Differentiable Optics with dLux II: Optical Design Maximising Fisher Information

The design of astronomical hardware operating at the diffraction limit requires optimisation of physical optical simulations of the instrument with respect to desired figures of merit, such as photometric or astrometric precision. System design entails many parameters some of which may entangle the fidelity of science observables with strongly nonlinear dependencies upon instrument properties. Here we present a differentiable optical simulation framework dLux, a software library designed to construct optical models that are integrated with automatic differentiation. This approach enables the direct evaluation of gradients and higher-order derivatives through the forward model, facilitating statistically principled design and optimisation of instrument configurations. The methodology leverages numerically stable second- and higher-order derivatives to directly compute Fisher information and covariance forecasts, enabling efficient Bayesian experimental design targeted toward optimising abstracted figures of merit, such as the precision of parameters recovered through complex sets of operations. The method is validated against analytical results and applied to optimise the astrometric precision achievable with a parametrised telescope model and a diffractive pupil design relevant to exoplanet detection missions. To support reproducibility and facilitate methodological extension, we provide example implementations via open-source code on the Github sharing platform.