Large and Middle-scale Aperture Aspheric Surfaces
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Professor Shengyi Li, College of Mechatronics and Automation, National University of Defense Technology, Hunan, China. Prior to moving to the NUDT, Professor Li was a Visiting Scholar at Rensselaer Polytechnic Institute, and Columbia University, both USA. He has contributed to over 200 publications, including 130 refereed journal articles, 6 edited books (all in Chinese) and 11 invited reports. Professor Li's current research interests include ultra-precision machining technology, magnetorheological finishing, ion beam figuring, measurement and control of precision mechatronic system, and theory and technology of modern optical testing.
Yifan Dai, Director, Department of Mechatronic Engineering, College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha, China.
Content
About the Author xiii
Foreword xv
Preface xvii
1 Foundation of the Aspheric Optical Polishing Technology 1
1.1 Advantages and Application of Aspheric Optics 1
1.1.1 Advantages of Optical Aspherics 1
1.1.2 The Application of Aspheric Optical Components in Military Equipment 2
1.1.3 The Aspheric Optical Components in the Civilian Equipment 2
1.2 The Characteristics of Manufacturing Aspheric Mirror 3
1.2.1 Requirements of Modern Optical System on Manufacturing Aspheric Parts 3
1.2.2 The Processing Analysis of Aspheric Optical Parts 7
1.3 The Manufacturing Technology for Ultra-Smooth Surface 9
1.3.1 Super-Smooth Surface and Its Applications 9
1.3.2 Manufacturing Technology Overview of Super-Smooth Surface 11
1.3.3 Manufacturing Technology of Ultra-Smooth Surface Based on the Mechanical Micro-Cutting Principles 12
1.3.4 The Traditional Abrasive Polishing Technology for Ultra-Smooth Surface 13
1.3.5 The Principles and Methods of Non-contact Ultra-Smooth Polishing 15
1.3.6 The Non-contact Chemical Mechanical Polishing (CMP) 17
1.3.7 The Magnetic Field Effect Auxiliary Processing Technology 17
1.3.8 The Particle Flowing Machining Technology 18
1.4 The Advanced Aspheric Optical Polishing Technology 19
1.4.1 The Classic Polishing for Aspheric Optical Parts 19
1.4.2 The Modern CNC Polishing Method of Aspheric Optical Parts 20
1.4.3 The Controllable Compliant Tool (CTT) Manufacturing Technology for Aspheric Optical Components 22
1.5 The CCT Based on Elasticity Theory 28
1.5.1 The Controlled Elastic Deformation Pad Polishing-Stressed-Lap Polishing (SLP) 29
1.5.2 The Controlled Mirror Body Elastic Deformation Polishing by Active Support 29
1.5.3 Bonnet Polishing with Precession Process 30
1.6 The Key Basic Theory of CCT Technology Based on the Multi-Energy Field 30
1.6.1 The Material Removal Mechanism and Mathematical Model 31
1.6.2 The Multi-Parameter Control Strategy 32
1.6.3 4D CNC Technology 34
1.6.4 The Evolution Theory and Control Technology of the Errors 36
1.6.5 The Equipment and Technology of the CCT 40
References 41
2 The Basic Theory of Aspheric Optical Lapping and Polishing Technology 45
2.1 The Preston Equation of Optical-Mechanical Polishing Technology and Its Application 45
2.1.1 The Preston Equation 45
2.1.2 The Application of Preston Equation in the Traditional Polishing 47
2.2 The Deterministic Processing Principle for Aspheric 49
2.3 The Molding Theory of Aspheric Surface Processing 51
2.3.1 The Dual-Series Model for the Aspheric Molding Process 51
