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Optimization of Reflectometry Experiments using Information Theory



Bradley W. Treece, Paul A. Kienzle, David Hoogerheide, Charles Majkrzak, Mathias Loesche, Frank Heinrich


A method based on Bayesian statistics and information theory is developed to analyze the information gain Δ}H of surface-sensitive reflectometry experiments. After presenting the underlying mathematical framework and its implementation, the method is applied to test problems, i.e. simplified structures for which the information gain of virtual neutron reflection experiments is determined. These virtual experiments are simulated based on the current generation of neutron reflectometers at the NIST Center for Neutron Research (NCNR). However, the simulation can be easily modified for x-ray or neutron instruments at any source. With application to structural biology in mind, this work analyzes the dependence of Δ}H on the scattering length density (SLD) of aqueous solutions in which the sample structure is bathed. For either one or two successive measurements of the sample with distinct solution SLDs, the optimum values of these SLDs are determined. The dependence of Δ}H on other experimental parameters, such as counting time and maximum momentum transfer, is further analyzed. Finally, the impact of a nanoscopic reference layer that is buried beneath that sample surface is investigated. Such a reference layer can boost the signal-to-noise ratio access the whole momentum transfer range with significant benefit to Δ}H. If the reference layer is composed of a magnetic material, its SLD becomes dependent on neutron polarization, thus providing two isomorphic contrasts. Our analysis of this situation provides the surprising conclusion that the resulting information gain from a polarized neutron refletometry experiment is only minor.
Journal of Applied Crystallography


information content, neutron reflectometry, experimental design


Treece, B. , Kienzle, P. , Hoogerheide, D. , Majkrzak, C. , Loesche, M. and Heinrich, F. (2019), Optimization of Reflectometry Experiments using Information Theory, Journal of Applied Crystallography, [online],, (Accessed April 14, 2024)
Created January 31, 2019, Updated October 12, 2021