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Spie Press Book

Integrated Optomechanical Analysis
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Book Description

This tutorial presents optomechanical modeling techniques to effectively design and analyze high-performance optical systems. It discusses thermal and structural modeling methods that use finite-element analysis to predict the integrity and performance of optical elements and optical support structures. Includes accompanying CD-ROM with examples.

Book Details

Date Published: 1 October 2002
Pages: 248
Volume: TT58

Table of Contents
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Introduction /

Chapter 1
Introduction to Mechanical Analysis Using Finite Elements / 1
1.1 Integrated Optomechanical Analysis Issues / 1
1.1.1 Integration issues / 1
1.1.2 Orbiting telescope example / 1
1.1.3 Lens barrel example / 3
1.2 Elasticity Review / 4
1.2.1 Three-dimensional elasticity / 4
1.2.2 Two-dimensional plane stress / 6
1.2.3 Two-dimensional plane strain / 8
1.2.4 Principal stress and equivalent stress / 9
1.3 Basics of Finite-element Analysis / 10
1.3.1 Finite-element theory / 10
1.3.2 Element performance / 12
1.3.3 Structural analysis equations / 14
1.3.4 Thermal analysis with finite-elements / 15
1.3.5 Thermal analysis equations / 16
1.4 Symmetry in FE Models / 17
1.4.1 General loads / 17
1.4.2 Symmetric loads / 18
1.4.3 Modeling techniques / 19
1.4.4 Axisymmetry / 20
1.4.5 Symmetry: pros and cons / 20
1.5 Stress Analysis / 21
1.5.1 Stress models / 21
1.5.2 Failure theories / 22
1.5.3 Stress plots / 24
1.5.4 Load envelopes / 25
1.6 Vibrations / 25
1.6.1 Natural frequencies / 25
1.6.2 Harmonic response / 26
1.6.3 Random response / 27
1.7 Model Checkout / 28
1.8 Summary / 30
References / 30
Chapter 2
Optical Fundamentals / 33
2.1 Electromagnetic Basics / 33
2.2 Polarization / 35
2.3 Rays, Wafefronts, and Wavefront Error / 36
2.4 Image Quality and Optical Performance / 38
2.4.1 Diffraction / 38
2.4.2 Measures of optical performance / 39
2.4.2.1 Spot diagrams / 40
2.4.2.2 Point spread function / 40
2.4.2.3 Encircled energy function / 40
2.5 Optical Resolution / 42
2.6 Modulation Transfer Function / 43
2.7 Image Formation / 44
2.7.1 Spatial domain / 45
2.7.2 Frequency domain / 46
2.8 Optical Surface Evaluation / 48
2.8.1 Zernike polynomials / 48
2.8.2 Computing the Zernike polynomial coefficients / 55
2.8.3 Legendre-Fourier polynomials / 57
References / 59
Chapter 3
Optomechanical Displacement Analysis Methods / 61
3.1 Displacement Models of Optics / 61
3.1.1 Definitions / 69
3.1.2 Single-point models / 63
3.1.3 Solid optics / 64
3.1.3.1 Two-dimensional models of solid optics / 65
3.1.3.2 Three-dimensional element models of solid optics / 65
3.1.4 Lightweight mirror models / 66
3.1.4.1 Two-dimensional equivalent-stiffness models of lightweight mirrors / 67
3.1.4.2 Three-dimensional element equivalent-stiffness models / 73
3.1.4.3 Three-dimensional plate/shell model / 75
3.1.4.4 Example: gravity deformation prediction comparison of a lightweight mirror / 76
3.1.4.4(a) Two-dimensional effective property calculations / 76
3.1.4.4(b) Three-dimensional effective property calculations / 78
3.1.4.4(c) Three-dimensional plate effective property calculations / 79
3.1.5 Generation of powered optic models / 81
3.2 Displacement models of adhesive bonds / 82
3.2.1 Elastic behavior of adhesives / 82
3.2.2 Detailed three-dimensional solid model / 85
3.2.3 Effective three-dimensional solid models / 85
3.2.3.1 Effective properties for "hockey-puck" type bonds / 86
3.2.3.2 Example: modeling of a hockey-puck type bond / 88
3.3 Displacement Models of Flexures and Mounts / 91
3.3.1 Classification of mounts / 91
3.3.2 Modeling of kinematic mounts / 91
3.3.3 Modeling of flexure mounts / 93
3.3.3.1 Modeling of beam flexures / 93
