Shape reconstruction of 3D metallic objects via a physical optics distributional approach

The problem of determining the shape of 3D perfect electric conducting (PEC) objects starting from the scattered far field under the incidence of plane waves with a fixed angle of incidence, varying frequency and two orthogonal polarizations is dealt with.Two strategies of reconstruction are presented and compared. In particular, in the first solution strategy the data acquired at the two polarizations are singularly exploited to achieve two different reconstructions and the object surface is then obtained as their “union”. In the second one, all the data (i.e., for both the adopted polarizations) are simultaneously exploited to obtain the reconstruction.In all the cases, by adopting a distributional formulation for the unknown of the problem and thanks to the exploitation of the Kirchhoff approximation, the problem is cast as a linear inverse one and the solution is made stable by adopting a regularization scheme based on the truncated singular value decomposition (TSVD).The reliability of the inversion approach is tested with synthetic data against model error and noise on data.