詳細

The development of integrated optomechanical analysis tools has increased significantly over the past decade to address the ever-increasing challenges in optical system design, leveraging advances in computational capability. This book presents not only finite element modeling techniques specific to optical systems but also methods to integrate the thermal and structural response quantities into the optical model for detailed performance predictions.

This edition updates and expands the content in the original SPIE Tutorial Text to include new illustrations and examples, as well as chapters about structural dynamics, mechanical stress, superelements, and the integrated optomechanical analysis of a telescope and a lens assembly.

Sample Pages (PDF)

1. Introduction to Mechanical Analysis Using Finite Elements
　1.1 Integrated Optomechanical Analysis Issues
　　1.1.1 Integration issues
　　1.1.2 Example: orbiting telescope
　　1.1.3 Example: lens barrel
　1.2 Elasticity Review
　　1.2.1 Three-dimensional elasticity
　　1.2.2 Two-dimensional plane stress
　　1.2.3 Two-dimensional plane strain
　　1.2.4 Principal stress and equivalent stress
　1.3 Materials
　　1.3.1 Overview
　　1.3.2 Properties of common materials in optical structures
　　1.3.2 Figures of Merit
　　1.3.5 Discussion of materials
　　1.3.6 Common telescope materials
　1.4 Basics of Finite Element Analysis
　　1.4.1 Finite element theory
　　1.4.2 Element performance
　　1.4.3 Structural analysis equations
　　1.4.4 Thermal analysis with finite elements
　　1.4.5 Thermal analysis equations
　　1.5 Symmetry in FE models
　　1.5.1 General loads
　　1.5.2 Symmetric loads
　　1.5.3 Modeling techniques
　　1.5.4 Axisymmetry
　　1.5.5 Symmetry: pros and cons
　1.6 Model Checkout
　1.7 Summary
　References
　Appendix
　　A.1 RMS calculations
　　A.2 Peak-to-Valley
　　A.3 Orthogonality
　　A.4 RSS calculations
　　A.5 Coordinate transformations for vectors
　　A.6 Coordinate transformations for stress and materials
　　A.7 Factor of Safety, Margin of Safety, Model Uncertainty Factor
2. Introduction to Optics for Mechanical Engineers
　2.1 Electromagnetic Basics
　2.2 Polarization
　2.3 Rays, Wavefronts, and Wavefront Error
　2.4 Optical Aberrations
　2.5 Image Quality and Optical Performance
　　2.5.1 Diffraction
　　2.5.2 Measures of image blur
　　　2.5.2.1 Spot diagrams
　　　2.5.2.2 Point spread function
　　　2.5.2.3 Encircled energy function
　　2.5.3 Optical resolution
　　2.5.4 Modulation transfer function
　2.6 Image Formation
　　2.6.1 Spatial domain
　　2.6.2 Frequency domain
　2.7 Imaging System Fundamentals
　2.8 Conic Surfaces
　2.9 Mechanical Obscurations
　　2.9.1 Obscuration periphery, area, and encircled energy
　　2.9.2 Diffraction effects for various spider configurations
　　2.9.3 Diffraction spikes
　2.10 Optical System Error Budgets
3. Zernike and Other Useful Polynomials
　3.1 Zernike Polynomials
　　3.1.1 Standard Zernike polynomials
　　3.1.2 Fringe Zernike polynomials
　　3.1.3 Magnitude and phase
　　3.1.4 Orthogonality of Zernike polynomials
　　3.1.4.1 Noncircular apertures
　　3.1.4.2 Discrete data
　　3.1.5 Computing the Zernike polynomial coefficients
　　　3.1.5.1 Amplitude normalization
　　　3.1.5.2 Radial normalization
　　　3.1.5.3 Goodness of fit
　　　3.1.5.4 Off-axis optics
　　　3.1.5.5 Singularities
　3.2 Annular Zernike Polynomials
　3.3 Aspheric and Forbes Polynomials
　3.4 X-Y and Legendre Polynomials
　3.5 Grazing Incidence Optics
　　3.5.1 Fourier-Legendre Polynomials
　　3.5.2 Legendre Polynomials
