Toward the solution of the inverse problem in neutron reflectometry

The authors show that the chemical depth profile of a film of unknown structure can be retrieved unambiguously from neutron reflection data by adding to the system a known magnetic layer. Three independent reflectivities are obtained by taking measurements with the sample magnetized in a magnetic field perpendicular to the surface and subsequently parallel to it, and using in the latter geometry neutrons polarized either in the direction of the field or opposite to it. The procedure consists of two steps. First, from the three reflectivities both the real and imaginary parts of the reflection coefficient of the unknown film are extracted within the framework of the rigorous dynamical theory. Second, the neutron scattering-length density (and consequently the chemical depth profile) is obtained by a suitable numerical technique for the conventional Schroedinger inverse scattering problem. Computer experiments were conducted for selected cases: starting from the profiles the reflectivities were calculated in a limited range of q and then the original profiles were successfully recovered. The influence on the accuracy of the recovered depth profile of the counting statistics and the cutoffs at low and high q are discussed