Optical Metrology Third Edition Kjell J. Gasvik˚ Spectra Vision AS, Trondheim, Norway Optical Metrology Third Edition Optical Metrology Third Edition Kjell J. Gasvik˚ Spectra Vision AS, Trondheim, Norway Copyright 2002 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. 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Contents Preface to the Third Edition xi 1Basics 1 1.1 Introduction 1 1.2 Wave Motion. The Electromagnetic Spectrum 1 1.3 The Plane Wave. Light Rays 3 1.4 Phase Difference 4 1.5 Complex Notation. Complex Amplitude 5 1.6 Oblique Incidence of A Plane Wave 5 1.7 The Spherical Wave 7 1.8 The Intensity 8 1.9 Geometrical Optics 8 1.10 The Simple Convex (Positive) Lens 10 1.11 A Plane-Wave Set-Up 11 2 Gaussian Optics 15 2.1 Introduction 15 2.2 Refraction at a Spherical Surface 15 2.2.1 Examples 19 2.3 The General Image-Forming System 19 2.4 The Image-Formation Process 21 2.5 Reflection at a Spherical Surface 23 2.6 Aspheric Lenses 25 2.7 Stops and Apertures 26 2.8 Lens Aberrations. Computer Lens Design 28 2.9 Imaging and The Lens Formula 29 2.10 Standard Optical Systems 30 2.10.1 Afocal Systems. The Telescope 30 2.10.2 The Simple Magnifier 32 2.10.3 The Microscope 34 vi CONTENTS 3 Interference 37 3.1 Introduction 37 3.2 General Description 37 3.3 Coherence 38 3.4 Interference between two Plane Waves 41 3.4.1 Laser Doppler Velocimetry (LDV) 45 3.5 Interference between other Waves 46 3.6 Interferometry 49 3.6.1 Wavefront Division 50 3.6.2 Amplitude Division 51 3.6.3 The Dual-Frequency Michelson Interferometer 54 3.6.4 Heterodyne (Homodyne) Detection 55 3.7 Spatial and Temporal Coherence 56 3.8 Optical Coherence Tomography 61 4 Diffraction 67 4.1 Introduction 67 4.2 Diffraction from a Single Slit 67 4.3 Diffraction from a Grating 70 4.3.1 The Grating Equation. Amplitude Transmittance 70 4.3.2 The Spatial Frequency Spectrum 73 4.4 Fourier Optics 75 4.5 Optical Filtering 76 4.5.1 Practical Filtering Set-Ups 78 4.6 Physical Optics Description of Image Formation 81 4.6.1 The Coherent Transfer Function 83 4.6.2 The Incoherent Transfer Function 85 4.6.3 The Depth of Focus 88 4.7 The Phase-Modulated Sinusoidal Grating 89 5 Light Sources and Detectors 99 5.1 Introduction 99 5.2 Radiometry. Photometry 99 5.2.1 Lambertian Surface 102 5.2.2 Blackbody Radiator 103 5.2.3 Examples 105 5.3 Incoherent Light Sources 108 5.4 Coherent Light Sources 109 5.4.1 Stimulated Emission 109 5.4.2 Gas Lasers 112 5.4.3 Liquid Lasers 114 5.4.4 Semiconductor Diode Lasers. Light Emitting Diodes 114 5.4.5 Solid-State Lasers 117 5.4.6 Other Lasers 119 CONTENTS vii 5.4.7 Enhancements of Laser Operation 119 5.4.8 Applications 122 5.4.9 The Coherence Length of a Laser 123 5.5 Hologram Recording Media 125 5.5.1 Silver Halide Emulsions 125 5.5.2 Thermoplastic Film 126 5.5.3 Photopolymer Materials 127 5.6 Photoelectric Detectors 127 5.6.1 Photoconductors 128 5.6.2 Photodiodes 129 5.7 The CCD Camera 131 5.7.1 Operating Principles 131 5.7.2 Responsitivity 134 5.8 Sampling 135 5.8.1 Ideal Sampling 135 5.8.2 Non-Ideal Sampling 138 5.8.3 Aliasing 139 5.9 Signal Transfer 139 6 Holography 147 6.1 Introduction 147 6.2 The Holographic Process 147 6.3 An Alternative Description 150 6.4 Uncollimated Reference and Reconstruction Waves 150 6.5 Diffraction Efficiency. The Phase Hologram 153 6.6 Volume Holograms 154 6.7 Stability Requirements 156 6.8 Holographic Interferometry 157 6.8.1 Double-Exposure Interferometry 157 