An exact far-field inversion for the Born approximation and plane wave decompositions for Hankel functions

1994 ◽  
Vol 45 (5) ◽  
pp. 784-793 ◽  
Author(s):  
Norbert Gorenflo
Keyword(s):  
Plane Wave ◽  
Born Approximation ◽  
Far Field ◽  
Hankel Functions ◽  
Field Inversion

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

scholarly journals Far-Field Inversion for the Deep Interior Scanning CubeSat

2019 ◽  
Vol 55 (4) ◽  
pp. 1683-1697 ◽  
Author(s):  
Mika Takala ◽  
Patrick Bambach ◽  
Jakob Deller ◽  
Esa Vilenius ◽  
Manfred Wittig ◽  
...  
Keyword(s):  
Far Field ◽  
Deep Interior ◽  
Field Inversion

scholarly journals Διάδοση κυμάτων σε ανομοιογενή μέσα

2007 ◽  
Author(s):  
Κωνσταντίνος Αναγνωστόπουλος
Keyword(s):  
Field Equation ◽  
Plane Wave ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Field Operator ◽  
Sampling Point ◽  
Far Field ◽  
Two Dimensional ◽  
Time Harmonic

The scope of this doctoral thesis is, first, to develop an analytical, in principle, method for the solution of the two-dimensional scattering problem of time-harmonic elastic plane waves by a homogeneous orthotropic scatterer, second, to establish the complete theoretical framework, which is necessary for the application of the Linear Sampling Method (LSM) to the problem of reconstructing the support of twodimensional elastic anisotropic inclusions embedded in isotropic media and, third, to derive an extension of the Factorization Method (FM) to the inverse elastic scattering problem by penetrable isotropic bodies for time-harmonic plane wave incidence. Aconcise description of the contents of the thesis is outlined below. Chapter one contains a detailed bibliographical search, which is related to the analytical and numerical methods (with emphasis on the former) usually employed for the solution of the direct scattering problem by anisotropic elastic bodies as well as to those inverse scattering techniques, which are usually referred to as sampling and probe methods and, in particular, the LSM and the FM. Chapter two commences with a brief discussion of some fundamental results from the linearized theory of dynamic elasticity. The problem of a rigorous analysis of the elasticity equation governing the elastic behaviour of an orthotropic material in two dimensions is then addressed. This analysis, which is based on a suitable diagonalization applied to the underlying differential system and a plane wave expansion of the sought field, results in a Fourier series expansion for the displacement field describing the elastic deformations of the orthotropic medium and is complemented by the results of appendix A. A mathematical model for the solution of the associated transmission scattering problem, taking advantage of the aforementioned expansion, is also settled and analyzed. The details of its numerical treatment can be found in appendix B. Finally, numerical results for several inclusion geometries and a system thereof with material properties characterized by the cubic symmetryclass -a special case of the orthotropic class of symmetry- are presented. In chapter three, the LSM is extended to the case of a two-dimensional homogeneous anisotropic inclusion embedded in an isotropic background medium. The concepts of the elastic Herglotz function, the elastic far-field operator and the corresponding far-field equation, on which the formulation of the LSM heavily relies, are first introduced. Then, the proposed inverse scattering scheme is introduced and discussed in detail. By means of an appropriate operator decomposition of the far-field operator,the main theorem of the method, concerning the characterization of the behaviour of an approximate solution to the far-field equation at the boundary of the scatterer, is proved. In the end of the third chapter, the performance of the LSM is examined by applying it to a set of different geometric configurations of the elastic inclusion, filled with a cubic anisotropic material. An investigation of the effect of the various parameters entering the problem, such as the scatterer’s degree of anisotropy, the polarization of the elastic point source located at the sampling point and the noise level in the synthetic far-field data, on the reconstructed geometric profiles’ quality,is carried out. In the fourth chapter, the FM is elaborated for the shape reconstruction of a penetrable isotropic elastic body from the knowledge of the far-field pattern of the scattered fields for plane incident waves. The theoretical analysis is conducted in three dimensions and focuses on deriving a factorization of the far-field operator, which is the cornerstone for the applicability of the particular inversion scheme, and investigating thorougly the properties of the involved operators. This investigation gave birth to a number of interesting by-products and one of them, namely, a regularity estimate for the solution of a particular form of the corresponding interior transmission problem, is the subject matter of appendix C. By means of the proposed factorization, a series of theorems, which finally lead to an explicit characterization of the scattering obstacle, is then proved. In the end of the chapter, the performance of the investigated inverse scattering technique is demonstrated by applying it to specific two-dimensional elastic scatterer reconstruction problems involving different scatterer configurations and various choices for their constitutive parameters. The effect of using different levels of additive random noise in the forward synthetic data and combining results obtained for different polarizations of the elastic point source located at the sampling point, on the quality of the reconstructed profiles, is also examined. Finally, chapter five draws the conclusions that flow from the foregoing chapters and discusses the contribution of this doctoral thesis. A brief discussion about possible future studies is also included.

LOW-FREQUENCY ACOUSTIC SCATTERING BY AN INHOMOGENEOUS MEDIUM

2005 ◽  
Vol 15 (10) ◽  
pp. 1459-1468 ◽  
Author(s):  
GEORGE VENKOV
Keyword(s):  
Refractive Index ◽  
Plane Wave ◽  
Inhomogeneous Medium ◽  
Acoustic Waves ◽  
Spherical Wave ◽  
Low Frequency ◽  
Far Field ◽  
Scattering Medium ◽  
Wave Incidence ◽  
Plane Wave Incidence

This paper deals with the scattering of time-harmonic acoustic waves by inhomogeneous medium. We study the problem to recover the near and the far field using a priori information about the refractive index and the support of inhomogeneity. The incident spherical wave is modified in such a way as to recover the plane wave incidence when the source point approaches infinity. Applying the low-frequency expansions, the scattering medium problem is reduced to a sequence of potential problems for the approximation coefficients in the presence of a monopole singularity located at the source of incidence. Complete expansions for the integral representation formula in the near field as well as for the scattering amplitude in the far field are provided. The method is applied to the case of a spherical region of inhomogeneity and a radial dependent refractive index. As the point singularity tends to infinity, the relative results recover the scattering medium problem for plane wave incidence.

scholarly journals Scattering of Alpha-particles by a Vibrational Nucleus

1962 ◽  
Vol 15 (2) ◽  
pp. 135 ◽  
Author(s):  
LJ Tassie
Keyword(s):  
Elastic Scattering ◽  
Plane Wave ◽  
Experimental Test ◽  
Born Approximation ◽  
Alpha Particles ◽  
Nuclear Surface ◽  
Vibrational States ◽  
Phonon Excitation ◽  
Plane Wave Born Approximation ◽  
Good Agreement

The elastic and inelastic scattering of cx-particles by a vibrational nucleus is calculated using plane-wave Born approximation. The excitation of both single-phonon and twophonon states is considered. The effect of the diffuseness of the nuclear surface is included. The result for elastic scattering and the excitation of the single-phonon 2+ and 3- states is in good agreement with experiment for .oNi. The approximations used are discussed, and it is suggested that excitation of 0+, 1-, and 5- states should provide the best experimental test of the theory of two-phonon excitation of nuclei. The energies of the vibrational states are also considered.

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