The one-dimensional transient problem of a wave incidence on a layer of inhomogeneous medium is considered. It is shown that a measurement of the internal fields allows one to reconstruct the permittivity profile in certain parts of the slab. Combining the embedding and differential run equations, we obtain the closed equations for the internal fields and construct the solution procedure for the inverse scattering problem. The generalization of the analytical solution of the inverse problem, for the case in which the time dependence of scattering field is exponential, is presented. ¿ American Geophysical Union 1995