2.3.2 The Influence of the Removal Function Size on the Processing 53
2.3.3 The Influence of Removal Function Disturbing 55
2.3.4 The Influence of the Positioning Errors 59
2.3.5 The Influence of Discrete Interval 60
2.4 The Figuring Theory of Linear Scanning Mode on Full-Aperture 63
2.4.1 The Iterative Algorithm Based on Bayesian 64
2.4.2 The Pulse Iterative Method 72
2.4.3 The Truncated Singular Value Decomposition 73
2.5 The Polar Scanning Mode of Surface Figuring 76
2.5.1 The Removal Function with Approximate Rotation Symmetry Property 76
2.5.2 The Removal Function without the Characteristics of Rotation Symmetry 78
2.6 The Frequency Domain Analysis of Forming 83
2.6.1 The Characteristics of the Spectrum Under the General Forming Conditions 84
2.6.2 The Figuring Ability of the Rotary Symmetric Removal Function 86
2.7 Maximum Entropy Principle of Polishing 87
2.7.1 The Entropy Principle Expression for Polishing 88
2.7.2 An Application Example of the Principle of Maximum Entropy in the Fixed Eccentric Flat Polishing 89
2.7.3 The Example of Processing Parameter Choice Based on Maximum Entropy Principle for Dual-Rotor Pad 92
2.7.4 The Example of Inhibition Medium and High Frequency Errors Based on the Entropy Increase Principle for the MRF 96
Appendix 2.A Two-Dimensional Hermite Series 102
Appendix 2.B Two-Dimensional Fourier Series 104
Appendix 2.C The Dual-Series Model Solution of Dwell Time 106
Appendix 2.D The Error Analysis of the Dual-Series Model Solution for Dwell Time 108
References 109
3 CCOS Technology Based on Small Polishing Pad 113
3.1 Review of CCOS Technology Based on Small Polishing Pad 113
3.1.1 Progress of Small Tool CCOS Technology 113
3.1.2 Key Problems of Small Tool CCOS Technology 115
3.2 Aspheric Optical Compound Machining Tool Optical Aspherical Mirror Process Machine Tool 118
3.3 Modeling and Analysis of Removal Function 120
3.3.1 Characteristics of Ideal Removal Function 120
3.3.2 Theoretical Model 121
3.3.3 Experimental Model 122
3.3.4 Figuring Ability Analysis of Removal Function 124
3.3.5 Modeling and Analysis of the Complex Shape Polishing Pad's Removal Function 128
3.4 Calculation and Analysis of Dwell Time in CCOS Technology 136
3.4.1 Pulse Iterative Method Based on Process Time 136
3.4.2 Influence of Convolution Effect on Residual Error 138
3.5 Removal Function Modeling Under the Edge Effect 147
3.5.1 Pressure Distribution When the Polishing Pad Out of Edge 148
3.5.2 Removal Function Modeling Under Edge Effect 152
3.6 Cause and Modification Method of Optical Surface Small-Scale Manufacturing Error 157
3.6.1 Cause and Evaluation of Optical Surface Small-Scale Manufacturing Error 157
3.6.2 Full Aperture Uniform Polishing Correction Method of Small-Scale Manufacturing Error 159
3.6.3 Deterministic Local Modification Method of Small-Scale Manufacturing Error 173
References 176
4 Ion Beam Figuring Technology 179
4.1 Outline of Ion Beam Figuring Technology 179
4.1.1 Application of Ion Beam Processing Technology 179
4.1.2 The Basic Mechanism and Character for Optical Machining by IBF 181
4.1.3 Development of IBF of Optical Mirror 183
4.2 Basic Principle of IBF for Optical Mirror 185
4.2.1 Description of Ion Sputter Process 185
4.2.2 Material Removal Rate of IBF 188
4.3 Analysis of Removal Function Model in IBF 199
4.3.1 Theoretical Modeling of Removal Function in IBF 199
