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(k) for time-harmonic electromagnetic waves is represented as a rational function of k, the wave number. 1-dimensional inverse scattering theory has been applied to obtain analytic, closed-form expressions for the profile functions q(x) from r(k). The profile reconstruction method is demonstrated with a 3-pole r(k), that results in a q(x) which resembles an ionospheric electron-density profile previously analysed by direct scattering methods. The present communication generalises previous results to oblique incidence and compares several.q(x) obtained from different rational approximations to r(k).