  Nuclear Reaction Analysis with ${}^{3}$He holds the promise to measure
Deuterium depth profiles up to large depths. However, the extraction of the
depth profile from the measured data is an ill-posed inversion problem. Here we
demonstrate how Bayesian Experimental Design can be used to optimize the number
of measurements as well as the measurement energies to maximize the information
gain. Comparison of the inversion properties of the optimized design with
standard settings reveals huge possible gains. Application of the posterior
sampling method allows to optimize the experimental settings interactively
during the measurement process.
