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Optical Metrology. Kjell J. G˚asvik Copyright  2002 John Wiley & Sons, Ltd. ISBN: 0-470-84300-4 Optical Metrology Third Edition

Optical Metrology Third Edition Kjell J. G˚asvik 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): cs-books@wiley.co.uk 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. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.co.uk, or faxed to (+44) 1243 770571. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Ofﬁces John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-84300-4 Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

Contents Preface to the Third Edition 1 Basics 1.1 Introduction 1.2 Wave Motion. The Electromagnetic Spectrum 1.3 The Plane Wave. Light Rays 1.4 Phase Difference 1.5 Complex Notation. Complex Amplitude 1.6 Oblique Incidence of A Plane Wave 1.7 The Spherical Wave 1.8 The Intensity 1.9 Geometrical Optics 1.10 The Simple Convex (Positive) Lens 1.11 A Plane-Wave Set-Up 2 Gaussian Optics 2.1 Introduction 2.2 Refraction at a Spherical Surface 2.2.1 Examples 2.3 The General Image-Forming System 2.4 The Image-Formation Process 2.5 Reﬂection at a Spherical Surface 2.6 Aspheric Lenses 2.7 Stops and Apertures 2.8 Lens Aberrations. Computer Lens Design 2.9 Imaging and The Lens Formula 2.10 Standard Optical Systems 2.10.1 Afocal Systems. The Telescope 2.10.2 The Simple Magniﬁer 2.10.3 The Microscope xi 1 1 1 3 4 5 5 7 8 8 10 11 15 15 15 19 19 21 23 25 26 28 29 30 30 32 34

vi CONTENTS 3 Interference 3.1 Introduction 3.2 General Description 3.3 Coherence 3.4 Interference between two Plane Waves 3.4.1 Laser Doppler Velocimetry (LDV) 3.5 Interference between other Waves 3.6 Interferometry 3.6.1 Wavefront Division 3.6.2 Amplitude Division 3.6.3 The Dual-Frequency Michelson Interferometer 3.6.4 Heterodyne (Homodyne) Detection 3.7 Spatial and Temporal Coherence 3.8 Optical Coherence Tomography 4 Diffraction 4.1 Introduction 4.2 Diffraction from a Single Slit 4.3 Diffraction from a Grating 4.3.1 The Grating Equation. Amplitude Transmittance 4.3.2 The Spatial Frequency Spectrum 4.4 Fourier Optics 4.5 Optical Filtering 4.5.1 Practical Filtering Set-Ups 4.6 Physical Optics Description of Image Formation 4.6.1 The Coherent Transfer Function 4.6.2 The Incoherent Transfer Function 4.6.3 The Depth of Focus 4.7 The Phase-Modulated Sinusoidal Grating 5 Light Sources and Detectors 5.1 Introduction 5.2 Radiometry. Photometry 5.2.1 Lambertian Surface 5.2.2 Blackbody Radiator 5.2.3 Examples 5.3 Incoherent Light Sources 5.4 Coherent Light Sources 5.4.1 Stimulated Emission 5.4.2 Gas Lasers 5.4.3 Liquid Lasers 5.4.4 Semiconductor Diode Lasers. Light Emitting Diodes 5.4.5 Solid-State Lasers 5.4.6 Other Lasers 37 37 37 38 41 45 46 49 50 51 54 55 56 61 67 67 67 70 70 73 75 76 78 81 83 85 88 89 99 99 99 102 103 105 108 109 109 112 114 114 117 119

5.4.7 Enhancements of Laser Operation 5.4.8 Applications 5.4.9 The Coherence Length of a Laser 5.5 Hologram Recording Media 5.5.1 Silver Halide Emulsions 5.5.2 Thermoplastic Film 5.5.3 Photopolymer Materials 5.6 Photoelectric Detectors 5.6.1 Photoconductors 5.6.2 Photodiodes 5.7 The CCD Camera 5.7.1 Operating Principles 5.7.2 Responsitivity 5.8 Sampling 5.8.1 Ideal Sampling 5.8.2 Non-Ideal Sampling 5.8.3 Aliasing 5.9 Signal Transfer 6 Holography 6.1 Introduction 6.2 The Holographic Process 6.3 An Alternative Description 6.4 Uncollimated Reference and Reconstruction Waves 6.5 Diffraction Efﬁciency. The Phase Hologram 6.6 Volume Holograms 6.7 Stability Requirements 6.8 Holographic Interferometry 6.8.1 Double-Exposure Interferometry 6.8.2 Real-Time Interferometry 6.8.3 Analysis of Interferograms 6.8.4 Localization of Interference Fringes 6.9 Holographic Vibration Analysis 6.10 Holographic Interferometry of Transparent Objects 7 Moir´e Methods. Triangulation 7.1 Introduction 7.2 Sinusoidal Gratings 7.3 Moir´e Between Two Angularly Displaced Gratings 7.4 Measurement of In-Plane Deformation and Strains 7.4.1 Methods for Increasing the Sensitivity CONTENTS vii 119 122 123 125 125 126 127 127 128 129 131 131 134 135 135 138 139 139 147 147 147 150 150 153 154 156 157 157 157 158 161 165 168 173 173 173 175 175 177

