From the Series Editor ........................................ xix
Preface ....................................................... xxi
Preface to First Edition .................................... xxiii
Author ........................................................ xxv
Chapter 1 Waves and Beams ...................................... 1
1.1 The Wave Equation .......................................... 1
1.2 Plane Waves ................................................ 2
1.3 Spherical Waves ............................................ 2
1.4 Cylindrical Waves .......................................... 2
1.5 Waves as Information Carriers .............................. 3
1.5.1 Amplitude/Intensity-Based Sensors ................... 4
1.5.2 Sensors Based on Phase Measurement .................. 4
1.5.3 Sensors Based on Polarization ....................... 5
1.5.4 Sensors Based on Frequency Measurement .............. 5
1.5.5 Sensors Based on Change of Direction ................ 5
1.6 The Laser Beam ............................................. 5
1.7 The Gaussian Beam .......................................... 6
1.8 ABCD Matrix Applied to Gaussian Beams ...................... 8
1.8.1 Propagation in Free Space ........................... 9
1.8.2 Propagation through a Thin Lens .................... 10
1.8.3 Mode Matching ...................................... 12
1.9 Nondiffracting Beams-Bessel Beams ......................... 12
1.10 Singular Beams ............................................ 13
Bibliography .............................................. 17
Additional Reading ........................................ 17
Chapter 2 Optical Interference ................................ 19
2.1 Introduction .............................................. 19
2.2 Generation of Coherent Waves .............................. 20
2.2.1 Interference by Division of Wavefront .............. 20
2.2.2 Interference by Division of Amplitude .............. 20
2.3 Interference between Two Plane Monochromatic Waves ........ 21
2.3.1. Young's Double-Slit Experiment ..................... 22
2.3.2 Michelson Interferometer ......................... 24
2.4 Multiple-Beam Interference ................................ 25
2.4.1 Multiple-Beam Interference: Division
of Wavefront ....................................... 25
2.4.2 Multiple-Beam Interference: Division
of Amplitude ....................................... 27
2.4.2.1 Interference Pattern in Transmission ...... 27
2.4.2.2 Interference Pattern in Reflection ........ 29
2.5 Interferometry ............................................ 29
2.5.1 Dual-Wavelength Interferometry ..................... 30
2.5.2 White Light Interferometry ......................... 31
2.5.3 Heterodyne Interferometry .......................... 31
2.5.4 Shear Interferometry ............................... 32
2.5.5 Polarization Interferometers ....................... 33
2.5.6 Interference Microscopy ............................ 34
2.5.7 Doppler Interferometry ............................. 36
2.5.8 Fiber-Optic Interferometers ........................ 37
2.5.9 Phase-Conjugation Interferometers .................. 38
Bibliography .............................................. 39
Additional Reading ........................................ 40
Chapter 3 Diffraction ......................................... 43
3.1 Fresnel Diffraction ....................................... 43
3.2 Fraunhofer Diffraction .................................... 44
3.3 Action of a Lens .......................................... 45
3.4 Image Formation and Fourier Transformation by a Lens ...... 45
3.4.1 Image Formation .................................... 47
3.4.2 Fourier Transformation ............................. 47
3.5 Optical Filtering ......................................... 49
3.6 Optical Components in Optical Metrology ................... 50
3.6.1 Reflective Optical Components ...................... 50
3.6.2 Refractive Optical Components ...................... 50
3.6.3 Diffractive Optical Components ..................... 52
3.6.3.1 Sinusoidal Grating ........................ 55
3.6.4 Phase Grating ...................................... 56
3.6.5 Diffraction Efficiency ............................. 57
3.7 Resolving Power of Optical Systems ........................ 57
Bibliography .............................................. 58
Chapter 4 Phase-Evaluation Methods ............................ 59
4.1 Interference Equation ..................................... 59
4.2 Fringe Skeletonization .................................... 60
4.3 Temporal Heterodyning ..................................... 61
4.4 Phase-Sampling Evaluation: Quasi-Heterodyning ............. 62
4.5 Phase-Shifting Method ..................................... 63
4.6 Phase-Shifting with Unknown but Constant Phase-Step ....... 63