4.3.2 Experiment Analysis of the Removal Function Character in IBF 203
4.3.3 Experiment Modeling of Removal Function in IBF 208
4.4 IBF System Design and Analysis 210
4.4.1 System Set-Up 210
4.4.2 System Analysis 213
4.5 Micro-Scale Error Evolution During IBF 222
4.5.1 Surface Roughness Evolution 222
4.5.2 Microscopic Morphology Evolution 223
4.6 The Polishing Experiment of IBF 230
4.6.1 Flat Optical Mirror Polishing Experiment 230
4.6.2 Curved Surface Figuring Experiment 232
References 235
5 Magnetorheological Figuring 237
5.1 Overview of Magnetorheological Figuring 237
5.1.1 Applications of Magnetorheological Fluid 237
5.1.2 Development of Magnetic-Effect-Assisted Polishing Techniques for Optics 239
5.1.3 Development of Deterministic Magnetorheological Figuring 240
5.2 Mechanism and Mathematical Model of MRF Material Removal 244
5.2.1 Mechanism of MRF Material Removal 244
5.2.2 Theoretical Calculation of Load on Single Abrasive and Indentation Depth 245
5.2.3 Fluid Dynamics Analysis and Calculation in Polishing 247
5.3 MRF Machine Tools 257
5.3.1 Basic Requirement on MRF Machine Structure 257
5.3.2 Machine Structure of MRF Experimental Prototype 258
5.3.3 Design of Upside Down MRF Polishing Devices 259
5.3.4 MR Fluid Circulation and Control System 263
5.4 MR Fluid and Its Performance 264
5.4.1 Current Situation of MR Fluid Research 264
5.4.2 Components of MR Fluid and Its Performance 265
5.4.3 Principles on Choosing MR Fluid Elements 269
5.4.4 Preparation of MR Fluid 272
5.5 Optimization of MRF Processing Parameters 272
5.5.1 Orthogonal Experiments on MRF Process Parameters 273
5.5.2 Grey Correlation Analysis 276
5.5.3 Parameter Optimization of Multiple Process Indexes 279
5.5.4 Comprehensive Optimization of Machining Process 280
5.6 MRF Optical Surfacing Technique and Machining Experiment 280
5.6.1 Algorithm of Dwell Time for Optical MRF Surfacing 280
5.6.2 MRF Polishing Examples 284
5.7 Magnetorheological Jet Polishing 294
5.7.1 Overview of Abrasive Jet Polishing 294
5.7.2 MJP Experiment and Analysis 295
5.7.3 CFD Analysis on MJP Removal Mechanism 298
5.7.4 MJP Polishing Experiments 303
References 304
6 Evaluation of Deterministic Optical Machining Errors 307
6.1 Introduction 307
6.2 Usual Evaluation Method of Optical Machining Errors 308
6.2.1 Evaluation Parameters of Geometrical Accuracy in Optical Machining Process 308
6.2.2 Evaluation Method of Optical Machining Errors Based on PSD Character Curve 310
6.2.3 Evaluation Method of Optical Machining Errors Based on Scattering Theory 311
6.2.4 Evaluation Method of Optical Machining Errors Based on Statistical Optical Theory 311
6.3 Analysis on Distribution Characteristics of Optical Machining Errors 312
6.3.1 Evaluation and Analysis on Machining Errors of Any Direction on Optical Surface 312
6.3.2 Evaluation and Analysis of Local Errors on Optical Surface 319
6.3.3 Influence of Processing Method on Optical Machining Errors 323
6.4 Scattering Evaluation of Optical Machining Errors 340
6.4.1 Binary Separation of Frequency Band for Optical Machining Errors 341
6.4.2 Evaluation Based on Harvey-Shack Scattering Theory 344
6.4.3 Influence of Optical Machining Errors on Scattering Properties 348
6.5 Evaluation of Frequency Band Errors Based on Optical Performance 353
6.5.1 Influence Characteristic of Different Frequency Errors on Optical Performance 353
