Near-field Imaging Point-like Scatterers and Extended Elastic Solid in a Fluid

2016 ◽  
Vol 19 (5) ◽  
pp. 1317-1342
Author(s):  
Tao Yin ◽  
Guanghui Hu ◽  
Liwei Xu
Keyword(s):  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Elastic Solid ◽  
Field Measurements ◽  
Factorization Method ◽  
Music Algorithm ◽  
Incident Wavelength ◽  
Imaging Point ◽  
Necessary And Sufficient

AbstractConsider the time-harmonic acoustic scattering from an extended elastic body surrounded by a finite number of point-like obstacles in a fluid. We assume point source waves are emitted from arrayed transducers and the signals of scattered near-field data are recorded by receivers not far away from the scatterers (compared to the incident wavelength). The forward scattering can be modeled as an interaction problem between acoustic and elastic waves together with a multiple scattering problem between the extend solid and point scatterers. We prove a necessary and sufficient condition that can be used simultaneously to recover the shape of the extended elastic solid and to locate the positions of point scatterers. The essential ingredient in our analysis is the outgoing-to-incoming (OtI) operator applied to the resulting near-field response matrix (or operator). In the first part, we justify the MUSIC algorithm for locating point scatterers from near-field measurements. In the second part, we apply the factorization method, the continuous analogue of MUSIC, to the two-scale scattering problem for determining both extended and point scatterers. Numerical examples in 2D are demonstrated to show the validity and accuracy of our inversion algorithms.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Determination of electromagnetic source localization with factorization method

2021 ◽  
pp. 1-10
Author(s):  
Nuri Gokmen Karakiraz ◽  
Agah Oktay Ertay ◽  
Ersin Göse
Keyword(s):  
Integral Equation ◽  
Incident Angle ◽  
Near Field ◽  
Field Measurements ◽  
Factorization Method ◽  
Field Equations ◽  
Direct Sampling ◽  
Test Equation ◽  
Inverse Source Problems ◽  
Electromagnetic Source

Abstract The factorization method (FM) is an attractive qualitative inverse scattering technique for the detection of geometrical features of unknown objects. This method depends on the selection of regularization parameters slightingly and has low calculation necessities. The aim of this work is to present a near-field FM for inverse source problems that have many applications. A modified test equation is obtained by converting the far-field term to Hankel's function. A different method has been proposed by manipulating the asymptotic approximation of Hankel's function in order to obtain near-field equations with incident angle and distance parameters. The novelty of this study is an integral equation based on the FM, which consists of multifrequency sparse near-field electric field measurements. We proved that the solution of the proposed integral equation gives information about the location of scatterers. The proposed algorithm is validated with simulation results and the capabilities of the presented method are assessed with several frequency regions and sources. Additionally, the presented method is compared with the direct sampling method in order to understand the performance of the proposed approach over a given scenario. The developed FM provides accurate results for electromagnetic source problems.

Scattering in a Shallow Ocean with an Elastic Seabed

1997 ◽  
Vol 05 (04) ◽  
pp. 403-431 ◽  
Author(s):  
R. P. Gilbert ◽  
Zhongyan Lin
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Near Field ◽  
Scattering Problem ◽  
Sufficient Conditions ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Parallel Computer ◽  
Hankel Transformation ◽  
Necessary And Sufficient

In this paper the boundary integral equation method is used to solve a scattering problem in a shallow ocean with an elastic seabed. The Hankel transformation and Mittag–Leffler decomposition were used to construct the propagating solution for both far-field and near-field. In particular, necessary and sufficient conditions are found for the existence of the propagating solution. Using the propagating solution, the scattering problem is recast as a boundary integral equation. A numerical algorithm is developed for solving this boundary integral equation and its implementation on a T3D parallel computer is used to compute an illustrative example.

LOW-FREQUENCY ACOUSTIC SCATTERING OF A PLANE WAVE FROM A SOFT AND HARD TORUS

2007 ◽  
Vol 15 (02) ◽  
pp. 181-197 ◽  
Author(s):  
GEORGE VENKOV
Keyword(s):  
Separation Of Variables ◽  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Low Frequency ◽  
Diagonal Form ◽  
Legendre Functions ◽  
Algebraic Equations ◽  
Analytical Technique ◽  
Linear Algebraic Equations

A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. It is shown that there exists exactly one toroidal coordinate system that fits the given geometry. The R-separation of variables is utilized to obtain the series expansion of the fields in terms of toroidal harmonics (half-integer Legendre functions of first and second kind). The scattering problem for the soft torus is solved analytically for the near field, governing the leading two low-frequency coefficients, as well as for the far field, where both the amplitude and the cross-section are evaluated. The scattering problem for the hard torus appears to be much more complicated in calculations. The Neumann boundary condition on the surface of the torus leads to a three-term recurrence relation for the series coefficients corresponding to the scattered fields. Thus, the potential boundary-value problem for the leading low-frequency approximations is reduced to infinite systems of linear algebraic equations with three-diagonal matrices. An analytical technique for solving systems of diagonal form is developed.