4.7 Spatial Phase-Shifting .................................... 66
4.8 Methods of Phase-Shifting ................................. 68
4.8.1 PZT-Mounted Mirror ................................. 68
4.8.2 Tilt of Glass Plate ................................ 69
4.8.3 Rotation of Polarization Component ................. 70
4.8.4 Motion of a Diffraction Grating .................... 72
4.8.5 Use of a CGH Written on a Spatial Light
Modulator .......................................... 72
4.8.6 Special Methods .................................... 72
4.9 Fourier Transform Method .................................. 72
4.10 Spatial Heterodyning ...................................... 73
Bibliography .............................................. 75
Additional Reading ........................................ 75
Chapter 5 Detectors and Recording Materials ................... 79
5.1 Detector Characteristics .................................. 79
5.2 Detectors ................................................. 80
5.2.1 Photoconductors .................................... 80
5.2.2 Photodiodes ........................................ 81
5.2.3 Photomultiplier Tube ............................... 84
5.3 Image Detectors ........................................... 84
5.3.1 Time-Delay and Integration Mode of Operation ....... 89
5.4 Recording Materials ....................................... 89
5.4.1 Photographic Films and Plates ...................... 90
5.4.2 Dichromated Gelatin ................................ 94
5.4.3 Photoresists ....................................... 95
5.4.4 Photopolymers ...................................... 95
5.4.5 Thermoplastics ..................................... 96
5.4.6 Photochromies ...................................... 96
5.4.7 Ferroelectric Crystals ............................. 97
Bibliography .............................................. 98
Additional Reading ........................................ 98
Chapter 6 Holographic Interferometry ......................... 101
6.1 Introduction ............................................. 101
6.2 Hologram Recording ....................................... 102
6.3 Reconstruction ........................................... 103
6.4 Choice of Angle of Reference Wave ........................ 104
6.5 Choice of Reference Wave Intensity ....................... 105
6.6 Types of Holograms ....................................... 105
6.7 Diffraction Efficiency ................................... 105
6.8 Experimental Arrangement ................................. 105
6.8.1 Lasers ............................................ 106
6.8.2 Beam-Splitters .................................... 107
6.8.3 Beam-Expanders .................................... 107
6.8.4 Object-Illumination Beam .......................... 107
6.8.5 Reference Beam .................................... 107
6.8.6 Angle between Object and Reference Beams .......... 108
6.9 Holographic Recording Materials .......................... 108
6.10 Holographic Interferometry ............................... 108
6.10.1 Real-TimeHI ....................................... 108
6.10.2 Double-Exposure HI ................................ 109
6.10.3 Time-Average HI ................................... 110
6.10.4 Real-Time, Time-Average HI ........................ 111
6.11 Fringe Formation and Measurement of Displacement
Vector ................................................... 115
6.12 Loading of the Object .................................... 116
6.13 Measurement of Very Small Vibration Amplitudes ........... 117
6.14 Measurement of Large Vibration Amplitudes ................ 117
6.14.1 Frequency Modulation of Reference Wave ............ 117
6.14.2 Phase Modulation of Reference Beam ................ 119
6.15 Stroboscopic Illumination/Stroboscopic HI ................ 120
6.16 Special Techniques in Holographic Interferometry ......... 121
6.16.1 Two-Reference-Beam HI ............................. 121
6.16.2 SandwichHI ........................................ 123
6.16.3 ReflectionHI ...................................... 125
6.17 Extending the Sensitivity of HI .......................... 127
6.17.1 Heterodyne HI ..................................... 127
6.18 Holographic Contouring/Shape Measurement ................. 129
6.18.1 Dual-Wavelength Method ............................ 129
6.18.2 Dual-Refractive Index Method ...................... 131
6.18.3 Dual-Illumination Method .......................... 132
6.19 Holographic Photoelasticity .............................. 132
6.20 Digital Holography ....................................... 132
6.20.1 Recording ......................................... 132
6.20.2 Reconstruction .................................... 133
6.21 Digital Holographic Interferometry ....................... 135