6.5.2 Requirement of Frequency Band Errors in Different Optical Applications 356
6.5.3 Evaluation of F200 mm Paraboloid Mirror Machined by IBF 365
References 370
7 Measurement Technology in Manufacturing of Large-Middle Optical Surfaces 373
7.1 Introduction 373
7.1.1 Requirements of Large-Middle Optical Surfaces 373
7.1.2 Overview of Measurement in Manufacturing of Large-Middle Optical Surfaces 375
7.2 Principles of Coordinate Measurement Technology in Manufacturing of Large-Middle Optical Surfaces 376
7.3 Interferometric Null Test in Manufacturing of Large-Middle Optical Surfaces 377
7.3.1 Basic Principle of Interferometric Null Test 377
7.3.2 Null Test of Large-Middle Planar and Spherical Surfaces 378
7.3.3 Null Test of Conic Surfaces Using Conjugates 379
7.3.4 Null Test of Aspheric Surfaces Using Compensators 383
7.3.5 Null Test with Computer Generated Holograms 384
7.4 Non-Null Test in Manufacturing of Large-Middle Optical Surfaces 386
7.4.1 Shear Interferometry 386
7.4.2 Interferometry with High Resolution CCD 386
7.4.3 Sub-Nyquist Interferometry 387
7.4.4 Long-Wavelength Interferometry 387
7.4.5 Subaperture Stitching Interferometry 387
7.5 Phase Retrieval Technology 388
7.6 Subsurface Quality Assessment 388
References 389
8 Coordinate Measuring Technology of Optical Aspheric Surface 391
8.1 State of the Art of the Coordinate Measuring Technology of Optical Aspheric Surface 391
8.1.1 Status and Characteristics of Coordinate Measuring Technology for Optical Aspheric Surface 391
8.1.2 State of the Art of Optical Aspheric Coordinate Measuring Technology and Development Tendency 393
8.2 Large Aperture Aspheric Coordinate Measuring Technology 397
8.2.1 The Design of Coordinate Measuring System 397
8.2.2 The Measurement Principle of Large Aspheric Coordinate Measuring 405
8.2.3 Analysis and Evaluation of Optical Aspheric Form Error Based on Multiple Section Line Measurement 408
8.2.4 Machining Case-Machining and Measuring of Ø500 mm Aspheric 421
8.3 The Swing Arm Measurement of Large Aspheric 425
8.3.1 The Analysis of Measuring Principle 425
8.3.2 The Structural Design of Measuring System 430
8.3.3 The Accuracy Analysis and Modeling of the Measuring System 431
8.3.4 The Optimization Algorithm for Swing Arm Profilometry Measuring Aspheric Vertex Curvature Radius 438
8.3.5 The Simulation of Measurement Algorithm and Measurement Experiments 442
References 446
9 Subaperture Stitching Interferometry 449
9.1 Introduction 449
9.1.1 Basic Principle of Subaperture Stitching Interferometry 449
9.1.2 Overview of Subaperture Stitching Interferometry 449
9.2 Fundamentals of Subaperture Stitching Algorithm 452
9.2.1 Mathematical Model of Two-Subaperture Stitching 452
9.2.2 Model and Algorithm for Simultaneous Stitching 453
9.3 Iterative Algorithm for Subaperture Stitching 454
9.3.1 Mathematical Model 455
9.3.2 Iterative Algorithm 460
9.3.3 Coarse-Fine Stitching Strategy for Large Optical Surfaces 463
9.4 Method for Subaperture Lattice Design 463
9.4.1 Rough Design of Lattice 464
9.4.2 Calculation of Best-Fit Spheres for Subapertures 467
9.4.3 Simulation and Verification of Lattice Design 469
9.5 Subaperture Stitching Interferometer 472
9.5.1 Mechanical Configurations of Subaperture Stitching Interferometer 472
9.5.2 Kinematics of Subaperture Stitching Interferometer 474
9.6 Case Study 477
9.6.1 Large Flats and Planar Wavefronts 477
9.6.2 Spherical Surfaces 488
