Modeling and system identification of transient STOP models of optical systems

Abstract

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 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.…”

“…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. Widely used approaches for DM control are based on pre-estimated linear time-invariant DM models in the form of influence matrices, see for example 18,30 and references therein.…”

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

“…In our previous work, 34 we investigated the potential of using a subspace system identification method 8,[35][36][37] for estimating STOP models of refractive optical systems. In, 34 we considered a test case consisting of a single lens with an optomechanical support structure.…”

“…In our previous work, 34 we investigated the potential of using a subspace system identification method 8,[35][36][37] for estimating STOP models of refractive optical systems. In, 34 we considered a test case consisting of a single lens with an optomechanical support structure. By using the simulation data, we demonstrated that the subspace system identification method has a promising potential for accurately estimating low-order transient STOP models.…”

“…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.…”