Differentiable Optics with dLux II: Optical Design Maximising Fisher Information

The design of astronomical hardware operating at the diffraction limit requires optimization of physical optical simulations of the instrument with respect to desired figures of merit, such as throughput or astrometric accuracy. These systems can be high dimensional, with highly nonlinear relationships between outputs and the adjustable parameters of the hardware. In this series of papers we present and apply dLux, an open-source end-to-end differentiable optical modelling framework. Automatic differentiation enables not just efficient high-dimensional optimization of astronomical hardware designs, but also Bayesian experimental design directly targeting the precision of experimental outcomes. Automatic second derivatives enable the exact and numerically stable calculation of parameter covariance forecasts, and higher derivatives of these enable direct optimization of these forecasts. We validate this method against analytic theory and illustrate its utility in evaluating the astrometric precision of a parametrized telescope model, and the design of a diffractive pupil to achieve optimal astrometric performance for exoplanet searches. The source code and tutorial software are open source and publicly available, targeting researchers who may wish to harness dLux for their own optical simulation problems.