Optimizing experimental design in neutron reflectometry.

Using the Fisher information (FI), the design of neutron reflectometry experiments can be optimized, leading to greater confidence in parameters of interest and better use of experimental time [Durant, Wilkins, Butler & Cooper (2021). J. Appl. Cryst. 54, 1100-1110]. In this work, the FI is utilized in optimizing the design of a wide range of reflectometry experiments. Two lipid bilayer systems are investigated to determine the optimal choice of measurement angles and liquid contrasts, in addition to the ratio of the total counting time that should be spent measuring each condition. The reduction in parameter uncertainties with the addition of underlayers to these systems is then quantified, using the FI, and validated through the use of experiment simulation and Bayesian sampling methods. For a 'one-shot' measurement of a degrading lipid monolayer, it is shown that the common practice of measuring null-reflecting water is indeed optimal, but that the optimal measurement angle is dependent on the deuteration state of the monolayer. Finally, the framework is used to demonstrate the feasibility of measuring magnetic signals as small as 0.01 µB per atom in layers only 20 Šthick, given the appropriate experimental design, and that the time to reach a given level of confidence in the small magnetic moment is quantifiable.

Determining the maximum information gain and optimizing experimental design in neutron reflectometry using the Fisher information.

An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be calculated analytically and used to provide sub-second predictions of parameter uncertainties. This approach can be used to influence real-time decisions about measurement angle, measurement time, contrast choice and other experimental conditions based on parameters of interest. The FI provides a lower bound on parameter estimation uncertainties, and these are shown to decrease with the square root of the measurement time, providing useful information for the planning and scheduling of experimental work. As the FI is computationally inexpensive to calculate, it can be computed repeatedly during the course of an experiment, saving costly beam time by signalling that sufficient data have been obtained or saving experimental data sets by signalling that an experiment needs to continue. The approach's predictions are validated through the introduction of an experiment simulation framework that incorporates instrument-specific incident flux profiles, and through the investigation of measuring the structural properties of a phospholipid bilayer.