Information Content and Experimental Design in Neutron Reflectometry

Optimal design of a scattering experiment seeks to maximize the information content of a measurement with respect to features of interest. This process includes choosing the best sample composition, measurement procedure, and instrument configuration. While there is a great flexibility in designing a scattering experiment, a quantitative measure for assessing which implementation maximizes the gain in information has been lacking and the community largely follows empirical best-practices.

We have introduced a quantitative framework to determine the gain in information from neutron reflectometry (NR) experiments using information theory and Bayesian statistics [1]. The information gain is computed as the difference in entropy between the posterior and prior parameter distributions from a model-fit to reflectivity data from virtual experiments. This measure of information gain is used as a tool for experimental optimization with regards to experimental variables such as isotopic scattering contrast, measurement time and momentum transfer range. We implemented marginalization of the entropy with respect to a subset of model parameters [2], which allows to optimize the experimental design with respect to a subset of parameters of interest to the experimenter. By describing the entire measurement process as an information theoretical problem, fundamental insights into why certain designs are more effective are obtained.

[1] Treece, B., Kienzle, P., Hoogerheide, D., Majkrzak, C., Lösche, M., Heinrich, F. (2019). Optimization of reflectometry experiments using information theory. Journal of Applied Crystallography 52:47.
[2] Heinrich, F., Kienzle, P., Hoogerheide, D., Lösche, M. (2020). Information gain from isotopic contrast variation in neutron reflectometry on protein–membrane complex structures Journal of Applied Crystallography 53:800.