viii CONTENTS 7.5 Measurement of Out-Of-Plane Deformations. Contouring 7.5.1 Shadow Moir´e 7.5.2 Projected Fringes 7.5.3 Vibration Analysis 7.5.4 Moir´e Technique by Means of Digital Image Processing 7.6 Reﬂection Moir´e 7.7 Triangulation 8 Speckle Methods 8.1 Introduction 8.2 The Speckle Effect 8.3 Speckle Size 8.4 Speckle Photography 8.4.1 The Fourier Fringe Method 8.4.2 The Young Fringe Method 8.5 Speckle Correlation 8.6 Speckle-Shearing Interferometry 8.7 White-Light Speckle Photography 9 Photoelasticity and Polarized Light 9.1 Introduction 9.2 Polarized Light 9.3 Polarizing Filters 9.3.1 The Linear Polarizer 9.3.2 Retarders 9.4 Unpolarized Light 9.5 Reﬂection and Refraction at an Interface 9.6 The Jones Matrix Formalism of Polarized Light 9.7 Photoelasticity 9.7.1 Introduction 9.7.2 The Plane Polariscope 9.7.3 The Circular Polariscope 9.7.4 Detection of Isochromatics of Fractional Order. Compensation 9.8 Holographic Photoelasticity 9.9 Three-Dimensional Photoelasticity 9.9.1 Introduction 9.9.2 The Frozen Stress Method 9.9.3 The Scattered Light Method 9.10 Ellipsometry 10 Digital Image Processing 10.1 Introduction 10.2 The Frame Grabber 179 179 180 186 188 189 190 193 193 193 195 197 197 201 203 208 212 217 217 217 219 219 221 223 223 227 230 230 231 232 234 237 239 239 241 242 245 249 249 249

10.3 Digital Image Representation 10.4 Camera Calibration 10.4.1 Lens Distortion 10.4.2 Perspective Transformations 10.5 Image Processing 10.5.1 Contrast Stretching 10.5.2 Neighbourhood Operations. Convolution 10.5.3 Noise Suppression 10.5.4 Edge Detection 10.6 The Discrete Fourier Transform (DFT) and the FFT 11 Fringe Analysis 11.1 Introduction 11.2 Intensity-Based Analysis Methods 11.2.1 Introduction 11.2.2 Prior Knowledge 11.2.3 Fringe Tracking and Thinning 11.2.4 Fringe Location by Sub-Pixel Accuracy 11.3 Phase-Measurement Interferometry 11.3.1 Introduction 11.3.2 Principles of TPMI 11.3.3 Means of Phase Modulation 11.3.4 Different Techniques 11.3.5 Errors in TPMI Measurements 11.4 Spatial Phase-Measurement Methods 11.4.1 Multichannel Interferometer 11.4.2 Errors in Multichannel Interferometers 11.4.3 Spatial-Carrier Phase-Measurement Method 11.4.4 Errors in the Fourier Transform Method 11.4.5 Space Domain 11.5 Phase Unwrapping 11.5.1 Introduction 11.5.2 Phase-Unwrapping Techniques 11.5.3 Path-Dependent Methods 11.5.4 Path-Independent Methods 11.5.5 Temporal Phase Unwrapping 12 Computerized Optical Processes 12.1 Introduction 12.2 TV Holography (ESPI) 12.3 Digital Holography 12.4 Digital Speckle Photography 13 Fibre Optics in Metrology 13.1 Introduction 13.2 Light Propagation through Optical Fibres 13.3 Attenuation and Dispersion CONTENTS ix 251 251 252 254 254 255 256 257 259 262 269 269 269 269 270 270 273 276 276 276 279 279 281 282 282 285 285 287 289 290 290 292 292 293 295 297 297 298 301 305 307 307 307 310

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