On the Inverse Problem of Scattering from a Perfectly Conducting Elliptic Cylinder

1972 ◽  
Vol 50 (17) ◽  
pp. 1987-1992 ◽  
Author(s):  
F. H. Vandenberghe ◽  
W. M. Boerner
Keyword(s):  
Inverse Problem ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Low Frequency ◽  
Elliptic Cylinder ◽  
Cylindrical Wave ◽  
Wave Functions ◽  
Principal Axes ◽  
Expansion Coefficients ◽  
Model Technique

The inverse problem of electromagnetic scattering from a perfectly conducting elliptic cylinder for the low-frequency case is considered. The approach is based on the model technique presented in Boerner and Vandenberghe, conjecturing that the salient features of the scatterer can be determined from the far scattered field via matrix inversion. This follows the low-frequency formulation of the scattered field as given by Udagawa and Miyazaki rather than from an expansion in the elliptic cylindrical wave functions. It is then shown that the characteristic parameters of the ellipse, i.e. the principal axes a′ and b′ and the numerical eccentricity ε, can be directly recovered from the expansion coefficients associated with circular cylindrical wave functions, as is presented in Udagawa and Miyazaki.

On the Inverse Problem of Scattering from a Perfectly Conducting Prolate Spheroid

1972 ◽  
Vol 50 (8) ◽  
pp. 754-759 ◽  
Author(s):  
F. H. Vandenberghe ◽  
W. M. Boerner
Keyword(s):  
Inverse Problem ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Spherical Wave ◽  
Prolate Spheroid ◽  
Wave Functions ◽  
Prolate Spheroidal ◽  
Spheroidal Wave Functions ◽  
Prolate Spheroidal Wave Functions ◽  
Model Technique

The inverse problem of electromagnetic scattering from a prolate spheroidal scatterer is considered. The approach is based on the model technique presented in Boerner and Vandenberghe, conjecturing that the salient features of the scatterer can be determined from the far scattered field via matrix inversion. An expansion in spherical wave functions for the scattered field based on the formulation of Senior is employed instead of an expansion in prolate spheroidal wave functions. It is then shown that the characteristic parameters of the ellipse generating the prolate spheroid (the interfocal distance d and the eccentricity ε) can be directly recovered from Senior's expansion coefficients.

Determination of the Electrical Radius ka of a Circular Cylindrical Scatterer from the Scattered Field

1971 ◽  
Vol 49 (7) ◽  
pp. 804-819 ◽  
Author(s):  
W. M. Boerner ◽  
F. H. Vandenberghe ◽  
M. A. K. Hamid
Keyword(s):  
Inverse Problem ◽  
Scattered Field ◽  
Measurement Techniques ◽  
Optimization Procedure ◽  
Cylindrical Wave ◽  
Matrix Inversion ◽  
Nonsingular Matrix ◽  
Double Precision ◽  
Scattering Geometry ◽  
Expansion Coefficients

The inverse problem of scattering for a circular cylindrical scattering geometry is considered. The transverse far field components are related to the Fourier coefficients of the circular cylindrical wave expansion in terms of the scattered field matrix. The associated determinant which describes the scattering geometry is formulated in closed form. To achieve nonsingular matrix inversion, a novel, determinate optimization procedure for the measurement aspect angles is derived and proved. Measurement techniques or experimental results are not presented. Yet, it is shown analytically that the unknown expansion coefficients can be recovered with standard double precision matrix inversion techniques to the degree of accuracy dictated only by any suitable measurement technique. Assuming the required set of expansion coefficients {an}TM and/or {bn}TE is found, it is shown that the electrical radius ka of the scatterer can be determined from four contiguous expansion coefficients in the TM as well as the mixed TM–TE cases. Only the TE case is an exception for which a more elaborate formulation exists. The relationships between contiguous expansion coefficients of both electric and magnetic type are relevant to the general cylindrical inverse problem, since the electrical radius can be directly recovered from the scattered field data. Furthermore, the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.

Determination of the Electrical Radius ka of a Spherical Scatterer from the Scattered Field

1971 ◽  
Vol 49 (11) ◽  
pp. 1507-1535 ◽  
Author(s):  
W. M. Boerner ◽  
F. H. Vandenberghe
Keyword(s):  
Inverse Problem ◽  
Closed Form ◽  
Scattered Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vector Wave ◽  
Wave Expansion ◽  
Spherical Scatterer ◽  
Expansion Coefficients ◽  
Spherical Vector

The inverse problem of scattering for a spherical vector scattering geometry is considered. The transverse scattered field components are related to the expansion coefficients of Hansen's vector wave expansion in terms of the scattered field matrix. This matrix needs to be inverted to obtain the unknown expansion coefficients which are required to recover the shape of the target in question. Since the particular properties of the spherical vector wave expansion may cause highly instable matrix inversion, an analytical, closed form solution of the determinant associated with the scattered field matrix was sought. For vector scattering geometries representing the mth degree multipole cases such closed form solutions for the associated determinant of truncated order 2N are derived, using a novel complementary series expansion for the employed forms of the associated Legendre's functions of the first kind. A novel determinate optimization procedure is presented which enables the specification of the optimal distribution of measurement aspect angles within any given finite measurement cone of the unit sphere of directions. The closed form solution for nonsymmetrical vector scattering geometries is presented in Appendix III only for the value N = 3 (m = 0 and 1) employing properties of quadratic forms as derived in Appendix II. It is then shown that the electrical radius ka of a perfectly conducting spherical scatterer can be directly recovered from a finite number of contiguous expansion coefficients similar to the cylindrical case presented in Boerner, Vandenberghe, and Hamid. Furthermore, relationships between contiguous expansion coefficients of both electric and magnetic type result, which are relevant to the general inverse problem since the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.

