TOWARD THE SOLUTION OF THE INVERSE PROBLEM IN NEUTRON REFLECTOMETRY

We 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 reflectivitie s 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 t he direction of the field or opposite to it. The procedure consists of tyro steps. First, from the three reflectivities both the real and im aginary parts of the reflection coefficient of the unknown film are ex tracted 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 c onventional Schrodinger inverse scattering problem. Computer experimen ts were conducted for selected cases: starting from the profiles the r eflectivities were calculated in a limited range of q and then the ori ginal profiles were successfully recovered. The influence on the accur acy of the recovered depth profile of the counting statistics and the cutoffs at low and high q are discussed.