Pose-varied Multi-axis Optical Finishing Systems (eBook)

Preface 5
Acknowledgments 6
Contents 7
1 Modeling on the Coverage of Free-Form Surfaces 10
Abstract 10
1.1 Questions for the Mapping of Free-Form Surfaces 10
1.2 Short Segments Generation 13
1.3 Modeling in Parallelogram Regions 15
1.4 Mapping Coverage of 3D Surfaces 18
1.4.1 Scanning the u-Strips 19
1.4.2 Partitioning 20
1.4.3 Simulations 21
1.5 Multiple Diagonal Segments 23
1.5.1 A Row of Parallelograms 24
1.5.2 Path with Multiple Diagonal Segments 26
1.5.3 Simulations 28
1.6 Process Validation 32
References 34
2 Define and Synthesis on Orbit Diversity 36
Abstract 36
2.1 Basic Model Along Orbit 36
2.2 Linear Orbit Features 40
2.2.1 Transformation Model of Gaussian Function 40
2.2.2 The Processing Steps with Multiplex Orbit 45
2.3 Curve Orbit Features 46
2.3.1 Effects of Curvatures 47
2.3.2 Effects of Corners with Different Angles 50
2.4 Combined Effect 53
2.4.1 Spiral Orbit 54
2.4.2 Raster Orbit 56
2.5 Process Validation 57
2.5.1 Spiral Orbit Finishing 57
2.5.2 Optimized Spiral Orbit 57
2.5.3 Raster Orbit Finishing 64
2.5.4 Optimized Raster Orbit 64
References 71
3 Conquering the Dynamic Limitation of Velocity 73
Abstract 73
3.1 Velocity Analysis 73
3.1.1 Analysis of Velocity and Position 75
3.1.2 Velocity Checking and Smoothing 77
3.2 Concept of Velocity-Variant Regime 79
3.2.1 Velocity-Variant Regime and Conflicts Between Convergence Rate and Efficiency 79
3.3 Models for Suppressing Velocity Limitation 82
3.3.1 Adding a Fictitious Removal Layer 82
3.3.2 Reducing the Removal Rate of TIFs 82
3.3.3 Traversing Nonuniform Orbits 83
3.4 The Controllable and Time-Variant TIFs Finishing Regime 84
3.4.1 The Construction of CTVT Regime 84
3.4.2 The Comparisons 87
3.5 Process Validation 88
3.5.1 Without CTVT Regime 88
3.5.2 With CTVT Regime 89
3.5.3 With CTVT and Larger Removal Rate 90
References 91
4 Prediction on Dwell Effects and Nonlinear Pressure Distribution 93
Abstract 93
4.1 Analysis of Nonuniform Dwell 93
4.1.1 Material Removal Profile 95
4.1.2 Discrepancy in Removal Near the Edge 96
4.1.3 Simulation of Edge Rectification 98
4.1.3.1 Nonoverlapping Dwells 99
4.1.3.2 Half-Overlapping Dwells 101
4.1.3.3 Two-Third Overlapping Dwells 103
4.1.3.4 Beyond Two-Third Overlapping Dwells 105
4.1.3.5 Error Remaining 106
4.2 Weaken of Edge Dwell Effects 107
4.2.1 Situation of Different Tools 108
4.2.2 Orbits Extension 109
4.2.3 Surface Error Matrix Extension 110
4.2.4 Extension Algorithms 110
4.2.4.1 Setting Zero 110
4.2.4.2 Gaussion Extension Algorithms 111
4.2.4.3 Neighbor Average Extension Algorithms 112
4.2.4.4 Gerchberg-Pupil Extension Algorithms 113
4.3 Effects of Nonlinear Pressure Related Distribution 115
4.3.1 Tool Influence Functions (TIFs) 116
4.3.2 Modified Pressure Distribution Model 117
4.3.3 Modified Emulational TIFs Model 119
4.3.4 Reverse-Calculation of Material Removal Rate 121
4.4 Process Validation 121
4.4.1 Validating the Edge Correction 121
4.4.2 Validating the Edge Extension 124
4.4.3 Validating the Removal Shape of e-TIFs 128
4.4.4 Validating the Effectiveness of the Predicting Model 131
References 132
5 Correction on Data Matching and Remounting Errors 135
Abstract 135
5.1 Aspheric Calculation and Nonlinear Mapping Correction 135
5.1.1 Description of an Off-Axis Aspheric Surface 136
5.1.2 Non-negative Minimized Removal Criterion 137
5.1.3 The Estimate of Radius of Curvature and Conic Constant 139
5.1.4 Design on the Interferometric Testing System 140
5.1.5 Calculation on the Distorted Surface Error 142
5.1.6 Multiregion Distribution Strategy 145
5.1.7 Process Validation 148
5.2 Remounting Errors Correction 152
5.2.1 Effect of Dismatched Coordinate Systems 152
5.2.2 Strategy for Reducing Remounting Errors 154
5.2.2.1 Mathematical Model of Remounting Error 154
5.2.2.2 Mask for Providing Reference Points 155
5.2.3 Process Validation 157
References 161