scholarly journals Two-Dimensional Scattering by a Homogeneous Gyrotropic-Type Elliptic Cylinder

2016 ◽  
Vol 5 (3) ◽  
pp. 106
Author(s):  
A. K. Hamid ◽  
F. Cooray
Keyword(s):  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Separation Of Variables ◽  
Elliptic Cylinder ◽  
Wave Functions ◽  
Two Dimensional ◽  
Vector Wave ◽  
Expansion Coefficients ◽  
Scattering Cross Sections ◽  
Uniform Plane

The separation of variables procedure has been employed for solving the problem of scattering from an infinite homogeneous gyrotropic-type (G-type) elliptic cylinder, when a uniform plane electromagnetic wave perpendicular to its axis, illuminates it. The formulation of the problem involves expanding each electric and magnetic field using appropriate elliptic vector wave functions and expansion coefficients. Imposing suitable boundary conditions at the surface of the elliptic cylinder yields the unknown expansion coefficients related to the scattered and the transmitted fields. To demonstrate how the various G-type materials and the size of the cylinder affects scattering from it, plots of scattering cross sections are given for cylinders having different permittivity/permeability tensors and sizes.

Electromagnetic scattering by a system of two parallel dielectric prolate spheroids

1990 ◽  
Vol 68 (4-5) ◽  
pp. 376-384 ◽  
Author(s):  
M. F. R. Cooray ◽  
I. R. Ciric ◽  
B. P. Sinha
Keyword(s):  
Electromagnetic Wave ◽  
Incident Wave ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Angle Of Incidence ◽  
Algebraic Equations ◽  
Column Matrix ◽  
Prolate Spheroids ◽  
Expansion Coefficients

An exact solution to the problem of scattering of a plane electromagnetic wave by two dielectric prolate spheroids with parallel major axes is obtained by expanding the incident, scattered, and transmitted electric and magnetic fields in terms of an appropriate set of vector spheroidal eigenfunctions. The incident wave is considered to be a monochromatic, uniform plane electromagnetic wave of arbitrary polarization and angle of incidence. The boundary conditions are imposed by expressing the electromagnetic field scattered by one spheroid in terms of the spheroidal coordinates attached to the other, using the translational addition theorems for vector spheroidal wave functions. The column matrix of the total transmitted and scattered field-expansion coefficients is equal to the product of a square matrix, which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident field-expansion coefficients. The solution of the associated set of algebraic equations gives the unknown transmitted and scattered field-expansion coefficients. Even though the problem is formulated in general, the numerical results are presented for the bistatic and backscattering cross sections of two lossless prolate spheroids with various axial ratios and center-to-center distances.

Electromagnetic scattering by a lossy dielectric-coated elliptic cylinder

2003 ◽  
Vol 81 (5) ◽  
pp. 771-778 ◽  
Author(s):  
A -K Hamid ◽  
M I Hussein
Keyword(s):  
Electromagnetic Wave ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Wave Scattering ◽  
Elliptic Cylinder ◽  
Numerical Results ◽  
Dielectric Constants ◽  
Mathieu Functions ◽  
Electromagnetic Wave Scattering ◽  
Lossy Dielectric

The problem of electromagnetic wave scattering by a lossy dielectric-coated elliptic cylinder is analyzed using elliptic waves expressed in terms of complex Mathieu functions. Numerical results are obtained for the scattered field in the far zone for different axial ratios, lossy dielectric constants, and angles of incidence. The numerical results show a significant change in backscattering echo due to the lossy dielectric coating. PACS No.: 42.25.Fx

Electromagnetic Scattering by a Metallic Cylinder Buried in a Lossy Medium With the Cylindrical-Wave Approach

2013 ◽  
Vol 10 (1) ◽  
pp. 179-183 ◽  
Author(s):  
Fabrizio Frezza ◽  
Lara Pajewski ◽  
Cristina Ponti ◽  
Giuseppe Schettini ◽  
Nicola Tedeschi
Keyword(s):  
Electromagnetic Scattering ◽  
Cylindrical Wave ◽  
Wave Approach ◽  
Lossy Medium ◽  
Metallic Cylinder

An inverse problem in low-frequency scattering by an ellipsoidally embossed surface

Wave Motion ◽  
1994 ◽  
Vol 20 (1) ◽  
pp. 33-39 ◽  
Author(s):  
George Dassios ◽  
R.J. Lucas
Keyword(s):  
Inverse Problem ◽  
Low Frequency
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