Inverse problem on the line without phase information

The one-dimensional Schrodinger equation is considered for real potentials that are integrable, have finite first moment, and contain no bound states. The recovery of a potential with support in a right half-line is studied in terms of the scattering data consisting of the magnitude of the reflection coefficient, a known potential placed to the left of the unknown potential, and the magnitude of the reflection coefficient of the combined potential. Several kinds of methods are described for retrieval of the reflection coefficient corresponding to the unknown potential. Some illustrative examples are provided.