INVERSE SCATTERING THEORY AND PROFILE RECONSTRUCTION

An analytic method for the reconstruction of the profiles of refractive indexes of inhomogeneous, stratified regions is presented. The reflection coefficient r( kappa ) for time-harmonic electromagnetic waves is represented as a rational function of kappa , the wave number. One-dimensional inverse scattering theory has been applied to obtain analytic, closed-form expressions for the profile functions q(x) from r( kappa ). The profile reconstruction method is demonstrated with a 3-pole r( kappa ), that results in a q(x) which resembles an ionospheric electron-density profile previously analyzed by direct scattering methods. Previous results are compared to r( kappa ) oblique incidence and several q(x) obtained from different rational approximations are compared to r( kappa ).