Shape reconstruction by the spectral data of the far-field operator: analysis and performances

The second version of the "linear sampling" method is considered with reference to perfectly conducting cylinders and its performances analyzed. It is pointed out that, for nonconvex objects, the shape of the object under test is not retrieved, whereas in its place the convex hull is recovered. We also point out that in the case of aspect limited data neither the convex hull of the object is reconstructed.