Reconstruction of a spherical scatterer from its natural frequencies
Abstract
A technique for an approximate reconstruction of the index of refraction of a spherical scatterer from natural frequencies is presented. The frequencies are treated as complex poles of the scattering amplitude in the wavenumber complex plane. A quantum mechanical inverse expression is defined for accounting for phase shifts. The index of refraction is then generated, after a Liouville transformation to remove the wavenumber dependency, from a scattering matrix at the location of its singularities. Usage of a Weierstrass product configuration for the scattering matrix is shown to yield an approximation which approaches the accuracy of an integral formulation.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 July 1984
 DOI:
 10.1109/TAP.1984.1143400
 Bibcode:
 1984ITAP...32..694E
 Keywords:

 Electromagnetic Scattering;
 Refractivity;
 Resonant Frequencies;
 S Matrix Theory;
 Scattering Amplitude;
 Liouville Equations;
 Weierstrass Functions;
 Communications and Radar