Basics of INTERFEROMETRY P Hariharan CSIRO Division of Applied Sydney, Australia Physics ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto
Contents Preface Acknowledgments xv xvii 1 Introduction 1 2 Interference: A Primer 3 2.1 Light Waves 3 2.2 Intensity in an Interference Pattern 5 2.3 Visibility of Interference Fringes 6 2.4 Interference with a Point Source 6 2.5 Localization of Fringes 8 2.6 Summary 10 2.7 Problems 10 3 Two-Beam Interferometers 15 3.1 Wavefront Division 16 3.2 Amplitude Division 16 3.3 The Rayleigh Interferometer 17 3.4 The Michelson Interferometer 18 3.4.1 Fringes Formed with a Point Source 20 3.4.2 Fringes Formed with an Extended Source 20 vn
viii CONTENTS 3.4.3 Pringes Formed with CoUimated Light 20 3.4.4 Applications 20 3.5 The Mach-Zehnder Interferometer 21 3.6 The Sagnac Interferometer 21 3.7 Summary 23 3.8 Problems 23 4 Light Sources 27 4.1 Coherence 27 4.2 Source-Size Effects 28 4.2.1 Slit Source 29 4.2.2 Circular Pinhole 29 4.3 Spectral Effects 29 4.4 Polarization Effects 30 4.5 White-Light Fringes 31 4.6 Channeled Spectra 31 4.7 Summary 33 4.8 Problems 33 5 Multiple-Beam Interference 37 5.1 Multiple-Beam Fringes by Transmission 37 5.2 Multiple-Beam Pringes by Reflection 40 5.3 Multiple-Beam Pringes of Equal Thickness 40 5.4 Fringes of Equal Chromatic Order (FECO Fringes)... 40 5.5 The Fabry-Perot Interferometer 41 5.6 Summary 42 5.7 Problems 43 6 The Laser as a Light Source 45 6.1 Lasers for Interferometry 46 6.2 Laser Modes 47 6.3 Single-Wavelength Operation of Lasers 49
CONTENTS ix 6.4 Polarization of Laser Beams 49 6.5 Wavelength Stabilization of Lasers 49 6.6 Laser Beam Expansion 50 6.7 Problems with Laser Sources 51 6.8 Laser Safety 53 6.9 Summary 53 6.10 Problems 53 7 Detectors 57 7.1 Photomultipliers 57 7.2 Photodiodes 58 7.3 Charge-Coupled Detector Arrays 59 7.3.1 Linear CCD Sensors 60 7.3.2 Area CCD Sensors 60 7.3.3 Frame-Transfer CCD Sensors 62 7.4 Photoconductive Detectors 62 7.5 Pyroelectric Detectors 63 7.6 Summary 63 7.7 Problems 64 8 Measurements of Length 67 8.1 The Definition of the Metre 67 8.2 Length Measurements 68 8.2.1 The Fractional-Fringe Method 68 8.2.2 Fringe Counting 70 8.2.3 Heterodyne Techniques 70 8.2.4 Synthetic Long-Wavelength Signals 71 8.2.5 Laser Frequency Modulation 72 8.2.6 Environmental Effects 72 8.3 Measurement of Changes in Length 73 8.3.1 Phase Compensation 73
x CONTENTS 8.3.2 Heterodyne Methods 73 8.4 Summary 74 8.5 Problems 74 9 Optical Testing 79 9.1 The Fizeau Interferometer 79 9.2 The Twyman-Green Interferometer 81 9.3 Analysis of Wavefront Aberrations 82 9.4 Laser Unequal-Path Interferometers 84 9.5 The Point-Diffraction Interferometer 85 9.6 Shearing Interferometers 86 9.6.1 Lateral Shearing Interferometers 87 9.6.2 Radial Shearing Interferometers 88 9.7 Summary 91 9.8 Problems 91 10 Digital Techniques 95 10.1 Digital Fringe Analysis 95 10.2 Digital Phase Measurements 96 10.3 Testing Aspheric Surfaces 98 10.3.1 Direct Measurements of Surface Shape 98 10.3.2 Long-Wavelength Tests 99 10.3.3 Tests with Shearing Interferometers 99 10.3.4 Tests with Computer-Generated Holograms... 99 10.4 Summary 101 10.5 Problems 101 11 Macro- and Micro-Interferometry 105 11.1 Interferometry of Refractive Index Fields 105 11.2 The Mach-Zehnder Interferometer 106 11.3 Interference Microscopy 108 11.4 Multiple-Beam Interference 108
CONTENTS xi 11.5 Two-Beam Interference Microscopes 110 11.6 The Nomarski Interferometer 111 11.7 Summary 113 11.8 Problems 113 12 Holographie and Speckle Interferometry 117 12.1 Holographie Interferometry 117 12.2 Holographie Nondestructive Testing 118 12.3 Holographie Strain Analysis 119 12.4 Holographie Vibration Analysis 120 12.5 Speckle Interferometry 122 12.6 Electronic Speckle-Pattern Interferometry 123 12.7 Studies of Vibrating Objects 125 12.8 Summary 126 12.9 Problems 126 13 Interferometric Sensors 129 13.1 Laser-Doppler Interferometry 129 13.2 Measurements of Vibration Amplitudes 130 13.3 Fiber Interferometers 131 13.4 Rotation Sensing 134 13.5 Summary 135 13.6 Problems 135 14 Interference Spectroscopy 139 14.1 Resolving Power and Etendue 139 14.2 The Fabry-Perot Interferometer 140 14.2.1 The Scanning Fabry-Perot Interferometer... 141 14.2.2 The Confocal Fabry-Perot Interferometer 142 14.2.3 The Multiple-Pass Fabry-Perot Interferometer.. 142 14.3 Interference Filters 143 14.4 Birefringent Filters 143
xii CONTENTS 14.5 Interference Wavelength Meters 144 14.6 Summary 145 14.7 Problems 145 15 Fourier-Transform Spectroscopy 151 15.1 The Multiplex Advantage 152 15.2 Theory of Fourier-Transform Spectroscopy 152 15.3 Practical Aspects of Fourier-Transform Spectroscopy.. 154 15.4 Computation of the Spectrum 155 15.5 Applications of Fourier-Transform Spectroscopy 156 15.6 Summary 156 15.7 Problems 156 16 Choosing an Interferometer 159 A Monochromatic Light Waves 163 A.l Complex Representation 163 A.2 Optical Intensity 164 B Phase Shifts on Reflection 165 C Diffraction 167 C.l Diffraction Grätings 168 D Polarized Light 171 D.l Production of Polarized Light 171 D.2 Quarter-Wave and Half-Wave Plates 172 E The Twyman-Green Interferometer 175 F Adjustment of the Mach-Zehnder Interferometer 179 G Fourier Transforms and Correlation 181 G.l Fourier Transforms 181 G.2 Correlation 182
CONTENTS xiii H Coherence 183 H.l Quasi-Monochromatic Light 183 H.2 The Mutual Coherence Function 184 H.3 Complex Degree of Coherence 185 H.4 Visibility of the Interference Fringes 185 H.5 Spatial Coherence 186 H.6 Temporal Coherence 187 H.7 Coherence Length 188 I Heterodyne Interferometry 189 J Laser Frequency Shifting 191 K Evaluation of Shearing Interferograms 193 K.l Lateral Shearing Interferometers 193 K.2 Radial Shearing Interferometers 194 L Phase-Stepping Interferometry 197 M Holographie Imaging 199 M.l Hologram Recording 199 M.2 Image Reconstruction 200 N Laser Speckle 203 O Laser Frequency Modulation 207 Index 209