Analytical Solution to Inverse Electromagnetic Scattering: Shape and Position Reconstruction of Dielectric Objects

An analytical approach to inverse electromagnetic scattering is proposed. Inverse electromagnetic scattering problems deal with the reconstruction of the actual position, the shape, the dimensions and dielectric properties of a dielectric object inside a bounded space region. The technique is based on the use of a known incident field illuminating the space region containing the object. By using a set of measurements of the electrical field scattered by the object under test, an analytical solution can be derived. The solution method makes use of an equivalent source as scattered field´s support. Such a source is considered a combination of non-radiating and radiating currents. Analytical results can be achieved by means of the singular system of the scattering operator in a very short computation time.