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Perturbation approach to shape reconstruction in a rectangular waveguide using experimental data

We consider the inverse problem of reconstructing the shape of a deformation in one of the broad walls of a rectangular waveguide. Assuming a small deformation, resulting in weak scattering, the direct problem is solved using a first order perturbation approach. Hence, the inverse problem becomes linear and is formulated as an equation system for a set of expansion coefficients. The illposedness of the inverse problem is handled with regularization, by adding a penalty term which weight is determined by the L-curve method. The theory is tested on experimental reflection data, using the dominant mode of the waveguide. The reconstructed shape is in qualitative agreement with the true shape, but a detailed resolution cannot be obtained due to insufficient quality of the experimental data. Extensions and improvements of the method are discussed.