4. Optical Surface Errors
　4.1 Optical Surface Rigid-Body Errors
　　4.1.1 Computing rigid-body motions
　　　4.1.1.1 Pros/Cons of subtracting RB before poly fit
　　　4.1.1.2 Combining results for segmented optics
　　　4.1.1.3 Transformation to alternate coordinate system
　　4.1.2 Representing rigid-body motions in the optical model
　4.2 Optical-Surface Shape Changes
　　4.2.1 Surface normal deformations
　　　4.2.1.1 Relating refractive surface errors to wavefront errors
　　　4.2.1.2 Relating reflective surface errors to wavefront errors
　　4.2.2 Sag deformations
　　　4.2.2.1 Radial Correction
　　　4.2.2.2 Isothermal example
　　　4.2.2.3 Rigid-body motion example
　4.3 Optical Surface Deformations and Zernike Polynomials
　4.4 Representing Elastic Shape Changes in the Optical Model
　　4.4.1 Polynomial surface definition
　　4.4.2 Interferogram files
　　4.4.3 Uniform arrays of data
　　　4.4.3.1 Grid sag surface
　　　4.4.3.2 Interpolation
　　4.4.4 Comparison of techniques
　　　4.4.4.1 Accuracy in Optical design codes
　　　4.4.4.2 dz vs dn (fomats, issues) in Optical design codes
　　　4.4.4.3 Residual error and quilting
　4.5 Predicting Wavefront Error Using Sensitivity Coefficients
　　4.5.1 Rigid-body and radius of curvature sensitivity coefficients
　　　4.5.1.1 Computing radius of curvature changes
　　4.5.2 Use of Zernike sensitivity coefficients
　4.6 Finite-Element-Derived Spot Diagrams
　4.7 Correlation of Test and Analysis
　　4.7.1 Interferometer output options
　　4.7.2 Orientation, order, normalization
　　4.7.3 Load effects vs Locked-in effects
　　4.7.4 Example
　　　4.7.4.1 Example
　4.8 References
5. Displacement Analysis of Optical Elements
　5.1 Displacement Models of Optics
　　5.1.1 Definitions
　　5.1.2 Single point models
　　5.1.3 Solid optics
　　　5.1.3.1 Two-dimensional models
　　　5.1.3.2 Three-dimensional element models
　　5.1.4 Lightweight mirror models
　　　5.1.4.1 Two-dimensional equivalent-stiffness models
　　　5.1.4.2 Three-dimensional equivalent-stiffness models
　　　5.1.4.3 Three-dimensional plate/shell model
　　　5.1.4.4 Example: comparison of a lightweight mirror models
　　　5.1.4.5 Example: LW mirror with significant quilting
　　5.1.5 Generation of powered optic models
　　　5.1.5.1 On-axis slumping
　　　5.1.5.2 Off-axis slumping
　　　5.1.5.3 Calculation of local segment sag
　　5.1.6 Symmetry in Optics
　　　5.1.6.1 Creating symmetric models
　　　5.1.6.2 Example of symmetry verification check
　5.2 Displacement Analysis Methods
　　5.2.1 Analysis of surface effects
　　　5.2.1.1 Composite-plate model
　　　5.2.1.2 Homogeneous-plate model
　　　5.2.1.3 Three-dimensional model
　　　5.2.1.4 Example: coating-cure shrinkage
　　　5.2.1.5 Example: Twyman effect
　References
6. Modeling of Mounts and Bonds
　6.1 Displacement Models of Adhesive Bonds
　　6.1.1 Elastic behavior of adhesives
　　6.1.2 Detailed three-dimensional solid model
　　　6.1.2.1 Conventional models
　　　6.1.2.2 Glued contact models
　　6.1.3 Equivalent stiffness bond models
　　　6.1.3.1 Effective properties of hockey-puck type bonds
　　　6.1.3.2 Example: modeling of a hockey-puck type bond
　　　6.1.3.3 Effective properties for ring bonds
　6.2 Displacement Models of Flexures and Mounts
　　6.2.1 Classification of structures and mounts
　　　6.2.1.1 Classification of structures
　　　6.2.1.2 Classification of mounts
　　　6.2.1.3 Mounts in 3D space
　　6.2.2 Modeling of kinematic mounts
　　6.2.3 Modeling of flexure mounts
　　　6.2.3.1 Arrangement of strut supports
　　　6.2.3.2 Optimal radial location of mounts
