Reconstruction of the impedance Schrödinger equation from the modulus of the reflection coefficients

We study the problem of determining the electromagnetic properties of a stratified medium given only the amplitude of the reflected waves. Under some assumptions, the problem is formulated as the inverse scattering problem for a Schrödinger operator in impedance form. We show that a unique reconstruction from the modulus of the reflection coefficients is in general impossible and explain the cause of non-uniqueness. Several augmented sets of data allowing a unique reconstruction are suggested, and the corresponding numerical examples are provided.

► We study the problem of determining the electric properties of a stratified medium from the amplitude of the reflected waves. ► A unique reconstruction of the medium from the modulus of the reflection coefficients is in general impossible. ► The cause of non-uniqueness is explained. ► Several augmented sets of data allowing a unique reconstruction are suggested.