Modeling and state-space identification of deformable mirrors

Haber, Aleksandar; Verhaegen, Michel

doi:10.1364/oe.382880

Cited by 28 publications

(18 citation statements)

References 48 publications

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“…To compute the initial values, we will assume that the influence matrix is constant. Under this assumption, from (14), we obtain…”

Section: A Initial Estimation Of the Influence Matrix And Control Act...mentioning

confidence: 99%

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Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Haber,

Bifano

2021

Preprint

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In this paper, we develop a novel data-driven method for Deformable Mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback control algorithm with an algorithm for recursive estimation of DM influence function models.In addition to this, we explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our resultsshow that the novel method produces the root-mean-square surface error in the 14 − 40 nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types, such as for example, segmented DMs. I. INTRODUCTION Deformable Mirrors (DMs) are one of the main components of Adaptive Optics (AO) systems [1], [2]. A typical DM consist of a reflective optical surface that is deformed by a set of actuators. By precisely shaping the surface of a DM, we can compensate for wave-front aberrations in AO systems [3]-[16].In this paper, we consider the problem of developing control algorithms for DMs. There are a large number of approaches for DM control. A complete survey of all the methods goes well beyond the length limits of this manuscript. Consequently, we briefly mention only the most

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“…To compute the initial values, we will assume that the influence matrix is constant. Under this assumption, from (14), we obtain…”

Section: A Initial Estimation Of the Influence Matrix And Control Act...mentioning

confidence: 99%

“…Even without this assumption, it is possible to derive the control algorithm, however, the mathematical apparatus will become more complex and it will involve expectation operators. Taking into account the general model (14), this assumption gives the following model…”

Section: B Control Algorithm Developmentmentioning

confidence: 99%

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Haber,

Bifano

2021

Preprint

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“…To develop high-performance Adaptive Optics (AO) systems, it is of paramount importance to develop sufficiently accurate models of active optical components, such as Deformable Mirrors (DMs) or spatial light modulators. [1][2][3][4] Once high-fidelity models are established and properly validated, they can be used to develop high-performance model-based controllers. [5][6][7][8][9][10][11][12][13][14][15][16][17] The main focus of this manuscript is on the development of control algorithms for DMs.…”

Section: Introductionmentioning

confidence: 99%

A novel method for adaptive control of deformable mirrors

Haber¹

2022

Preprint

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For sufficiently wide ranges of applied control signals (control voltages), MEMS and piezoelectric Deformable Mirrors (DMs), exhibit nonlinear behavior. The nonlinear behavior manifests itself in nonlinear actuator couplings, nonlinear actuator deformation characteristics, and in the case of piezoelectric DMs, hysteresis. Furthermore, in a number of situations, DM behavior can change over time, and this requires a procedure for updating the DM models on the basis of the observed data. If not properly modeled and if not taken into account when designing control algorithms, nonlinearities, and time-varying DM behavior, can significantly degrade the achievable closed-loop performance of Adaptive Optics (AO) systems. Widely used approaches for DM control are based on pre-estimated linear time-invariant DM models in the form of influence matrices. Often, these models are not being updated during system operation. Consequently, when the nonlinear DM behavior is excited by control signals with wide operating ranges, or when the DM behavior changes over time, the state-of-the-art DM control approaches relying upon linear control methods, might not be able to produce a satisfactory closed-loop performance of an AO system. Motivated by these key facts, we present a novel method for data-driven DM control. Our approach combines a simple open-loop control method with a recursive least squares method for dynamically updating the DM model. The DM model is constantly being updated on the basis of the dynamically changing DM operating points. That is, the proposed method updates both the control actions and the DM model during the system operation. We experimentally verify this approach on a Boston Micromachines MEMS DM with 140 actuators. Preliminary experimental results reported in this manuscript demonstrate good potential for using the developed method for DM control.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Haber¹,

Draganov²,

Krainak³

2022

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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.

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Modeling and state-space identification of deformable mirrors

Cited by 28 publications

References 48 publications

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

A novel method for adaptive control of deformable mirrors

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

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