Basics of Interferometry (eBook)

Front cover 1
Title page 4
Copyright page 5
Contents 8
Preface to the First Edition 18
Preface to the Second Edition 20
Acknowledgments 22
1 Introduction 24
2 Interference: A Primer 26
2.1 Light Waves 26
2.2 Intensity in an Interference Pattern 28
2.3 Visibility of Interference Fringes 29
2.4 Interference with a Point Source 29
2.5 Localization of Fringes 30
2.6 Summary 32
2.7 Problems 33
Further Reading 35
3 Two-Beam Interferometers 36
3.1 Wavefront Division 36
3.2 Amplitude Division 37
3.3 The Rayleigh Interferometer 38
3.4 The Michelson Interferometer 39
3.5 The Mach-Zehnder Interferometer 41
3.6 The Sagnac Interferometer 42
3.7 Summary 43
3.8 Problems 43
Further Reading 45
4 Source-Size and Spectral Effects 46
4.1 Coherence 46
4.2 Source-Size Effects 47
4.3 Spectral Effects 48
4.4 Polarization Effects 48
4.5 White-Light Fringes 49
4.6 Channeled Spectra 50
4.7 Summary 51
4.8 Problems 51
Further Reading 53
5 Multiple-Beam Interference 54
5.1 Multiple-Beam Fringes by Transmission 54
5.2 Multiple-Beam Fringes by Reflection 56
5.3 Multiple-Beam Fringes of Equal Thickness 57
5.4 Fringes of Equal Chromatic Order (FECO Fringes) 57
5.5 The Fabry-Perot Interferometer 58
5.6 Summary 59
5.7 Problems 59
Further Reading 59
6 The Laser as a Light Source 62
6.1 Lasers for Interferometry 62
6.2 Laser Modes 63
6.3 Single-Wavelength Operation of Lasers 65
6.4 Polarization of Laser Beams 66
6.5 Wavelength Stabilization of Lasers 66
6.6 Laser-Beam Expansion 66
6.7 Problems with Laser Sources 68
6.8 Laser Safety 69
6.9 Summary 69
6.10 Problems 69
Further Reading 71
7 Photodetectors 72
7.1 Photomultipliers 72
7.2 Photodiodes 73
7.3 Charge-Coupled Detector Arrays 74
7.4 Photoconductive Detectors 77
7.5 Pyroelectric Detectors 77
7.6 Summary 77
7.7 Problems 78
Further Reading 79
8 Measurements of Length 80
8.1 The Definition of the Metre 80
8.2 Length Measurements 81
8.3 Measurements of Changes in Length 85
8.4 Summary 86
8.5 Problems 86
Further Reading 89
9 Optical Testing 90
9.1 The Fizeau Interferometer 90
9.2 The Twyman-Green Interferometer 93
9.3 Analysis of Wavefront Aberrations 94
9.4 Laser Unequal-Path Interferometers 95
9.5 The Point-Diffraction Interferometer 95
9.6 Shearing Interferometers 96
9.7 Grazing-Incidence Interferometry 100
9.8 Summary 100
9.9 Problems 101
Further Reading 104
10 Digital Techniques 106
10.1 Digital Fringe Analysis 106
10.2 Digital Phase Measurements 107
10.3 Testing Aspheric Surfaces 108
10.4 Summary 111
10.5 Problems 111
Further Reading 114
11 Macro- and Micro-Interferometry 116
11.1 Interferometry of Refractive Index Fields 116
11.2 The Mach-Zehnder Interferometer 116
11.3 Interference Microscopy 118
11.4 Multiple-Beam Interferometry 119
11.5 Two-Beam Interference Microscopes 119
11.6 The Nomarski Interferometer 122
11.7 Summary 123
11.8 Problems 124
Further Reading 126
12 White-Light Interference Microscopy 128
12.1 White-Light Interferometry 128
12.2 White-Light Phase-Shifting Microscopy 129
12.3 Spectrally Resolved Interferometry 130
12.4 Coherence-Probe Microscopy 130
12.5 Summary 132
12.6 Problems 132
Further reading 133
13 Holographic and Speckle Interferometry 134
13.1 Holographic Interferometry 134
13.2 Holographic Nondestructive Testing 135
13.3 Holographic Strain Analysis 135
13.4 Holographic Vibration Analysis 136
13.5 Speckle Interferometry 137
13.6 Electronic Speckle-Pattern Interferometry 140
13.7 Studies of Vibrating Objects 141
13.8 Summary 142
13.9 Problems 142
Further Reading 143
14 Interferometric Sensors 144
14.1 Laser-Doppler Interferometry 144
14.2 Measurements of Vibration Amplitudes 145
14.3 Fiber Interferometers 146
14.4 Rotation Sensing 148
14.5 Laser-Feedback Interferometers 149
14.6 Gravitational Wave Detectors 150
14.7 Optical Signal Processing 151
14.8 Summary 152
14.9 Problems 152
Further Reading 155
15 Interference Spectroscopy 156
15.1 Resolving Power and Etendue 156
15.2 The Fabry-Perot Interferometer 157
15.3 Interference Filters 159
15.4 Birefringent Filters 160
15.5 Interference Wavelength Metres 160
15.6 Laser Frequency Measurements 161
15.7 Summary 162
15.8 Problems 163
Further Reading 166
16 Fourier Transform Spectroscopy 168
16.1 The Multiplex Advantage 168
16.2 Theory 169
16.3 Practical Aspects 171
16.4 Computation of the Spectrum 172
16.5 Applications 172
16.6 Summary 172
16.7 Problems 172
Further Reading 174
17 Interference with Single Photons 176
17.1 Interference-the Quantum Picture 176
17.2 Single-Photon States 177
17.3 Interference with Single-Photon States 179
17.4 Interference with Independent Sources 180
17.5 Fourth-Order Interference 184
17.6 Summary 185
17.7 Problems 185
Further Reading 186
18 Building an Interferometer 188
Further Reading 190
A Monochromatic Light Waves 192
A.1 Complex Representation 192
A.2 Optical Intensity 193
B Phase Shifts on Reflection 194
C Diffraction 196
C.1 Diffraction Gratings 197
D Polarized Light 200
D.1 Production of Polarized Light 200
D.2 Quarter-Wave and Half-Wave Plates 200
D.3 The Jones Calculus 202
D.4 The Poincaré Sphere 203
E The Pancharatnam Phase 206
E.1 The Pancharatnam Phase 206
E.2 Achromatic Phase Shifters 206
E.3 Switchable Achromatic Phase Shifters 208
F The Twyman-Green Interferometer: Initial Adjustment 210
G The Mach-Zehnder Interferometer: Initial Adjustment 214
H Fourier Transforms and Correlation 216
H.1 Fourier Transforms 216
H.2 Correlation 217
I Coherence 218
I.1 Quasi-Monochromatic Light 218
I.2 The Mutual Coherence Function 219
I.3 Complex Degree of Coherence 220
I.4 Visibility of the Interference Fringes 220
I.5 Spatial Coherence 221
I.6 Temporal Coherence 222
I.7 Coherence Length 222
J Heterodyne Interferometry 224
K Laser Frequency Shifting 226
L Evaluation of Shearing Interferograms 228
L.1 Lateral Shearing Interferometers 228
L.2 Radial Shearing Interferometers 228
M Phase-Shifting Interferometry 232
M.1 Error-Correcting Algorithms 233
N Holographic Imaging 234
N.1 Hologram Recording 234
N.2 Image Reconstruction 235
O Laser Speckle 238
P Laser Frequency Modulation 242
Index 244