalent SLE shell, using a simple scheme originated from the mechanics of composite materials in the sense that the so-constructed SLE shell has essentially the same acoustic scattering characteristics as the DLE shell within a low frequency range.     

Shell waves and acoustic scattering from ultrasound contrast agents

Ultrasound contrast agents are encapsulated microbubbles, filled either with air or a higher weight molecular gas, ranging in size from 1 to 10 μm in diameter. The agents are modeled as air-filled spherical elastic shells of variable thickness and material properties. The scattered acoustic field is computed from a modal series solution, and reflectivity and angular scattering are then determined from the computed fields for agents of various properties. We show that contrast agents also support shell resonance responses in addition to the monopole response, which has been the focus of previous contrast agent studies. Lamb waves appear to be the source of these additional responses. A shell or curvature Lamb wave generates dipole peaks in the 1- to 40-MHz range for 2.5 to 3.5 μm radius agents with elastic properties approximating those of albumin protein. The inclusion of damping affects the lower frequency dipole peaks but is less important for responses occurring above approximately 30 MHz. Moreover, these responses hold untapped potential for clinical ultrasound applications such as tissue perfusion studies and high frequency contrast agent imaging     

Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies

In this paper, we present a novel framework for discretizing integral equations--specifically, those used for analyzing scattering from dielectric bodies. The candidate integral equations chosen for the analysis are the well-known Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and the Müller equations. Discrete solutions to these equations are typically obtained by representing the spatial variation of the currents using the Rao-Wilton-Glisson (RWG) basis functions or their higher order equivalents. In this paper, we propose a framework for defining basis functions that departs significantly from those of RWG functions in that approximation functions can be chosen independent of continuity constraints. We will show that using this framework together with a quasi-Helmholtz type representation has a number of benefits. Namely, (i) it shows excellent convergence, (ii) it permits inclusion of different orders of polynomials or different functions as basis functions without imposition of additional constraints, (iii) the method can easily handle nonconformal meshes, and (iv) the method is well conditioned at all frequencies. These features will be demonstrated via a number of numerical experiments.     

Shape optimization of acoustic scattering bodies

Shape optimization of acoustic scattering bodies is carried out using genetic algorithms (GA) coupled to a boundary element method for exterior acoustics. The BEM formulation relies on a modified Burton-Miller algorithm to resolve exterior acoustics and to address the uniqueness issue of the representation problem associated with the Helmholtz integral equation at the eigenvalues of the associated interior problem. The particular problem of interest considers an incident wave approaching an axisymmetric shaped body. The objective is to arrive at a geometric configuration that minimizes the acoustic intensity captured by a receiver located at a distance from the scattering body. In particular, the acoustic intensity is required to be minimum as measured proportional to the integral of the product of the potential and its complex conjugate over a volume of space which models the receiver. This is opposed to the more traditional measure of the potential at a single point in space.     

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary-element-method approach to the impedance boundary-value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree nu) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval [a,b], which only requires the discretization of [a,b], we show theoretically and experimentally that the L(2) error in computing the acoustic field on [a,b] is O(log(nu+3/2)|k(b-a)|M(-(nu+1)), where M is the number of degrees of freedom and k is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.     

Diffuse x-ray scattering from a crystal modulated by surface acoustic wave

The process of diffuse x-ray scattering from a crystal modulated by surface acousdtic wave is considered. It is shown that the angular distribution of the diffuse scattering intensity depends on variation of the gradient of the ultrasonic wave amplitude in depth of the crystal. This distribution is formed both in the vicinity of the main diffraction peak and around its satellites. Theoretical reciprocal space maps of the diffuse scattering intensity distribution are obtained and compared to the experimental data.     

分舱段圆柱壳声散射数值和试验研究

基于有限元方法建立了填充不同介质的有限长分舱段圆柱壳声散射数值计算模型,仿真了填充空气-空气、空气-水、水-水三类两舱段圆柱壳声散射特性,并完成了三类两舱段圆柱壳体声散射试验,获取和分析了两舱段圆柱壳体声散射的时间角度谱和频率角度谱特性。利用物理声学方法分析了壳体表面、端面以及内部填充水介质对散射声场的影响,揭示了两舱段圆柱壳声散射频率角度谱中呈现的干涉条纹特征形成机理,为水下分舱段目标,如水下无人航行器的主动声呐探测和识别提供理论支撑。     

Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.     

Single-shot color fringe projection for three-dimensional shape measurement of objects with discontinuities

A simple but effective fringe projection profilometry is proposed to measure 3D shape by using one snapshot color sinusoidal fringe pattern. One color fringe pattern encoded with a sinusoidal fringe (as red component) and one uniform intensity pattern (as blue component) is projected by a digital video projector, and the deformed fringe pattern is recorded by a color CCD camera. The captured color fringe pattern is separated into its RGB components and division operation is applied to red and blue channels to reduce the variable reflection intensity. Shape information of the tested object is decoded by applying an arcsine algorithm on the normalized fringe pattern with subpixel resolution. In the case of fringe discontinuities caused by height steps, or spatially isolated surfaces, the separated blue component is binarized and used for correcting the phase demodulation. A simple and robust method is also introduced to compensate for nonlinear intensity response of the digital video projector. The experimental results demonstrate the validity of the proposed method.