Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method

A novel network method used to reconstruct the permittivity profile of a dielectric slab of arbitrary depth or a half-space medium is investigated. The nonlinear Riccati type differential equation for the reflection coefficient of the medium is derived in a new way, from which an approximate closed-form reconstruction formula is obtained, relating the permittivity profile of the medium to the Fourier transform of the reflection coefficient. It is shown that this approximation is valid when it is used to invert the permittivity profile in shallow region. By means of the equivalent network of an inhomogeneous dielectric slab, the approximation can be subsequently used to invert the permittivity profile in an arbitrarily deep inhomogeneous region. Reconstruction examples for both continuous and discontinuous media are given to show the applicability of this scheme. The effect of noise on the inversion process is discussed