6.8.2 Real-Time Interferometry 157 6.8.3 Analysis of Interferograms 158 6.8.4 Localization of Interference Fringes 161 6.9 Holographic Vibration Analysis 165 6.10 Holographic Interferometry of Transparent Objects 168 7Moire´ Methods. Triangulation 173 7.1 Introduction 173 7.2 Sinusoidal Gratings 173 7.3 Moire´ Between Two Angularly Displaced Gratings 175 7.4 Measurement of In-Plane Deformation and Strains 175 7.4.1 Methods for Increasing the Sensitivity 177 viii CONTENTS 7.5 Measurement of Out-Of-Plane Deformations. Contouring 179 7.5.1 Shadow Moire´ 179 7.5.2 Projected Fringes 180 7.5.3 Vibration Analysis 186 7.5.4 Moire´ Technique by Means of Digital Image Processing 188 7.6 Reflection Moire´ 189 7.7 Triangulation 190 8 Speckle Methods 193 8.1 Introduction 193 8.2 The Speckle Effect 193 8.3 Speckle Size 195 8.4 Speckle Photography 197 8.4.1 The Fourier Fringe Method 197 8.4.2 The Young Fringe Method 201 8.5 Speckle Correlation 203 8.6 Speckle-Shearing Interferometry 208 8.7 White-Light Speckle Photography 212 9 Photoelasticity and Polarized Light 217 9.1 Introduction 217 9.2 Polarized Light 217 9.3 Polarizing Filters 219 9.3.1 The Linear Polarizer 219 9.3.2 Retarders 221 9.4 Unpolarized Light 223 9.5 Reflection and Refraction at an Interface 223 9.6 The Jones Matrix Formalism of Polarized Light 227 9.7 Photoelasticity 230 9.7.1 Introduction 230 9.7.2 The Plane Polariscope 231 9.7.3 The Circular Polariscope 232 9.7.4 Detection of Isochromatics of Fractional Order. Compensation 234 9.8 Holographic Photoelasticity 237 9.9 Three-Dimensional Photoelasticity 239 9.9.1 Introduction 239 9.9.2 The Frozen Stress Method 241 9.9.3 The Scattered Light Method 242 9.10 Ellipsometry 245 10 Digital Image Processing 249 10.1 Introduction 249 10.2 The Frame Grabber 249 CONTENTS ix 10.3 Digital Image Representation 251 10.4 Camera Calibration 251 10.4.1 Lens Distortion 252 10.4.2 Perspective Transformations 254 10.5 Image Processing 254 10.5.1 Contrast Stretching 255 10.5.2 Neighbourhood Operations. Convolution 256 10.5.3 Noise Suppression 257 10.5.4 Edge Detection 259 10.6 The Discrete Fourier Transform (DFT) and the FFT 262 11 Fringe Analysis 269 11.1 Introduction 269 11.2 Intensity-Based Analysis Methods 269 11.2.1 Introduction 269 11.2.2 Prior Knowledge 270 11.2.3 Fringe Tracking and Thinning 270 11.2.4 Fringe Location by Sub-Pixel Accuracy 273 11.3 Phase-Measurement Interferometry 276 11.3.1 Introduction 276 11.3.2 Principles of TPMI 276 11.3.3 Means of Phase Modulation 279 11.3.4 Different Techniques 279 11.3.5 Errors in TPMI Measurements 281 11.4 Spatial Phase-Measurement Methods 282 11.4.1 Multichannel Interferometer 282 11.4.2 Errors in Multichannel Interferometers 285 11.4.3 Spatial-Carrier Phase-Measurement Method 285 11.4.4 Errors in the Fourier Transform Method 287 11.4.5 Space Domain 289 11.5 Phase Unwrapping 290 11.5.1 Introduction 290 11.5.2 Phase-Unwrapping Techniques 292 11.5.3 Path-Dependent Methods 292 11.5.4 Path-Independent Methods 293 11.5.5 Temporal Phase Unwrapping 295 12 Computerized Optical Processes 297 12.1 Introduction 297 12.2 TV Holography (ESPI) 298 12.3 Digital Holography 301 12.4 Digital Speckle Photography 305 13 Fibre Optics in Metrology 307 13.1 Introduction 307 13.2 Light Propagation through Optical Fibres 307 13.3 Attenuation and Dispersion 310 x CONTENTS 13.4 Different Types of Fibres 313 13.5 Fibre-Optic Sensors 315 13.6 Fibre-Bragg Sensors 318 Appendices A.