　　　6.2.3.3 Modeling of beam flexures
　　　6.2.3.4 Example: modeling of bipod flexures
　　　6.2.3.5 Design issues with bipod flexures
　　　6.2.3.6 Modeling of blade flexures
　6.3 Modeling of Test Supports
　　6.3.1 Modeling of air bags
　　6.3.2 Example: test support deformation analysis of a nonaxisymmetric optic
　　6.3.3 Modeling of V-block test supports
　　6.3.4 Modeling of sling and roller-chain test supports
　　6.3.5 Comparison of three test supports
　6.4 Tolerancing Analysis of Mounts
　　6.4.1 Monte Carlo analysis
　　6.4.2 Example: Flatness tolerance of mirror mount
　6.5 Analysis of Assembly Processes
　　6.5.1 Theory
　　6.5.3 Example: assembly analysis of mirror mounting
　References
7. Structural Dynamics and Optics
　7.1 Natural Frequencies and Mode Shapes
　7.2 Damping
　7.3 Frequency Response Analysis
　　7.3.1 Force excitation
　　7.3.2 Absolute motion due to base excitation
　　7.3.3 Relative motion due to base excitation
　7.4 Random Vibration
　　7.4.1 Random vibration in the time domain
　　7.4.2 Random vibration in the frequency domain
　　7.4.3 Random vibration SDOF approximations
　　7.4.4 Random vibration design levels
　7.5 Force Limiting
　7.6 Vibro-Acoustic Analyses
　7.7 Shock Analysis
　7.8 Line-of-Sight Jitter
　　7.8.1 Performing LOS jitter analyses
　　7.8.2 Cassegrain telescope LOS jitter example
　　7.8.3 Identifying the critical structural modes
　　7.8.4 Effects of LOS jitter on Image quality
　　　7.8.4.1 Constant velocity image motion
　　　7.8.4.2 High-frequency sinusoidal image motion
　　　7.8.4.3 Low-frequency sinusoidal image motion
　　　7.8.4.4 Random image motion
　　　7.8.4.5 Impact of sensor integration time
　7.9 Active Image Stabilization
　7.10 State-Space Matrices
　7.11 Multi-Axis Vibration Isolation
　　7.11.1 Hexapod isolation systems
　7.12 Optical Surface Errors due to Dynamic Loads
　　7.12.1 System wavefront error
　References
8. Mechanical Stress and Optics
　8.1 Stress Analysis Using FEA
　　8.1.1 Coarse models
　　8.1.2 Stress singularities
　　8.1.3 FEA post-processing
　8.2. Analysis of Ductile Materials
　　8.2.1 Micro-yield
　　8.2.2 Ultimate strength
　8.3 Analysis of brittle materials
　　8.3.1 Fracture toughness
　　8.3.2 FEA methods to compute the stress intensity
　8.4 Design Strength of Optical Glass
　　8.4.1 Surface flaws
　　8.4.2 Controlled polishing and grinding
　　8.4.3 Inert strength
　　　8.4.3.1 Residual stress and inert strength
　　　8.4.3.2 Inert strength based on Weibull statistics
　　　8.4.3.3 Design strength using Weibull statistics
　　　8.4.3.3.1 Extrapolating test data to components
　　8.4.3 Environmentally enhanced fracture
　　　8.4.3.1 Crack growth studies
　　　8.4.3.2 Static and dynamic fatigue testing
　　　　8.4.3.2.1 Effects of residual stress on the fatigue resistance parameter
　　　8.4.3.3 Lifetime and time-to-failure analyses
　　　8.4.3.4 Lifetime prediction and probability of failure
　　　8.4.3.5 Effects of residual stress on time-to-failure
　　8.4.4 Proof testing
　　8.4.5 Cyclic fatigue
　8.5 Stress Birefringence
　　8.5.1 Mechanical stress and the index ellipsoid
　　8.5.2 Optical errors due to stress birefringence
　　8.5.3 Stress-optical coefficients
　　8.5.4 Non-uniform stress distributions
　　8.5.5 Stress birefringence example
　　8.5.6 Stress birefringence and optical modeling
　References
9. Optothermal Analysis Methods
　9.1 Thermal Analysis
　9.2 Thermo-Elastic Analysis
　　9.3.1 CTE temperature dependence
　　9.3.2 CTE inhomogeneity
　9.3 Index of Refraction Changes with Temperature
　　9.3.1 Sellmeier dispersion equation
