scholarly journals Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3089
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Single Frequency ◽  
Limited Data ◽  
Scattering Problems ◽  
Approximation Accuracy ◽  
Imaging Results ◽  
Exact Evaluation ◽  
Spread Function ◽  
Scattered Fields

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

scholarly journals NDF of Scattered Fields for Strip Geometries

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 202
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Singular Value ◽  
Scattering Operator ◽  
Scattering Problems ◽  
First Order ◽  
Incident Plane ◽  
Minimum Number ◽  
Scattered Fields ◽  
Value Decomposition

Solving inverse scattering problems by numerical methods requires investigating the number of independent pieces of information that can be reconstructed stably. To this end, we address the evaluation of the Number of Degrees of Freedom (NDF) of far-zone scattered fields for some strip geometries under the first-order Born approximation. The analysis is performed by employing the Singular Value Decomposition (SVD) of the scattering operator in the two-dimensional scalar geometry of one or more strips illuminated by a TM polarized plane wave. It is known that investigating the scattering scene at different incident plane waves (multi-view configuration) enhances the NDF. Therefore we mean to examine the minimum number of incident plane waves providing the NDF of the scattered fields both by theoretical estimations and numerical verifications.

Use of Wave Boundary Elements for Acoustic Computations

2003 ◽  
Vol 11 (02) ◽  
pp. 305-321 ◽  
Author(s):  
Emmanuel Perrey-Debain ◽  
Jon Trevelyan ◽  
Peter Bettess
Keyword(s):  
Boundary Element ◽  
Degrees Of Freedom ◽  
Plane Waves ◽  
Current Method ◽  
Boundary Element Methods ◽  
Element Formulation ◽  
Scattering Problems ◽  
Direct Collocation ◽  
New Type ◽  
New Formulation

Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this work, a new type of interpolation for the acoustic field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation has been found in the current work to be highly successful. Results are shown for a variety of classical scattering problems, and also for scattering from nonconvex obstacles. Notable results include a conclusion that, using this new formulation, only approximately 2.5 degrees of freedom per wavelength are required. Compared with the 8 to 10 degrees of freedom normally required for conventional boundary (and finite) elements, this shows the marked improvement in storage requirement. Moreover, the new formulation is shown to be extremely accurate. It is estimated that for 2D Helmholtz problems, and for a given computational resource, the frequency range allowed by this method is extended by a factor of three over conventional direct collocation Boundary Element Method. Recent successful developments of the current method for plane elastodynamics problems are also briefly outlined.

scholarly journals PSF Analysis of the Inverse Source and Scattering Problems for Strip Geometries

Electronics ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 754
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Closed Form ◽  
Point Spread Function ◽  
Scattered Field ◽  
Numerical Results ◽  
Main Lobe ◽  
Scattering Problems ◽  
Approximation Accuracy ◽  
Point Spread ◽  
Spread Function ◽  
Form Evaluation

This paper is concerned with estimating the achievable resolution in the reconstruction of strip sources from the knowledge of its radiated field and strip objects from the knowledge of its scattered field. In particular, the study focuses on the evaluation of the point spread function (PSF), providing the reconstruction of a point-like unknown. Since this can be performed only numerically for most geometries, an approximate closed-form evaluation is introduced and compared with the exact one. Numerical results confirm the approximation accuracy, at least in the main lobe region of the PSF, which is the most important, as far as the discussion about resolution is concerned. The main results of the analysis concern the space invariance of the PSF of the considered geometries, which means that resolution is the same over the whole investigation domain, and the appreciation of its values for the inverse source and scattering problems.

scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

Numerical Simulation of Multiple Floating Structures With Nonlinear Constraints

2002 ◽  
Vol 124 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Subrata K. Chakrabarti
Keyword(s):  
Degrees Of Freedom ◽  
Order Theory ◽  
Frequency Domain Analysis ◽  
Body Motion ◽  
Single Frequency ◽  
Integration Scheme ◽  
Mooring Lines ◽  
Floating Structures ◽  
Irregular Wave ◽  
Exciting Forces

A versatile and efficient numerical analysis is developed to compute the responses of a moored floating system composed of multiple floating structures. Structures such as tankers, semisubmersibles, FPSOs, SPARs, TLPs, and SPMs connected by mooring lines, connectors or fenders may be analyzed individually or collectively including multiple interaction. The analysis is carried out in the time domain assuming rigid body motion for the structures, and the solution is generated by a forward integration scheme. The analysis includes the nonlinearities in the excitation, damping, and restoring terms encountered in a typical mooring system configuration. It also allows for instabilities in the tower oscillation as well as slack mooring lines. Certain simplifications in the analysis have been made, which are discussed. The exciting forces in the analysis are wind, current, and waves (including a steady and an oscillating drift force), which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. For regular waves either linear, stretched linear or fifth order theory may be used. The irregular wave may be included as a given spectral model (e.g., PM or JONSWAP). The vessels are free to respond to the exciting forces in six degrees of freedom—surge, sway, heave, roll, pitch, and yaw. The tower, when present, is free to respond in two degrees of freedom—oscillation and precession. The loads in the mooring lines are determined from prescribed tension-strain tables for the lines. Rigid mooring arms can be analyzed by allowing for compression in the load-strain table. Fenders may be input similarly through load compression tables. In order to establish the stability and accuracy of the solution, comparison of the results with linearized frequency domain analysis was made. The analysis is verified by several different model test results for different structure configurations in regular and random seas. Some of the interesting aspects of nonlinear system are shown with a few examples.

On the degrees of freedom of scattered fields

1989 ◽  
Vol 37 (7) ◽  
pp. 918-926 ◽  
Author(s):  
O.M. Bucci ◽  
G. Franceschetti
Keyword(s):  
Degrees Of Freedom ◽  
Scattered Fields

Scattering of a Gaussian beam by an anisotropic-coated eccentric conducting circular cylinder

2020 ◽  
Vol 12 (9) ◽  
pp. 900-905
Author(s):  
Shi-Chun Mao ◽  
Zhen-Sen Wu ◽  
Zhaohui Zhang ◽  
Jiansen Gao ◽  
Lijuan Yang
Keyword(s):  
Gaussian Beam ◽  
Plane Waves ◽  
Approximate Expression ◽  
Transverse Magnetic ◽  
Addition Theorem ◽  
Electric Polarization ◽  
Electric Conductor ◽  
Solution Convergence ◽  
Local Coordinates ◽  
Scattered Fields

AbstractA solution to the problem of Gaussian beam scattering by a circular perfect electric conductor coated with eccentrically anisotropic media is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with Taylor's series. The transmitted field in the anisotropically coated region is expressed as an infinite summation of Eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The addition theorem for cylindrical functions is applied to transfer from the local coordinates to the global ones. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting a similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the eccentric geometry comes to the concentric one.

scholarly journals Computing the T-matrix of a scattering object with multiple plane wave illuminations

2017 ◽  
Vol 8 ◽  
pp. 614-626 ◽  
Author(s):  
Martin Fruhnert ◽  
Ivan Fernandez-Corbaton ◽  
Vassilios Yannopapas ◽  
Carsten Rockstuhl
Keyword(s):  
Plane Waves ◽  
The Finite Element Method ◽  
Full Wave ◽  
Electric Dipoles ◽  
Complicated Object ◽  
T Matrix ◽  
Multiple Plane ◽  
Optical Nanostructures ◽  
Scattered Fields ◽  
Matrix Calculation

Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers.

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