Modeling and system identification of transient STOP models of optical systems

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.