Bibliography ............................................. 136
Additional Reading ....................................... 137
Chapter 7 Speckle Metrology .................................. 149
7.1 The Speckle Phenomenon ................................... 149
7.2 Average Speckle Size ..................................... 149
7.2.1 Objective Speckle Pattern ......................... 150
7.2.2 Subjective Speckle Pattern ........................ 150
7.3 Superposition of Speckle Patterns ........................ 151
7.4 Speckle Pattern and Object Surface Characteristics ....... 152
7.5 Speckle Pattern and Surface Motion ....................... 152
7.5.1 Linear Motion in the Plane of the Surface ......... 152
7.5.2 Out-of-Plane Displacement ......................... 152
7.5.3 Tilt of the Object ................................ 153
7.6 Speckle Photography ...................................... 155
7.7 Methods of Evaluation .................................... 158
7.7.1 Pointwise Filtering ............................... 158
7.7.2 Wholefield Filtering .............................. 160
7.7.3 Fourier Filtering: Measurement of Out-of-Plane
Displacement ...................................... 161
7.8 Speckle Photography with Vibrating Objects: In-Plane
Vibration ................................................ 161
7.9 Sensitivity of Speckle Photography ....................... 162
7.10 Particle Image Velocimetry ............................... 162
7.11 White-Light Speckle Photography .......................... 162
7.12 Shear Speckle Photography ................................ 163
7.13 Speckle Interferometry ................................... 164
7.14 Correlation Coefficient in Speckle Interferometry ........ 167
7.15 Out-of-Plane Speckle Interferometer ...................... 168
7.16 In-Plane Measurement: Duffy's Method ..................... 169
7.17 Filtering ................................................ 171
7.17.1 Fringe Formation .................................. 171
7.18 Out-of-Plane Displacement Measurement .................... 173
7.19 Simultaneous Measurement of Out-of-Plane and In-Plane
Displacement Components .................................. 174
7.20 Other Possibilities for Aperturing the Lens .............. 175
7.21 Duffy's Arrangement: Enhanced Sensitivity ................ 176
7.22 Speckle Interferometry—Shape Measurement/ Contouring ..... 177
7.23 Speckle Shear Interferometry ............................. 177
7.23.1 The Meaning of Shear .............................. 177
7.24 Methods of Shearing ...................................... 178
7.25 Theory of Speckle Shear Interferometry ................... 180
7.26 Fringe Formation ......................................... 181
7.26.1 The Michelson Interferometer ...................... 181
7.26.2 The Apertured Lens Arrangement .................... 182
7.27 Shear Interferometry without Influence of the In-Plane
Component ................................................ 183
7.28 Electronic Speckle Pattern Interferometry ............... 183
7.28.1 Out-of-Plane Displacement Measurement ............. 184
7.28.2 In-Plane Displacement Measurement ................. 185
7.28.3 Vibration Analysis ................................ 185
7.28.4 Measurement on Small Objects ...................... 186
7.28.5 Shear ESPI Measurement ............................ 187
7.29 Contouring in ESPI ....................................... 187
7.29.1 Change of Direction of Illumination ............... 188
7.29.2 Change of Wavelength .............................. 189
7.29.3 Change of Medium Surrounding the Object ........... 189
7.29.4 Tilt of the Object ................................ 189
7.30 Special Techniques ....................................... 189
7.30.1 Use of Retro-Reflective Paint ..................... 189
7.31 Spatial Phase-Shifting ................................... 190
Bibliography ............................................. 191
Additional Reading ....................................... 191
Chapter 8 Photoelasticity .................................... 201
8.1 Superposition of Two-Plane Polarized Waves ............... 201
8.2 Linear Polarization ...................................... 202
8.3 Circular Polarization .................................... 203
8.4 Production of Polarized Light ............................ 203
8.4.1 Reflection ........................................ 204
8.4.2 Refraction ........................................ 204
8.4.3 Double Refraction ................................. 204
8.4.3.1 Phase Plates ............................. 205
8.4.3.2 Quarter-Wave Plate ....................... 206
8.4.3.3 Half-Wave Plate .......................... 206
8.4.3.4 Compensators ............................. 206
8.4.4 Dichroism ......................................... 207
