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Monotonicity in inverse scattering for Maxwell’s equations

Albicker, Annalena; Griesmaier, Roland

We consider the inverse scattering problem to recover the support of penetrable scattering objects in three-dimensional free space from far field observations of scattered time-harmonic electromagnetic waves. The observed far field data are described by far field operators that map superpositions of plane wave incident fields to the far field patterns of the corresponding scattered waves. We discuss monotonicity relations for the eigenvalues of linear combinations of these operators with suitable probing operators. These monotonicity relations yield criteria and algorithms for reconstructing the support of scattering objects
from the corresponding far field operators. To establish these results we combine the monotonicity relations with certain localized vector wave functions that have arbitrarily large energy in some prescribed region while at the same time having arbitrarily small energy on some other prescribed region. Throughout we suppose that the relative magnetic permeability of the scattering objects is one, while their real-valued relative electric permittivity maybe inhomogeneous and the permittivity contrast may even change sign. ... mehr

Volltext §
DOI: 10.5445/IR/1000134454
Veröffentlicht am 25.06.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 06.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000134454
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 34 S.
Serie CRC 1173 Preprint ; 2021/29
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter inverse scattering, Maxwell’s equations, monotonicity, far field operator, inhomogeneous medium
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