Quantitative damage imaging using Lamb wave diffraction tomography

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated numerically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern(SDP) of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional(1D) Fourier transform of the scattered projection and two-dimensional(2D) spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode(TMDT) and reflection mode diffraction tomography(RMDT),respectively. The reconstructed results of the two projections for a non-converted S0 scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor.     

The method of multifrequency near-field acoustical tomography of bulk inhomogeneities of the sea bottom

In this work, we propose a method of near-field acoustical multi-frequency coherent tomography of spatially localized inhomogeneities of the shallow-sea bottom. In the framework of the developed method, two-dimensional spatial scanning of the radiating-receiving system along the bottom over the region of location of the inhomogeneities is performed at multiple frequencies. Using the Born approximation, the initial three-dimensional integral equation for the scattered field is reduced to one-dimensional Fredholm equation of the first kind with respect to the depth profile of the transverse spatial spectrum of the inhomogeneities. In the solution of this integral equation for each pair of spectral components, we use the method of generalized residual and obtain the sought three-dimensinal distribution via the inverse Fourier transform of the reconstructed spectrum. Results of numerical simulation of the tomography scheme and visualized inhomogeneities of shallow-sea bottom are presented.     

Polarization changes and beam profile deformation of light during acousto-optic interaction in isotropic media

A spatial Fourier transform approach is proposed to investigate the effects of polarization changes and beam profile deformation of light during acousto-optic (AO) interaction in isotropic media. The behaviour of the total scattered optical fields inside the AO cell can be properly described by a vector wave equation of which the permittivity is perturbed by an acoustic wave propagating inside the medium. In the Bragg regime, using a spatial Fourier transform approach, two coupled differential equations can be derived from the wave equation to depict AO interaction in the spatial frequency domain. Analytic solutions, which comprise the effects of changing polarization, beam deformation and propagating diffraction, can be found from the coupled equations. Detailed numerical simulations, including Fourier transforming the incident light profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented.     

一种有效解决离轴数字全息相图倾斜畸变的数字参考平面方法

离轴数字全息中使用倾斜的平面参考波以消除成像中的零级衍射和共轭像是一种简捷和常用的方法,然而该方法遇到的一个困扰是,由于倾斜参考波引入了附加的载波频率并很难通过实验测量准确地获得附加的载波频率值或倾角,因此会导致重建的相图出现一定的倾斜畸变而无法完全修正.本文提出了一种数字参考平面算法以解决这一问题.该算法利用重建相图的平坦区域选点构建一个能准确表征相图倾斜的数字参考平面,并建立该平面参量与参考波载波频率的数学关系和作为随后相图畸变修正迭代计算的判据.该算法简单有效,不仅能实现对倾斜相位畸变的准确修正,而且能准确地获得倾斜平面参考波的附加载波频率.由于在相位解包裹重建中结合了抑噪处理,因此该方法在环境和系统噪声的影响下仍然有效,实验结果验证了理论设计的有效性.     

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.     

融合结构先验信息的稳态扩散光学断层成像重建算法研究

扩散光学断层成像作为一种无辐射损伤、低成本的光学在体成像技术,有着良好的应用前景,但具有空间分辨率低、难以定量的缺陷.为了提高扩散光学断层成像的分辨率,实现光学参数分布的精确重建,基于有限元方法,提出了融合结构先验信息的稳态扩散光学断层成像重建算法.该算法以扩散近似作为成像模型,通过软先验的Laplace 正则化方法引入由MicroCT提供的空间结构信息.采用伴随法计算Jacobian矩阵,Levenberg-Marquardt方法用来进行迭代优化.仿真结果表明该算法不仅能获得精确的光学参数值分布,而且显著地提高了迭代收敛的速度.     

Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Inversion of synthetic and experimental acoustical scattering data for the comparison of two reconstruction methods employing the Born approximation

This work is concerned with the reconstruction, from measured (synthetic or real) data, of a 2D penetrable fluid-like object of arbitrary cross-section embedded in a fluid of infinite extent and insonified by a plane acoustic wave. Green's theorem is used to provide a domain integral representation of the scattered field. The introduction therein of the Born approximation gives rise to a linearized form of the inverse problem. The actual inversion is carried out by two methods. The first diffraction tomography (DT), exhibits the contrast function very conveniently and explicitly in the form of a wave number/incident angle Fourier transform of the far backscattered field and thus requires measurements of this field for incident waves all around the object and at all frequencies. The second discretized domain integral equation with Born approximation method, is numerically more intensive, but enables a wider choice of configurations and requires less measurements (one or several frequencies, one or several incident waves, choice of measurement points) than the DT method. A comparison of the two methods is carried out by inversion of both simulated and experimental scattered field data.     

