Distributed actuation systems for adaptive optics: from structural modeling to design optimization

Abstract

1 introduction 1 1.1 Adaptive optics 1 1.2 Hysteretic deformable mirror 3 1.3 Outline and contributions 5 1.3.1 Publications 8 2 preliminaries 9 2.1 Design parameters and performance measures 9 2.2 Actuator technologies for deformable mirrors 12 2.3 Space-based applications and deformable mirror technology 17 2.3.1 Deformable mirror requirements 17 2.3.2 State of the art 18 2.4 Hysteresis models for asymmetric butterfly loops 19 2.4.1 Preisach model 19 2.4.2 Duhem model 20 3 semi-analytical plate model 23 3.1 Overview of plate models 23 3.2 Influence functions for the hysteretic deformable mirror 26 3.2.1 Determination of the influence matrix 26 3.2.2 Actuator model 31 3.3 Results and discussion 33 3.3.1 2D pattern for influence functions (Case 1 -5) 33 3.3.2 Least-square fitting 33 3.3.3 Simulation results 34 3.3.4 Comparison to conventional modeling approaches 41 3.4 Concluding remarks 43 4 investigation of the electrical coupling phenomenon 45 4.1 Consideration of the phenomenon in surface fitting process 46 4.2 Fundamental analysis of the electrical coupling 48 4.3 Theoretical frameworks for detailed analysis 50 4.3.1 Model of the hysteretic deformable mirror 51 4.3.2 Modeling of the memory material 53 4.3.3 Sensitivity analysis of the facesheet 56 4.4 Implementation and results 57 4.4.1 Hysteretic deformable mirror model in 3D 57 xi xii contents 4.4.2 Memory material implementation 58 4.4.3 Sensitivity of the facesheet 60 4.4.4 Discussion 63 4.5 Concluding remarks 64 5 development of 2.5d metamaterial actuation array 67 5.1 Introduction 67 5.2 Modular actuation array based on kirigami 68 5.2.1 Design of cut patterns 69 5.2.2 Numerical validation of cut patterns 69 5.2.3 Proof of concept experiments 70 5.3 Application of kirigami array in adaptive optics 74 5.3.1 Design concept of a deformable mirror 74 5.4 Discussion and concluding remarks 81 6 conclusions and outlook 87 a coefficient calculation by solution to poisson's equation 91 a.1 Respective formulas 91 a.2 Numerical integration 91 a.3 Coefficient calculation in Case 1 91 a.3.1 Sub-functions of f 1 94 a.3.2 Sub-functions of f 2 94 a.4 Coefficient calculation in Case 2 95 a.4.1 Sub-functions of f 1 95 a.4.2 Sub-functions of f 2 95 a.5 Coefficient calculation in Case 3 96 a.5.1 Sub-functions of f 1 97 a.5.2 Sub-functions of f 2 97 a.6 Coefficient calculation in Case 4 98 a.6.1 Sub-functions of f 1 99 a.6.2 Sub-functions of f 2 99 a.7 Coefficient calculation in Case 5 100 a.7.1 Sub-functions of f 1 101 a.7.2 Sub-functions of f 2 101 bibliography 103 summary 117 samenvatting 119 zusammenfassung 123