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

Abstract

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.

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

“…In the same paper, we used modelorder reduction techniques to develop low-order state-space models of thermal dynamics. The results reported in 38 indicate that the transient thermal dynamics of reflective optics can be approximated by low-order models. However, in, 38 we only consider thermal dynamics without coupling the heat equation with other equations mathematically describing thermal deformation and optical ray propagation.…”

“…The results reported in 38 indicate that the transient thermal dynamics of reflective optics can be approximated by low-order models. However, in, 38 we only consider thermal dynamics without coupling the heat equation with other equations mathematically describing thermal deformation and optical ray propagation. Consequently, it is not clear if an integrated STOP transient dynamics of reflective optics can be approximated by low-dimensional models.…”

“…However, the feasibility of the subspace identification method for estimating low-dimensional STOP models of reflective optics has not been investigated. Then, in, 38 we derived and experimentally verified a model of transient thermal dynamics of an 8-inch aluminum mirror prototype. In the same paper, we used modelorder reduction techniques to develop low-order state-space models of thermal dynamics.…”

“…Motivated by the promising results presented in, 34,38 and above described open research questions, in this paper, we investigate the feasibility and performance of the subspace system identification method for estimating STOP models of reflective optical systems. As a test case, we use a Newtonian telescope structure.…”

A novel method for adaptive control of deformable mirrors

“…This is especially the case for space optics and for optics operating with high-power lasers, where DMs can directly absorb a significant portion of external heat fluxes, or the heat conduction from the supporting elements and devices can cause nonuniform DM temperature increases and significant temperature gradients over active DM surface areas. 14,[21][22][23][24][25][26][27] To properly analyze, predict, and control the influence of thermal phenomena on DM behavior, it is often necessary to use data-driven techniques to estimate thermal dynamics. 21,28,29 If not properly modeled and if not taken into account when designing control algorithms, these nonlinearities and time-varying DM behavior, can significantly degrade the achievable closed-loop performance of AO systems.…”