Toward the solution of the inverse problem in neutron reflectometry Page: 3 of 20
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TOWARD THE SOLUTION OF THE INVERSE PROBLEM
IN NEUTRON REFLECTOMETRY
V.O. de Haan and A.A. van Well
Interfacultair Reactor Instituut. Delft University of Technology, 2629 JB Delft.
Dept. of Mathematics, Iowa State University, Ames, Iowa 50011, USA
S. Adenwalla and G.P. Felcher
Argonne National Laboratory, Argonne, Illinois 60439, USA
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 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 Schr6dinger inverse scattering problem. Computer experiments were
conducted for selected cases: starting from the profiles the reflectivities ware 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.
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Haan, V.O. de; Well, A.A. van; Sacks, P.E.; Adenwalla, S. & Felcher, G.P. Toward the solution of the inverse problem in neutron reflectometry, report, August 1, 1995; Illinois. (digital.library.unt.edu/ark:/67531/metadc694730/m1/3/: accessed August 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.