Optimization of reflectometry experiments using information theory.

Bradley W. Treece,Paul A. Kienzle,David P. Hoogerheide,Mathias Lösche,Charles F. Majkrzak,Frank Heinrich

doi:10.1107/s1600576718017016

Abstract

A framework based on Bayesian statistics and information theory is developed to optimize the design of surface-sensitive reflectometry experiments. The method applies to model-based reflectivity data analysis, uses simulated reflectivity data and is capable of optimizing experiments that probe a sample under more than one condition. After presentation of the underlying theory and its implementation, the framework is applied to exemplary test problems for which the information gain ΔH is determined. Reflectivity data are simulated for the current generation of neutron reflectometers at the NIST Center for Neutron Research. 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 explores the dependence of ΔH on the scattering length density of aqueous solutions in which the sample structure is bathed, on the counting time and on the maximum momentum transfer of the measurement. Finally, the impact of a buried magnetic reference layer on ΔH is investigated.

Highlights

Neutron reflectometry (NR) is a structure determination technique that resolves the thickness and composition of thin films at interfaces and surfaces with near-angstrom resolution (Smith & Majkrzak, 2006)
We showed for the same sample structure that an extension obtained by approximating the mutual information between of the measurement time t per reflectivity curve above the the prior and posterior parameter density function (PDF) using virtual experiments
We neglected other losses those y(), we showed that the observed standard deviation of of information that might occur during the calculation of the noise-free reflectivity x, and we relied on the assumption that the Monte Carlo Markov chain (MCMC) robustly finds the global solution of the fitting problem

Summary

Introduction

Neutron reflectometry (NR) is a structure determination technique that resolves the thickness and composition of thin films at interfaces and surfaces with near-angstrom resolution (Smith & Majkrzak, 2006). Given the limited availability of neutrons for scattering experiments and the flexibility in isotopic labeling of distinct components of the surface structure, it is worthwhile to optimize the experimental design with respect to the information gain. We implement a quantitative and predictive framework to plan reflectometry work based on rigorous estimates of the information gained in a particular implementation of the experiment. With minor changes, this framework is applicable to X-ray reflectometry and, with some extension, to neutron and X-ray small-angle scattering

Results

Discussion

Conclusion