　9.4 Effects of Temperature on Simple Lens Elements
　　9.4.1 Focus shift of a doublet lens due to isothermal change
　　9.4.2 Radial gradients
　9.5 Thermal Effects Using Optical Design Software
　　9.5.1 Representing OPD maps in the optical model
　9.6 Thermo-Optic Analysis
　　9.6.1 Thermo-optic finite element models
　　　9.6.1.1 Multiple reflecting surfaces
　　9.6.2 Thermo-optic errors using integration techniques
　　9.6.3 User-defined surfaces and gradients
　9.7 Bulk Volumetric Absorption
　9.8 Mapping of Temperature Fields from the Thermal Model to the Structural Model
　　9.8.1 Nearest-node methods
　　9.8.2 Conduction analysis
　　9.8.3 Shape function interpolation
　9.9 Analogous Techniques
　　9.9.1 Moisture absorption
　　9.9.2 Adhesive curing
　References
10. Adaptive Optics Analysis Methods
　10.1 Introduction
　10.2 Method of Simulation
　　10.2.1 Determination of actuator inputs
　　10.2.2 Characterization metrics of adaptive optics
　　　10.2.2.1 Example: Adaptive control simulation of a mirror segment
　　10.2.3 Practical implementation
　　　10.2.3.1 Augment actuators
　　　10.2.3.2 Example of augment actuators
　　　10.2.3.3 Slope control
　　　10.2.3.4 Actuator failure
　　　10.2.3.5 Actuator stroke limits
　　　10.2.3.6 Actuator resolution and tolerancing
　　　10.2.3.7 Example of actuator resolution analysis
　10.3 Design Optimization of Adaptively Controlled Optics
　　10.3.1 Adaptive control simulation in design optimization
　　　10.3.1.1 Example: Structural design optimization of an adaptively controlled optic
　　10.3.2 Actuator placement optimization
　　　10.3.2.1 Example: actuator layout optimization of a grazing incidence optic
　10.5 Stressed-Optic Polishing
　　10.5.1 Adaptive control simulation in stressed-optic polishing
　　10.5.2 Example: stressed-optic polishing of hexagonal array optics
　10.6 Analogies Solved via Adaptive Tools
　　10.6.1 Correlation of CTE variation
　　10.6.2 Mount distortion
　References
11. Optimization of Optomechanical Systems
　11.1 Overview
　11.2 Optimization Theory
　11.3 Structural Optimization of Optical Performance
　　11.3.1 Use of design response equations in the FE model
　　11.3.2 Use of external design responses in FEA
　11.4 Integrated Thermal-Structural-Optical Optimization
　References
12. Superelements in Optics
　12.1 Background
　　12.2 Superelement Theory
　　　12.2.1 Static analysis
　　　12.2.2 Dynamic analysis
　　　　12.2.2.1 Guyan reduction
　　　　12.2.2.2 Component mode synthesis
　　　12.2.3 Types of superelements
　　　　12.2.3.1 Conventional SE
　　　　12.2.3.2 External SE
　12.3 Application to Optics
　　12.3.1 Kinematic mounts
　　12.3.2 Segmented optics
　12.4 Advantages of Superelements
　12.5 Telescope Example
　References
13. Integrated Optomechanical Analysis of a Telescope
　13.1 Overview
　13.2 Optical Model Description
　13.3 Structural Model Description
　13.4 Optimizing the PM with Optical Measures
　13.5 Line-of-Sight Calculations
　13.6 On-Orbit Image Motion Random Response
　13.7 Detailed Primary Mirror Model
　13.8 RTV vs Epoxy Bond
　13.9 Gravity Static Performance
　13.10 Thermoelastic performance
　13.11 Polynomial coefficients
　13.12 Assembly Analysis
　13.13 Other Analyses
　13.14 Superelements
　References
14. Integrated Optomechanical Analysis of a Lens Assembly
　14.1 Double Gauss Lens Assembly
　　14.1.2 Steady-state thermal analysis
　　14.1.3 Thermo-elastic analysis
　　14.1.4 Stress birefringence analysis
　　14.1.5 Thermo-optic analysis
　　14.1.6 Optical performance versus thermal loading