paper 150205145611

Published: 2015-07-09

Microwave Imaging of Dispersive Scatterers Using Vectorial Lagrange Multipliers

Ioannis T. Rekanos,

Ioannis T. Rekanos

Aristotle University of Thessaloniki, Greece

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Theodoros I. Kosmanis,

Theodoros I. Kosmanis

Alexander Technological Educational Institute of Thessaloniki, Greece

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Theseus G. Papadopoulos

Aristotle University of Thessaloniki, Greece

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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)1926-1931

Abstract

A time-domain microwave imaging method is proposed for the reconstruction of the spatial distribution of the electromagnetic properties of dispersive scatterers. The method is based on the minimization of a cost functional, which describes the discrepancy between mea- sured and estimated scattered field data. The Maxwell’s curl equations are introduced in an augmented cost functional, as equality constraints, via vectorial Lagrange multipliers. By means of the calculus of variations and the stationarity condition, it is shown that the vectorial Lagrange multipliers are the solution of the adjoint scattering problem. Moreover, the Fréchet derivatives of the cost functional with respect to the distributions of the scatterer properties are derived analytically. As a result, the Fréchet derivatives obtained can be utilized by any gradient-based optimization technique that updates the estimated scatterer properties iteratively. In this study, two-dimensional dispersive scatterers have been investigated. In the case of Debye scatterers, the spatial distributions of the relaxation time, the static and the optical permittivity, are re- constructed simultaneously. Also, the method is applied to the reconstruction of the resonant frequency, the damping factor, the static and the optical permittivity of Lorentz dispersive media.

Citation

Ioannis T. Rekanos, Theodoros I. Kosmanis, and Theseus G. Papadopoulos, "Microwave Imaging of Dispersive Scatterers Using Vectorial Lagrange Multipliers," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)1926-1931

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