  An approach based on the Fisher information metric (FIM) is developed to
quantify the maximum information gain and optimal experimental design in
neutron reflectometry experiments. In these experiments, the FIM can be
analytically calculated 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 FIM provides a lower bound on
parameter estimation errors. These are shown to decrease with the square root
of measurement time, providing useful information for the planning and
scheduling of experimental work. As the FIM 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 has been obtained;
or saving experimental datasets 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 investigation of the specific case of
measuring the structural properties of a phospholipid bilayer.
