### Abstract

*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 language | English |
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Article number | RS2020 |

Number of pages | 10 |

Journal | Radio Science |

Volume | 39 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

MoE publication type | A1 Journal article-refereed |

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### Keywords

- inverse problems
- minimum energy sources
- prolate spheroid

### Cite this

*Radio Science*,

*39*(2), [RS2020]. https://doi.org/10.1029/2003RS002973

}

*Radio Science*, vol. 39, no. 2, RS2020. https://doi.org/10.1029/2003RS002973

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

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

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

AU - Stén, Johan

PY - 2004

Y1 - 2004

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

DO - 10.1029/2003RS002973

M3 - Article

VL - 39

JO - Radio Science

JF - Radio Science

SN - 0048-6604

IS - 2

M1 - RS2020

ER -