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Abstract
A very accurate inverse scattering method for reconstructing the contours of perfectly conducting cylinders of arbitrary crosssection illuminated by electromagnetic waves under TM polarization with time-harmonic dependence is presented. No assumption is made on the shapes of the contours nor on their number. Inversion strategy consists in computing a special deformation velocity, defined on the contours of the objects, and allowing to decrease a cost function at each iteration. Level set methods, used in as diverse fields as fluid dynamics, image processing and crystal growth, are used to perform the evolution of the contours. These methods allow to handle automatically topological changes by using a Eulerian point of view built on a level set representation of the contours. Hence, several objects can be retrieved from one single initial contour. Moreover, contours regularization is easily performed by adding a curvature term to the velocity. The inverse scattering method is based on a very accurate forward scattering algorithm characterized by the use of well-behaved pseudo-currents which are developed in Fourier series along the contours. The frequency hopping technique turns out to play a key role in the inversion process. The method is proved to be flexible, allowing to reconstruct accurately complex and multiple shape contours from one single initial guess. The deformation velocity is even able to retrieve very sharp corners and is quite robust with respect to high noise levels.