Modeling, experimental validation, and model order reduction of mirror thermal dynamics

A large variety of optical systems and devices are highly sensitive to temperature variations and gradients induced by the absorption of thermal energy. Temperature gradients developed across optical elements, mounts, and supporting structures can lead to thermally induced wavefront aberrations and, consequently, to the reduction of optical performance. Consequently, modeling, estimation, and control of thermal dynamics are important problems that need to be carefully addressed by optical system designers. However, the development of accurate and experimentally validated models of thermal dynamics that are suitable for prediction, estimation, and control is a challenging problem. The main modeling challenges originate from model uncertainties, nonlinearities, and the fact that the thermal dynamics is inherently large-dimensional. In this manuscript, we present a synergistic modeling framework that combines first-principle heat transfer modeling, experimental validation, finite element techniques, and model order reduction techniques. We experimentally validate our approach on a recently developed 8-inch mirror prototype equipped with heaters and temperature sensors. We are able to accurately predict the temperature transients lasting for several hours. Furthermore, we apply our modeling approach to a parabolic mirror with an optimized honeycomb back structure. We investigate how the choice of mirror materials, such as aluminum, beryllium, Zerodur, and ULE, influence the ability to derive reduced-order models. Our results show that mirror thermal dynamics can be approximated by low-order state-space models. The modeling approach used in this manuscript is relevant for the prediction, estimation, and control of thermal dynamics and thermally induced aberrations in optical systems. MATLAB, COMSOL Multiphysics, and LiveLink codes used in this manuscript are available online.