3.3.3.2 Example: modeling of bipod flexures / 96
3.3.3.3 Modeling of blade flexures / 97
3.3.4 Modeling of test supports / 99
3.4 Displacement analysis methods / 108
3.4.1 Analysis of surface effects / 108
3.4.1.1 Composite-plate model / 108
3.4.1.2 Homogenous-plate model / 109
3.4.1.3 Three-dimensional models / 111
3.4.1.4 Example: coating-cure shrinkage / 112
3.4.1.4(a) Composite-plate model / 112
3.4.1.4(b) Homogenous-plate model / 112
3.4.1.4(c) Three-dimensional model / 113
3.4.2 Analysis of assembly processes / 114
3.4.2.1 Example: assembly analysis of mirror mounting / 116
References / 117
Chapter 4
Integrated Optomechanical Analyses / 119
4.1 Optical-Surface Positional Errors / 119
4.2 Optical Surface Shape Changes / 121
4.2.1 Optical surface deformations and wavefront error / 121
4.2.2 Surface-normal deformation / 123
4.2.3 Sag deformation / 123
4.2.4 Radius of curvature changes / 126
4.2.5 Finite-element-derived spot diagrams / 127
4.2.6 Surface interferogram files / 128
4.2.7 Interpolation / 128
4.3 Line-of-Sight Jitter / 129
4.3.1 Computing image motion / 130
4.3.1.1 Constant-velocity image motion / 135
4.3.1.2 High Frequency sinusoidal image motion / 135
4.3.1.3 Low-frequency sinusoidal image motion / 136
4.3.4.4 Example: modulation-transfer-function loss
4.4 Stress Birefringence / 138
4.4.1 Mathematical description / 138
4.4.2 Stress-optical coefficients / 142
4.4.3 Computing stress birefringence for nonuniform stress distributions
/ 143
4.4.4 Example: stress birefringence / 145
4.5 Effects of Mechanical Obscurations / 149
4.5.1 Relationship between obscuration periphery, area, and encircled energy / 150
4.5.2 Example: encircled energy for Cassegrain telescope / 150
4.6.4 Diffraction pattern / 151
References / 152
Chapter 5
Modeling the Effects of Temperature / 155
5.1. Thermo-elastic Analysis / 155
5.1.1 Coefficient of thermal expansion as a function of temperature / 156
5.1.2 Coefficient of thermal expansion inhomogeneity / 158
5.2 Thermo-Optic Effects / 159
5.2.1 Wavefront error / 159
5.2.2 Sellmeier-dispersion equation / 160
5.3 First-order Effects of Temperature on Optical System Performance / 161
5.4 Optical Design Software / 164
5.5 Thermo-Optic Finite-Element Models / 166
5.6 Wavefront Interferogram Files / 166
5.7 Absorption of Radiation / 166
5.8 Mapping of Temperature Fields from the Thermal Model to the Structural Model / 168
5.8.1 Nearest-node methods / 168
5.8.2 Conduction analysis / 168
5.8.3 Shape-function interpolation / 169
5.9 Analogous Techniques / 170
5.9.1 Moisture Absorption/ 171
5.9.2 Adhesive Curing / 171
References / 172
Chapter 6
Adaptive Optics Analysis Methods / 173
6.1 Introduction / 173
6.2 Method of simulation / 174
6.2.1 Determination of actuator inputs / 174
6.2.2 Characterization metrics of adaptive and adaptive optics / 176
6.3 Coupled Adaptive Control Simulation and Structural Design Optimization / 179
6.3.1 Method of modeling actuators in design optimization / 180
6.3.2 Guidelines for adaptive control design optimization / 182
References / 184
Chapter 7
Optimization of Optomechanical Systems / 185
7.1 Overview / 185
7.2 Optimization Theory / 186
7.3 Structural Optimization, Including Optical Measures / 190
7.4 Integrated Thermal-Structural-Optical Optimization / 193
References / 195
Chapter 8
Example Telescope Analysis / 197
8.1 Overview / 197
8.2 Optical Model Description / 197
8.3 Structural Model Description / 198
8.4 One-gravity Static Preformance / 199
8.5 On-Orbit Image Motion Random Response / 199
8.6 Optimize PMA with Optical Measures / 201
8.7 Adaptive PM / 202
8.8 System-level Multidisciplinary Optimization / 202
Chapter 9
Integrated Optomechanical Analysis of a Lens Assembly / 203
9.1 Overview / 203
9.2 Thermal Analysis / 204
9.3 Thermo-elastic Analysis / 206
9.4 Thermo-Optic Analysis / 208
9.5 Optical Analysis / 209

