Structural, Thermal, and Optical Performance (STOP) analysis is important for understanding the dynamics and for predicting the performance of a large number of optical systems whose proper functioning is negatively influenced by thermally induced aberrations. Furthermore, STOP models are being used to design and test passive and active methods for the compensation of thermally induced aberrations. However, in many cases and scenarios, the lack of precise knowledge of system parameters and equations governing the dynamics of thermally induced aberrations can significantly deteriorate the prediction accuracy of STOP models. In such cases, STOP models and underlying parameters need to be estimated from the data. To the best of our knowledge, the problem of estimating transient state-space STOP models from the experimental data has not received significant attention. Similarly, little attention has been dedicated to the related problem of obtaining low-dimensional state-space models of thermally induced aberrations that can be used for the design of high-performance model-based control and estimation algorithms. Motivated by this, in this manuscript, we present a numerical proof of principle for estimating low-dimensional state-space models of thermally induced aberrations and for characterizing the transient dynamics. Our approach is based on the COMSOL Multiphysics simulation framework for generating the test data and on a system identification approach. We numerically test our method on a lens system with a temperature-dependent refractive index that is used in high-power laser systems. The dynamics of such a system is complex and described by the coupling of thermal, structural, and ray-tracing models. The approach proposed in this paper can be generalized to other types of optical systems.

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.

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In this paper, we investigate the feasibility of using subspace system identification techniques for estimating transient Structural-Thermal-Optical Performance (STOP) models of reflective optics. As a test case, we use a Newtonian telescope structure. This work is motivated by the need for the development of model-based datadriven techniques for prediction, estimation, and control of thermal effects and thermally-induced wavefront aberrations in optical systems, such as ground and space telescopes, optical instruments operating in harsh environments, optical lithography machines, and optical components of high-power laser systems. We estimate and validate a state-space model of a transient STOP dynamics. First, we model the system in COMSOL Multiphysics. Then, we use LiveLink for MATLAB software module to export the wavefront aberrations data from COMSOL to MATLAB. This data is used to test the subspace identification method that is implemented in Python. One of the main challenges in modeling and estimation of STOP models is that they are inherently large-dimensional. The large-scale nature of STOP models originates from the coupling of optical, thermal, and structural phenomena and physical processes. Our results show that large-dimensional STOP dynamics of the considered optical system can be accurately estimated by low-dimensional state-space models. Due to their lowdimensional nature and state-space forms, these models can effectively be used for the prediction, estimation, and control of thermally-induced wavefront aberrations. The developed MATLAB, COMSOL, and Python codes are available online.