Inverse scattering technique applied to remote sensing of layered media

An inverse scattering technique applied to a remote estimation of the dielectric and conductivity profile of an inaccessible layered medium is presented. The inaccessible region is illuminated by plane waves at normal incident, and the data are taken as the reflected power at a fixed remote location for a set of discrete frequencies. The problem of estimating the dielectric and conductivity profile from this set of data is posed as a nonlinear integral equation. This formulation based on reflected power is appealing for practical purpose, in that the phase information of the reflected field is not required. The equation is solved by developing a quasi-Newton iterative scheme in functional space which produces a dielectric and conductivity profile that fits the data. The Backus and Gilbert resolving-power theory is used to assess the reliability of the estimates and the resolving length of the data. Results are given for the numerical reconstruction of various dielectric and conductivity profiles from an artificial data set, together with local averages estimates and resolving kernels.