Index /

Introduction

In the development of an optical instrument, the optical system error budget underscores the multidisciplinary aspect of the design effort. At the top level, an optical performance goal is specified and a systematic allocation of acceptable errors is typically divided between the design, fabrication, and alignment of the optics along with environmental effects. Environmental effects may be further divided between thermal and structural effects. The ability to determine the thermal and structural effects on the system are therefore fundamental in the design process and critical in the evaluation of design trades during the development of an optical instrument.

The emphasis of this tutorial is to present optomechanical modeling techniques to effectively design and analyze high-performance optical systems. The first goal is to discuss thermal and structural modeling methods using finite element analysis to predict the integrity and performance of optical elements and optical support structures. The second goal addresses the process of integrating thermal and structural responses into optical design software packages. Such integrated techniques allow the numerical simulation of optical system performance while including the multidisciplinary aspects of the design process. This leads to shorter design cycles, optimized designs, and models that accurately predict hardware behavior. An example of a detailed finite-element model and the corresponding hardware is shown below for NASA's Earth Observer-1, which was successfully launched in November 2000.

The first two chapters provide a review and act as reference material for the rest of the chapters in the text. The first chapter provides a review of mechanical engineering and finite element theory. Included in this section are the equations of elasticity, fracture mechanics, failure theories, heat transfer, structural dynamics, and a discussion on finite-element modeling issues. The second chapter discusses optical fundamentals and performance metrics including polarization, image quality, and image formation. In addition, the use of Zernike polynomials and Legendre-Fourier polynomials are introduced to represent optical surface data. Chapter 3 discusses finite-element model construction and analysis methods for predicting displacements of optical components and support structures. Topics include modeling methods for optical components, adhesive bond models, surface coating effects, flexure mounts, test supports, and assembly processes. Chapters 4 and 5 discuss methods to integrate structural and thermal response quantities into the optical model and the effect they have on optical performance. Chapter 4 details how to represent optical element rigid-body motions and the use of interferogram files to represent optical surface deformations in the optical model. Also discussed are methods to predict line-of-sight error using finite- element analysis and design equations to minimize the effect of mechanical obscurations on image quality. Chapter 5 discusses thermoelastic and thermo-optic modeling techniques. Also included in this chapter are modeling techniques to account for bulk volumetric absorption, mapping temperatures from the thermal to structural model, and methods to account for moisture and adhesive curing. Chapter 6 provides an introduction to the analysis of adaptive optics. Concepts and definitions including correctability and influence functions are discussed. Also, the mathematics to compute actuator inputs to minimize optical surface deformations are presented along with examples. Chapter 7 discusses structural optimization theory and applications, including the use of optical responses as constraints in structural optimization models. An application of multidisciplinary optimization is reviewed.

In Chapter 8, a simple telescope serves as an example for many of the analysis techniques discussed in earlier chapters. Model files and results files are included on a CD so that readers can review specific details of input and output and even run the example cases as desired. In Chapter 9, an integrated optomechanical analysis example is presented for a lens assembly with laser loading. Thermal, structural, and optical analyses are performed to compute the change in focus, wavefront error, point spread function, and modulation transfer function as a function of laser power.

Numerical simulation plays an integral role in the development of a successful hardware program. The goals of this tutorial are to present optomechanical modeling and integrating techniques to develop multidisciplinary models to effectively design and analyze high-performance optical systems. Ultimately, these techniques may be employed to perform detailed design trades, minimize schedule and cost, and maximize optical performance.


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