Optical metrology

359 Pages·2002·3.265 MB·English

by  Kjell J. Gåsvik

OpticalMetrology.KjellJ.Ga˚svik
Copyright2002JohnWiley&Sons,Ltd.
ISBN:0-470-84300-4
Optical Metrology
Third Edition
Optical Metrology
Third Edition
Kjell J. Ga˚svik
Spectra Vision AS, Trondheim, Norway
Copyright2002 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,
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Contents
Preface to the Third Edition xi
1 Basics 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
7 Moire´ 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. Complex Numbers 325
B. Fourier Optics 327
B.1 The Fourier Transform 327
B.2 Some Functions and Their Transforms 329
B.3 Some Implications 332
C. Fourier Series 335
D. The Least-Squares Error Method 339
E. Semiconductor Devices 343
References and Further Reading 347
Index 355
Preface to the Third Edition
This edition of Optical Metrology contains a new chapter about computerized optical
processes, including digital holography and digital speckle photography. Chapter 2, on
Gaussian optics, and Chapter 5, on light sources and detectors, are greatly expanded
to include descriptions of standard imaging systems, light-emitting diodes and solid-state
detectors.Separatenewsectionsonopticalcoherencetomography,specklecorrelation,the
FastFourierTransform,temporalphaseunwrappingandfibreBraggsensorsareincluded.
Finally, a new appendix about Fourier series is given. Solutions to the end-of-chapter
problems can be found at http://www.wiley.co.uk/opticalmetrology.
Since the previous edition, the electronic camera has taken over more and more as the
recording medium. The word ‘digital’ is becoming a prefix to an increasing number of
techniques. I think this new edition reflects this trend.
It gives me great pleasure to acknowledge the many stimulating discussions with Pro-
fessor H.M. Pedersen at The Norwegian University of Science and Technology. Thanks
also to John Petter Ga˚svik for designing many of the new figures.