Novel applications of an approximate profile inversion for one-dimensional medium

In one-dimensional inverse scattering, the approximate formulas to reconstruct the permittivity profiles are very interesting because of their closed forms. Nevertheless, as the result of Born approximation, they are invalid under the strong-scattering conditions which restrict their applications. In this paper, a novel approximation for inverting the permittivity profile of a one-dimensional inhomogeneous medium is derived by using an equivalent microwave networking technique. Compared with the published formulas of Ladoucer and Jordan (1985), the novel approximation is not only more general in the form, but suitable for both weak-scattering and strong-scattering conditions. Reconstruction examples show that when the relative permittivity reaches 80, the novel formula is effective, which show the validity of this scheme