9.6.3 Aspheric Surfaces 491
9.7 Future Development of Subaperture Stitching Interferometry 495
9.7.1 Non-null Subaperture Stitching Test 496
9.7.2 Null Subaperture Stitching Test 496
9.7.3 Near-Null Subaperture Stitching Test 500
Appendix 9.A Derivation of the Linearized Configuration Optimization Subproblem 503
Appendix 9.B Block-Wise QR Decomposition Procedure for Linear LS Problem 506
References 507
10 Phase Retrieval In Situ Testing of Large-Middle Optical Surfaces 511
10.1 Introduction to Phase Retrieval Technology 511
10.1.1 Significance of Phase Retrieval In Situ Testing 511
10.1.2 Application of Phase Retrieval Method 512
10.1.3 Theory of Phase Retrieval Algorithm 513
10.2 Basic Principle and Algorithm for Phase Retrieval Optical Testing 514
10.2.1 Principle of Phase Retrieval Optical Testing 514
10.2.2 Diffraction Computation for Optical Field Propagation 517
10.2.3 Phase Retrieval Algorithm for Surface Figure Testing 519
10.3 Phase Retrieval Testing of Spherical Wavefronts 524
10.3.1 Measurement Setup 524
10.3.2 Measurement of Large Diameter Spherical Surface 524
10.4 Subpixel Phase Retrieval Testing 528
10.4.1 Principle of Subpixel Phase Retrieval Testing 529
10.4.2 Design of Subpixel Intensity Constraint Function 531
10.4.3 Subpixel Phase Retrieval Testing Experiments 533
10.5 Aspheric Phase Retrieval 535
10.5.1 Aspheric Departure 535
10.5.2 Characteristic of Aspheric Defocused Field 536
10.5.3 Measurement Plan for Aspheric Phase Retrieval 539
10.5.4 Aspheric Phase Retrieval Algorithm Design 541
10.5.5 Testing of a 170 mm Aperture Parabolic Surface 543
10.5.6 Phase Retrieval Testing of Aspheres Using Paraxial Conjugates 547
10.6 High Dynamic Range Phase Retrieval 550
10.6.1 High Dynamic Range Algorithm 550
10.6.2 Parametric Conjugate Gradient Method 552
10.6.3 Testing of Roughly Polished Surfaces 554
10.7 Phase Retrieval Testing of Off-Axis Aspheric 555
10.7.1 Phase Retrieval Principle for Off-Axis Aspheric 557
10.7.2 Testing of an Off-Axis Elliptical Surface 564
References 569
11 Subsurface Damage of Optical Components in Manufacturing Processes 573
11.1 Compendium of Subsurface Damage 573
11.1.1 Concept of Subsurface Damage 573
11.1.2 Influence of Subsurface Damage on the Service Performance of Optical Elements 574
11.2 Production Mechanism of Subsurface Damage 575
11.2.1 Production Mechanism of Subsurface Damage Induced in Grinding and Lapping Processes 575
11.2.2 Production Mechanism of Subsurface Damage Induced in Polishing Process 577
11.3 Measurement Techniques of Subsurface Damage 578
11.3.1 Destructive Measuring Methods 578
11.3.2 Non-destructive Measuring Methods 586
11.4 Relationship between Subsurface Damage and Surface Roughness of Optical Materials in Grinding and Lapping Processes 588
11.4.1 Measurement Ratio of Subsurface Damage Depth to Surface Roughness 589
11.4.2 Theoretical Analysis with Indentation Fracture Mechanics 591
11.5 Influence of Machining Parameters on Subsurface Damage Depth 594
11.5.1 Influence of Grinding Parameters on Subsurface Damage Depth 595
11.5.2 Influence of Lapping Parameters on Subsurface Damage Depth 597
11.6 Polishing Subsurface Damage and Its Elimination Process 608
11.6.1 Characteristics and Evaluation of Polishing Subsurface Damage 609
11.6.2 Improvement of Laser Induced Damage Threshold through the Elimination of Subsurface Damage 611
References 615
Index 617
