Reconstruction of electromagnetic minimum energy sources in a prolate spheroid

Johan Sten

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)

Abstract

The inverse problem of reconstructing time‐harmonic minimum energy current distributions in a spheroidal volume from given data of far‐field radiation is addressed. Following the procedure outlined by Marengo and Devaney [1999], we formulate, upon deriving a spherical harmonics expansion of the electromagnetic field radiated by a current inside a prolate spheroid, the inverse problem in terms of linear operator theory. Owing to the lack of orthogonality of spheroidal vector wave functions, every eigenfunction will couple with several spherical radiation modes at a time, making the solution rather involved. Simplification is achieved in the special case of rotationally symmetric fields, for which numerical examples are given. As an application, the use of minimum energy currents for identifying distributions of nonradiating current in a spheroidal volume is pointed out.
Original languageEnglish
Article numberRS2020
Number of pages10
JournalRadio Science
Volume39
Issue number2
DOIs
Publication statusPublished - 2004
MoE publication typeA1 Journal article-refereed

Fingerprint

prolate spheroids
energy sources
inverse problem
Inverse problems
electromagnetism
Radiation
spherical harmonics
electromagnetic field
Wave functions
Eigenvalues and eigenfunctions
Electromagnetic fields
energy
Mathematical operators
linear operators
orthogonality
radiation
current distribution
simplification
eigenvectors
electromagnetic fields

Keywords

  • inverse problems
  • minimum energy sources
  • prolate spheroid

Cite this

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Reconstruction of electromagnetic minimum energy sources in a prolate spheroid. / Sten, Johan.

In: Radio Science, Vol. 39, No. 2, RS2020, 2004.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Reconstruction of electromagnetic minimum energy sources in a prolate spheroid

AU - Sten, Johan

PY - 2004

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N2 - The inverse problem of reconstructing time‐harmonic minimum energy current distributions in a spheroidal volume from given data of far‐field radiation is addressed. Following the procedure outlined by Marengo and Devaney [1999], we formulate, upon deriving a spherical harmonics expansion of the electromagnetic field radiated by a current inside a prolate spheroid, the inverse problem in terms of linear operator theory. Owing to the lack of orthogonality of spheroidal vector wave functions, every eigenfunction will couple with several spherical radiation modes at a time, making the solution rather involved. Simplification is achieved in the special case of rotationally symmetric fields, for which numerical examples are given. As an application, the use of minimum energy currents for identifying distributions of nonradiating current in a spheroidal volume is pointed out.

AB - The inverse problem of reconstructing time‐harmonic minimum energy current distributions in a spheroidal volume from given data of far‐field radiation is addressed. Following the procedure outlined by Marengo and Devaney [1999], we formulate, upon deriving a spherical harmonics expansion of the electromagnetic field radiated by a current inside a prolate spheroid, the inverse problem in terms of linear operator theory. Owing to the lack of orthogonality of spheroidal vector wave functions, every eigenfunction will couple with several spherical radiation modes at a time, making the solution rather involved. Simplification is achieved in the special case of rotationally symmetric fields, for which numerical examples are given. As an application, the use of minimum energy currents for identifying distributions of nonradiating current in a spheroidal volume is pointed out.

KW - inverse problems

KW - minimum energy sources

KW - prolate spheroid

U2 - 10.1029/2003RS002973

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JO - Radio Science

JF - Radio Science

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