Abstract
An exact theory of the inverse scattering problems related to cylindrical bodies buried in a slab is established in two-dimensional scalar case. The theory dwells on two functional equations interrelating the outgoing wave solutions of the wave equation, which can be observed physically, with incoming wave solutions that are physically meaningless and irrealizable. One of these functional equations involves the measured radiation pattern in its kernel (material relation) while the other is independent of the measured data (universal relation). To establish the material relation one has to make far-field measurements with various incidence angles at various observation points and frequencies. The universal relation which guarantees some analytical properties of the field function results in a Stieltjes type integral equation. By solving these equations one gets the location, shape and permittivity of the inaccessible body. When the material of the half-space below the slab is made identical to that of the slab, then the results are reduced to that of the bodies buried in a half-space.
Résumé
Une théorie exacte de la diffraction scalaire inverse à deux dimensions par des objets noyés dans une plaque est établie. La théorie se base sur deux équations fonctionnelles liant les solutions en ondes sortantes de ľéquation des ondes, qui peuvent être observées physiquement avec les solutions en ondes entrantes qui sont physiquement sans signification et irréalisable. Une de ces équations fonctionnelles demande dans son noyau la fonction de rayonnement mesurée (relation matérielle) tandis que la seconde est indépendante des données mesurées (relation universelle). Pour établir la relation matérielle, on a à effectuer des mesures en champ lointain pour différents angles ďincidence, à différents points ďobservation et différentes fréquences. La relation universelle qui garantit des propriétés analytiques au champ nous donne une équation intégrale de Stieltjes. En résolvant ces équations, on obtient la localisation, la forme et la permittivité de ľobjet enfoui. Quand le matériau constituant ľespace sous la plaque est identique à celui de la plaque, le résultat se réduit à celui pour un objet enfoui dans un demi-espace.
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This work was partly supported by the Turkish Academy of Sciences (Tuba).
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Idemen, M., Alkumru, A. & Akduman, I. Inverse electromagnetic scattering by cylindrical bodies buried in a slab or a half-space. Ann. Télécommun. 50, 540–550 (1995). https://doi.org/10.1007/BF02995754
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DOI: https://doi.org/10.1007/BF02995754
Key words
- Wave diffraction
- Electromagnetic wave
- Inverse problem
- Cylindrical shape
- Half space
- Scalar field
- Bidimensional model
- Functional equation