[Paper Review] Optimising experimental design in neutron reflectometry

James H. Durant, Lucas Wilkins+1 more|arXiv (Cornell University)|Aug 12, 2021

Nuclear Physics and Applications32 references4 citations

TL;DR

This paper presents a Fisher information (FI)-based framework to optimise neutron reflectometry experimental design, enabling data-driven selection of measurement angles, contrasts, and counting time allocation. It demonstrates that optimal designs reduce parameter uncertainties by up to a factor of 10, enabling detection of magnetic moments as small as 0.01 μB/atom in 20 Å layers and quantifying required measurement times for statistical confidence.

ABSTRACT

Using the Fisher information (FI), the design of neutron reflectometry experiments can be optimised, 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 utilised in optimising 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 $0.01μ_{B}/ ext{atom}$ in layers only $20Å$ thick, given the appropriate experimental design, and that time to reach a given level of confidence in the small magnetic moment is quantifiable.

Motivation & Objective

• To address the challenge of suboptimal experimental design in neutron reflectometry, where limited beamtime and high costs necessitate efficient use of resources.
• To develop a computationally efficient framework for quantitatively optimising experimental parameters such as angles, contrasts, and time allocation.
• To demonstrate the framework’s utility across diverse systems, including lipid bilayers, degrading monolayers, and magnetic thin films.
• To quantify the impact of underlayers and contrast choices on parameter uncertainty reduction.
• To enable prediction of required measurement duration to achieve a desired confidence level in detecting small signals, such as weak magnetic moments.

Proposed method

• The Fisher information (FI) matrix is computed from simulated reflectivity data under Poisson counting statistics, quantifying the maximum information content of an experiment.
• The minimum eigenvalue of the FI matrix is used as a scalar metric to evaluate experimental design quality, with higher values indicating lower parameter uncertainty.
• Optimisation is performed via maximin strategy, selecting parameters that maximise the minimum eigenvalue across all model parameters.
• The framework integrates with reflectivity simulation tools (refnx, Refl1D) and uses nested sampling (dynesty) for Bayesian validation of uncertainty estimates.
• The approach is extended to magnetic measurements by incorporating spin-dependent scattering and assessing detectability of small magnetic moments.
• The method is validated against full Bayesian sampling and experimental simulations, ensuring consistency with posterior uncertainty estimates.

Experimental results

Research questions

• RQ1 What combination of measurement angles and liquid contrasts minimises parameter uncertainty in lipid bilayer reflectometry experiments?
• RQ2 How does adding an underlayer to the substrate affect the information content and uncertainty in reflectometry measurements?
• RQ3 What is the optimal contrast choice for kinetic measurements of a degrading lipid monolayer, and does it depend on deuteration state?
• RQ4 What is the minimum detectable magnetic moment in a 20 Å thick layer, and how long must the experiment be to achieve a given confidence level?
• RQ5 Can the FI framework predict the required measurement time to confidently detect a small magnetic signal, and how does this compare to standard practices?

Key findings

• For lipid bilayer systems, adding an appropriate underlayer can improve the minimum eigenvalue of the Fisher information matrix by over a factor of 10, significantly reducing parameter uncertainty.
• The optimal third contrast in multi-contrast experiments is model-dependent, but silicon-matched water is a robust, widely applicable compromise when the model is uncertain.
• For kinetic measurements of a degrading lipid monolayer, measuring air-matched water is optimal, but the optimal angle depends on the monolayer’s deuteration state.
• The framework demonstrates that magnetic moments as small as 0.01 μB/atom can be detected in 20 Å thick layers with a properly designed experiment.
• The required measurement time to achieve a given confidence level in detecting a small magnetic signal can be quantitatively predicted using the FI framework.
• The FI-based optimisation method provides a computationally efficient alternative to Bayesian sampling, with results that closely match full posterior uncertainty estimates.