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.     

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography(CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform(NUFFT) is presented in this work along with advanced total variation(TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.     

On the use of discrete wavelet transform for solving integral equations of acoustic scattering

In this paper, the discrete wavelet transform (DWT) is used to solve the dense system of equations which arises from integral equation of acoustic scattering. The DWT using appropriate wavelet family for acquiring larger sparsification of the system matrix is used to obtain a sparse approximation to the transformed matrix that is used in place of the original matrix in an iterative solver. Alternatively DWT is also used to design sparse preconditioners for an iterative method. Also, DWT-based preconditioners are constructed to accelerate iterative Krylov subspace methods. Convergence rates and number of operations are discussed for each case.

     

Specular propagation over rough surfaces: numerical assessment of Uscinski and Stanek's mean Green's function technique

The purpose of this paper is to numerically evaluate the effectiveness and accuracy of Uscinski and Stanek's mean Green's function technique for computing the mean field of a wave scattered by a rough surface. We present here a direct comparison of this technique with a rigorous numerical method, the forward scattering integral equation method, and another analytical method, the first-order smoothing approximation. Furthermore, we compare the roughness generated equivalent admittance using the three methods. Numerical computations reveal that the scattered field calculated by this technique is not accurate particularly for the equivalent admittance at low grazing angles, even though the mean surface current density is recovered when the wave has traversed several correlation lengths on the surface.     

Exact Periodic Wave Solution of Extended (2+1)-Dimensional Shallow Water Wave Equation with Generalized Dp-operators

With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized D_p-operators in term of the Hirota direct method when the appropriate value of p is determined. Furthermore, the resulting approach is applied to solve the extended (2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis.     

Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A₁, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, in-cluding the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations.     

ELASTIC WAVE SCATTERING AND DYNAMIC STRESS CONCENTRATIONS IN CYLINDRICAL SHELLS WITH A CIRCULAR CUTOUT

In this paper, based on the theory of elastic wave motion for open cylindrical shell, wave scattering and dynamic stress concentrations in open cylindrical shells with a hole are studied by making use of small parameter perturbation methods and boundary-integral equation techniques. The boundary-integral equations and iterative imminent series of scattered waves around the cavity of the cylindrical shell are derived. By employing this method, the approximately analytical solutions of scattered waves on the edge of cutout are gained. The computational formula for getting the dynamic stress concentration factors on the contour of cavity is developed. As an example, the numerical results of these dynamic stress concentration factors are graphically presented and discussed. The analytical methods put forward in the present work have practical significances for solving the problem of elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout.     

Phase retrieval and coherent diffraction imaging by a linear scanning pinhole sampling array

We propose a new method for phase retrieval and coherent diffraction imaging by a specially designed pinhole sampling array (PSA) based on a liquid crystal spatial light modulation. We demonstrate that the phase and the amplitude of the wave front passing through a pinhole sampling array plate can be directly extracted from the inverse Fourier transform of the far-field diffraction intensity pattern. Scanning the whole surface of the wave front by such a series of the PSA plates, we can assemble the extracted complex amplitude to a two-dimensional discrete distribution of the sampled wave front covering the entire PSA plate plane in the scanning consequence. We called it linear scanning pinhole sampling array (LSPSA). Thus the wave front can be reconstructed which avoids any iterative algorithms. Furthermore, it provides a feasible approach for lensless coherent diffraction imaging in real-time.     

三维粗糙面电磁双站散射的直接型区域分解计算

提出三维粗糙面双站电磁散射的直接型有限元-区域分解方法.首先建立含有迭代Robin边界条件(IRBC)的区域分解法耦合模型,再用内视法导出高度稀疏分块的分区耦合矩阵,之后给出缩减耦合矩阵带宽的子区域排序方法和IRBC的FFT加速算法.用有限元-完全匹配层和未分区的有限元-IRBC方法验证数值结果.     

An ART iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging

X-ray diffraction enhanced imaging (DEI) has extremely high sensitivity for weakly absorbing low-Z samples in medical and biological fields. In this paper, we propose an Algebra Reconstruction Technique (ART) iterative reconstruction algorithm for computed tomography of diffraction enhanced imaging (DEI-CT). An Ordered Subsets (OS) technique is used to accelerate the ART reconstruction. Few-view reconstruction is also studied, and a partial differential equation (PDE) type filter which has the ability of edge-preserving and denoising is used to improve the image quality and eliminate the artifacts. The proposed algorithm is validated with both the numerical simulations and the experiment at the Beijing synchrotron radiation facility (BSRF).