8.4.5 Scattering ........................................ 207
8.5 Malus's Law .............................................. 207
8.6 The Stress-Optic Law ..................................... 207
8.7 The Strain-Optic Law ..................................... 209
8.8 Methods of Analysis ...................................... 210
8.8.1 Plane Polariscope ................................. 210
8.8.2 Circular Polariscope .............................. 212
8.9 Evaluation Procedure ..................................... 216
8.10 Measurement of Fractional Fringe Order ................... 217
8.10.1 Tardy's Method .................................... 217
8.11 Phase-Shifting ........................................... 220
8.11.1 Isoclinics Computation ............................ 220
8.11.2 Computation of Isochromatics ...................... 221
8.12 Birefringent Coating Method: Reflection Polariscope ...... 222
8.13 Holophotoelasticity ...................................... 223
8.13.1 Single-Exposure Holophotoelasticity ............... 224
8.13.2 Double-Exposure Holophotoelasticity ............... 225
8.14 Three-Dimensional Photoelasticity ........................ 229
8.14.1 The Frozen-Stress Method .......................... 229
8.14.2 Scattered-Light Photoelasticity ................... 230
8.15 Examination of the Stressed Model in Scattered Light ..... 230
8.15.1 Unpolarized Incident Light ........................ 230
8.15.2 Linearly Polarized Incident Beam .................. 232
Bibliography ............................................. 233
Additional Reading ....................................... 234
Chapter 9 The Moiré Phenomenon ............................... 239
9.1 Introduction ............................................. 239
9.2 The Moiré Fringe Pattern between Two Linear Gratings ..... 239
9.2.1 a ≠ b but θ = 0 ................................... 241
9.2.2 a = b but θ ≠ 0 ................................... 241
9.3 The Moiré Fringe Pattern between a Linear Grating
and a Circular Grating ................................... 242
9.4 Moiré between Sinusoidal Gratings ........................ 243
9.5 Moiré between Reference and Deformed Gratings ............ 245
9.6 Moiré Pattern with Deformed Sinusoidal Grating ........... 246
9.6.1 Multiplicative Moiré Pattern ...................... 247
9.6.2 Additive Moiré Pattern ............................ 247
9.7 Contrast Improvement of the Additive Moiré Pattern ....... 248
9.8 Moiré Phenomenon for Measurement ......................... 248
9.9 Measurement of In-Plane Displacement ..................... 248
9.9.1 Reference and Measurement Gratings of Equal
Pitch and Aligned Parallel to Each Other .......... 248
9.9.2 Two-Dimensional In-Plane Displacement
Measurement ....................................... 249
9.9.3 High-Sensitivity In-Plane Displacement
Measurement ....................................... 251
9.10 Measurement of Out-of-Plane Component and Contouring ..... 253
9.10.1 The Shadow Moiré Method ........................... 254
9.10.1.1 Parallel Illumination and Parallel
Observation .............................. 254
9.10.1.2 Spherical-Wave Illumination and Camera
at Finite Distance ....................... 255
9.10.2 Automatic Shape Determination ..................... 257
9.10.3 Projection Moiré .................................. 257
9.10.4 Light-Line Projection with TDI Mode of Operation
of CCD Camera ..................................... 260
9.10.5 Coherent Projection Method ........................ 262
9.10.5.1 Interference between Two Collimated
Beams .................................... 262
9.10.5.2 Interference between Two Spherical
Waves .................................... 263
9.10.6 Measurement of Vibration Amplitudes ............... 264
9.10.7 Reflection Moiré Method ........................... 265
9.11 Slope Determination for Dynamic Events ................... 267
9.12 Curvature Determination for Dynamic Events ............... 268
9.13 Surface Topography with Reflection Moiré Method .......... 269
9.14 Talbot Phenomenon ........................................ 271
9.14.1 Talbot Effect in Collimated Illumination .......... 272
9.14.2 Cut-Off Distance .................................. 273
9.14.3 Talbot Effect in Noncollimated Illumination ....... 273
9.14.4 Talbot Effect for Measurement ..................... 274
9.14.4.1 Temperature Measurement .................. 274
9.14.4.2 Measurement of the Focal Length of a
Lens and the Long Radius of Curvature
of a Surface ............................. 275
Bibliography ............................................. 275
Additional Reading ....................................... 275
Index ......................................................... 283
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