Shape reconstruction of 2-D dielectric objects by an analytical method

An analytical approach to shape reconstruction of dielectric scatterers is proposed. It is assumed that the cross-section of the scatterer does not depend on the z coordinate, hence a 2-D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. From this solution the scattered electric field can be computed in closed form, too, and can be used to reconstruct the shape of the body under test. This is a preliminary step toward a more complete solution, which will take into account also the non-radiating sources. Numerical simulations show the capabilities of the method and, thanks to the closed-form solution, results can be obtained in a very short computation time.