Abstract FR:

This work concerns the non-linearised reconstruction of a bidimensional homogeneous object,infinitely long in the axial direction), possibly multiply connected, buried in a free or half space, from the measurement of the time-harmonic wave field, which is scattered from it. The problem in an inverse one and its solution is sought iteratively by using a representation of the object as a level set. Its deformation is controlled by a velocity field satisfying minimisation conditions of an objective functional, characterising the discrepancy between the true scattered field and the reconstructed one; both are computed without approximation and using a method of moments derived from domain integrals. The novelty of this approach lies in the extension of the method to the layered configuration as well as the use of a lagrangian formulation of the objective functional, in order to properly calculate its derivative. This is made possible due to the good use of Green functions properties, which gather the complete geometry of the experiment. The analysis was developed in the context of the Transverse Magnetic polarisation (TM) and particularly the Transverse Electric polarisation (TE), as this is new work. Particular attention is given to the numerical subtlety required to handle this problem. Furthermore, an algorithm combining an optimisation method involving level stes and the Levenberg-Marquardt method has enabled the retrieval of obstacles of unknow contrast. Finally, a so-called"fixed-point" algorithm is developed, which involves a direct discretisation of the optimality conditions, given the volume of the object. This is shown to achieve satisfactory results within one or two iterations. Experimental laboratory data, involving the illumination of conductive or dielectric objects in the microwage regime, have been processed and provide good results.