Application of the factorization method to retrieve a crack from near field data

2016 ◽  
Vol 24 (5) ◽  
Author(s):  
Jun Guo ◽  
Junhao Hu ◽  
Guozheng Yan
Keyword(s):  
Inverse Problems ◽  
Field Data ◽  
Near Field ◽  
Scattering Problem ◽  
Factorization Method ◽  
Point Sources ◽  
Impedance Boundary Condition ◽  
Complex Conjugate ◽  
Inversion Algorithm ◽  
Impedance Boundary

AbstractWe consider the inverse scattering problem of determining the shape of a crack with impedance boundary condition on one side from the complex conjugate of point sources placed on a closed curve which contains the crack. The near field factorization method is established to reconstruct the crack from the measurements on the same curve. Then, we deduce an inversion algorithm and present some numerical examples to show the viability of our method. So far as we know, when the incident waves are the point sources, the near field operator cannot be directly decomposed into the form that the factorization method required. However, we overcome this difficulty with the complex conjugate of point sources which are recently used in [Inverse Problems 30 (2014), Article ID 095005], [Inverse Problems 30 (2014), Article ID 045008] for the justification of the factorization method from near field data.

scholarly journals The factorization and monotonicity method for the defect in an open periodic waveguide

2020 ◽  
Vol 28 (6) ◽  
pp. 783-796
Author(s):  
Takashi Furuya
Keyword(s):  
Field Data ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Infinite Medium ◽  
Periodic Waveguide ◽  
Reconstruction Algorithms ◽  
Transmission Eigenvalues ◽  
Numerical Examples

AbstractWe consider the inverse scattering problem to reconstruct the defect in an infinite medium with periodicity in the upper half space from near field data. This paper has two contributions. Firstly, we mention that there is a mistake in the factorization method of the earlier paper [A. Lechleiter, The factorization method is independent of transmission eigenvalues, Inverse Probl. Imaging 3 2009, 1, 123–138] and give the correct one. Secondly, we give two reconstruction algorithms for the unknown defect by a combination of the factorization method and the monotonicity method. We also give numerical examples based on the former algorithm.

Scattering of aerodynamic noise by a semi-infinite compliant plate

1970 ◽  
Vol 43 (4) ◽  
pp. 721-736 ◽  
Author(s):  
D. G. Crighton ◽  
F. G. Leppington
Keyword(s):  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Aerodynamic Noise ◽  
Reciprocal Theorem ◽  
Volume Distribution ◽  
Fluid Loading ◽  
Plate Edge ◽  
Loading Effects ◽  
The Reciprocal Theorem

The acoustic scattering properties of a semi-infinite compliant plate immersed in turbulent flow are considered in the context of Lighthill's theory of aerodynamic noise. The turbulent eddies are replaced by a volume distribution of quadrupoles, and the reciprocal theorem used to transform the quadrupole scattering problem into one of the diffraction of a plane acoustic wave. This problem is solved by the Wiener–Hopf technique for the case when elastic forces in the plate are negligible, so that a local impedance condition relates the plate velocity to the pressure difference across the plate. Strong scattering of the near-field into propagating sound occurs when certain types of quadrupole lie sufficiently close to the plate edge, and we derive explicit expressions for the scattered fields in various cases. When fluid loading effects are small, and the plate relatively rigid, the results of Ffowcs Williams & Hall (1970) are recovered, in particular the U5 law for radiated intensity. A quite different behaviour is found in the case of high fluid loading, when the plate appears to be relatively limp. The radiated intensity then increases with flow velocity U according to a U6 law. In aeronautical situations, surface compliance is negligible in its effect on the scattering process, and the U5 law must then apply provided the surface is sufficiently large. On the other hand, the effect of appreciable surface compliance is to greatly inhibit the near-field scattering from the surface edge. This weaker scattering is likely to be observed in underwater applications, where fluid loading effects are generally so high as to render unattainable the condition for a plate to be effectively rigid.

scholarly journals The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yao Mao ◽  
Yongguang Chen ◽  
Jun Guo
Keyword(s):  
Boundary Condition ◽  
Inverse Scattering ◽  
Surface Impedance ◽  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Inverse Scattering Problem ◽  
Impedance Boundary Condition ◽  
Mathematical Basis ◽  
Impedance Boundary

We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.

scholarly journals Far-field to Near-field Data Relations for the Inverse Electromagnetic Scattering Problem

2021 ◽  
pp. 22-28
Author(s):  
Arnold Abramov ◽  
Yutao Yue
Keyword(s):  
Electromagnetic Scattering ◽  
Field Data ◽  
Near Field ◽  
Scattering Problem ◽  
Optimization Procedure ◽  
Field Measurements ◽  
The Other ◽  
Far Field ◽  
Dielectric Cylinder ◽  
Material Parameters

This paper considers (in general form) the problem of recovering information (size and material parameters) about the scattering object from far-field measurements. The order of solution and functions of each equation for the fields inside and outside the scattering object are discussed. Using well-known mathematical theorems, a simple equation has been derived that connects the far-field data on one side to the near-field data on the other side. Consequently, this equation has been used in an optimization procedure to find the parameters of the dielectric cylinder.

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