Equalization of the Antenna Pattern in Shape Reconstruction of Metallic Objects

We address the problem of reconstructing the shape of perfectly electric conducting cylinders for a two-dimensional scalar geometry when the physical optics (PO) model is exploited. We are interested in analyzing how the radiation pattern of the source providing the incident field affects the shape reconstruction problem. We find that, owing to the regularization necessary to deal with the ill-posedness of the problem, the more "weakly" illuminated objects are more "weakly" reconstructed. As a consequence, these objects can be mistaken for spurious artifacts appearing in the reconstruction and thus can be discarded when a threshold procedure is employed to curtail spurious artifacts. In order to overcome such a problem, we present a simple equalization strategy based on the knowledge of the incident field to compensate for the differences in amplitude of reconstructed image. Furthermore, we give a criterion which restricts the region over which we apply the procedure which enables us to perform the equalization in a stable way. The effectiveness of the equalization procedure is shown by reconstructions obtained with synthetic data and considering the unknown cylinders embedded in both a homogeneous and a half-space background medium, under single- and multi-view/multi-frequency measurement configuration