Basics of INTERFEROMETRY

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1 Basics of INTERFEROMETRY Second Edition P. HARIHARAN School ofphysics, Sydney, Australia University of Sydney CPi AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO ÜLoÜVlliK. Academic Press is an imprint of Elsevier ACADEMIC PRESS

Contents Preface to the First Edition xvii Preface to the Second Edition xix Acknowledgments xxi Introduction 1 Interf erence: A Primer 3 2.1 Light Waves 3 2.

2 Contents Preface to the First Edition xvii Preface to the Second Edition xix Acknowledgments xxi Introduction 1 Interf erence: A Primer Light Waves Intensity in an Interf erence Pattern Visibility of Interference Fringes Interference with a Point Source Localization of Fringes Summary Problems 10 Further Reading 12 Two-Beam Interferometers Wavefront Division Amplitude Division The Rayleigh Interferometer The Michelson Interf erometer Fringes Formed with a Point Source Fringes Formed with an Extended Source Fringes Formed with Collimated Light 17

3.4.4 Applications 18 3.5 The Mach-Zehnder Interferometer 18 3.6 The Sagnac Interferometer 19 3.7 Summary 20 3.8 Problems 20 Further Reading 22 Source-Size and Spectral Effects 23 4.1 Coherence 23 4.

3 3.4.4 Applications The Mach-Zehnder Interferometer The Sagnac Interferometer Summary Problems 20 Further Reading 22 Source-Size and Spectral Effects Coherence Source-Size Effects SlitSource Circular Pinhole 25 A3 Spectral Effects Polarization Effects White-Light Fringes Channeled Spectra Summary Problems 28 Further Reading 30 Multiple-Beam Interference Multiple-Beam Fringes by Transmission Multiple-Beam Fringes by Reflection Multiple-Beam Fringes of Equal Thickness Fringes of Equal Chromatic Order (FECO Fringes) 5.5 The Fabry-Perot Interferometer Summary Problems 36 Further Reading 36

The Laser as a Light Source 39 6.1 Lasers for Interferometry 39 6.2 Laser Modes 40 6.3 Single- Wavelength Operation of Lasers 42 6.4 Polarization of Laser Beams 43 6.

4 The Laser as a Light Source Lasers for Interferometry Laser Modes Single- Wavelength Operation of Lasers Polarization of Laser Beams Wavelength Stabilization of Lasers Laser-Beam Expansion Problems with Laser Sources Laser Safety Summary Problems 46 Further Reading 48 r 7 Photodetectors Photomultipliers Photodiodes Charge-Coupled Detector Arrays Linear CCD Sensors Area CCD Sensors Frame-Transfer CCD Sensors Photoconductive Detectors Pyroelectric Detectors Summary Problems 55 Further Reading 56 5 Measurements of Length The Definition of the Metre Length Measurements 58

8.2.1 The Fractional-Fringe Method 59 8.2.2 Fringe Counting 59 8.2.3 Heterodyne Techniques 59 8.2.4 Synthetic Long-Wavelength Signals 60 8.2.5 Frequency Scanning 61 8.2.6 Environmental Effects 62 8.

5 8.2.1 The Fractional-Fringe Method Fringe Counting Heterodyne Techniques Synthetic Long-Wavelength Signals Frequency Scanning Environmental Effects Measurements of Changes in Length Phase Compensation Heterodyne Methods Dilatometry Summary Problems 63 Further Reading 66 : ;f Optical Testing The Fizeau Interferometer The Twyman-Green Interferometer Analysis of Wavefront Aberrations Laser Unequal-Path Interferometers The Point-Diffraction Interferometer Shearing Interferometers Lateral Shearing Interferometers Radial Shearing Interferometers Grazing-Incidence Interferometry Summary Problems 78 Further Reading 81 In Digital Techniques Digital Fringe Analysis 83

$4 Summary 88 10.5 Problems 88 Further Reading 91 Macro- and Micro-Interf erometry 93 11.1 Interferometry of Refractive Index Fields 93 11.2 The Mach-Zehnder Interferometer 93 11.$

6 10.2 Digital Phase Measurements Testing Aspheric Surfaces Direct Measurements ofsurface Shape Long-Wavelength Tests Tests with Shearing Interferometers Tests with Computer-Generated Holograms Summary Problems 88 Further Reading 91 Macro- and Micro-Interf erometry Interferometry of Refractive Index Fields The Mach-Zehnder Interferometer Interference Microscopy Multiple-Beam Interferometry Two-Beam Interference Microscopes The Nomarski Interferometer Summary Problems 101 Further Reading 103 White-Light Interference Microscopy White-Light Interferometry White-Light Phase-Shifting Microscopy Spectrally Resolved Interferometry Coherence-Probe Microscopy Summary Problems 109 Further reading 110

: - : : : : '.-.. Holographie Xll Contents and Speckle Interferometry 111 13.1 Holographie Interferometry 111 13.2 Holographie Nondestructive Testing 112 13.3 Holographie Strain Analysis 112 13.

7 : - : : : : '.-.. Holographie Xll Contents and Speckle Interferometry Holographie Interferometry Holographie Nondestructive Testing Holographie Strain Analysis Holographie Vibration Analysis Speckle Interferometry Electronic Speckle-Pattern Interferometry Studies of Vibrating Objects Summary Problems 119 Further Reading Inle rf e rom e tri cse S rs Laser-Doppler Interferometry Measurements of Vibration Amplitudes Fiber Interferometers Rotation Sensing Laser-Feedback Interferometers Gravitational Wave Detectors Optical Signal Processing InterferometricSwitch.es Interferometric Logic Gates Summary Problems 129 Further Reading 132 Interference Spectroscopy Resolving Power and Etendue The Fabry-Perot Interferometer 134

Contents xiu 15.2.1 The Scanning Fabry-Perot Interferometer 135 15.2.2 The Confocal Fabry Perot Interferometer 135 15.2.3 The Multiple-Pass Fabry-Perot Interferometer 136 15.

8 Contents xiu The Scanning Fabry-Perot Interferometer The Confocal Fabry Perot Interferometer The Multiple-Pass Fabry-Perot Interferometer Interference Filters Birefringent Filters Interference Wavelength Meters Laser Frequency Measurements Summary Problems 140 Further Reading Fourier Transform Spectroscopy The Multiplex Advantage Theory Practical Aspects Computation of the Spectrum Applications Summary Problems 149 Further Reading 151 1;p;;;;;;;;!;;;; ;i : / Interference with Single Photons Interference The Quantum Picture Single-Photon States Interference with Single-Photon States Interference with Independent Sources Fourth-Order Interference 161

$2 Optical Intensity 170 Phase Shifts on Reflection 171 Diffraction 173 C.l Diffraction Grätings 174 Polarized Light 177 D.l Production of Polarized Light 177 D.$

9 Contents 17.6 Summary Problems 162 Further Reading 163 ; Building an Interferometer 165 Further Reading 167 f % B Monochromatic Light Waves 169 A.l Complex Representation 169 A.2 Optical Intensity 170 Phase Shifts on Reflection 171 Diffraction 173 C.l Diffraction Grätings 174 Polarized Light 177 D.l Production of Polarized Light 177 D.2 Quarter-Wave and Half-Wave Plates 177 D.3 The Jones Calculus 179 D.4 The Poincare Sphere 180 :;: The Pancharatnam Phase 183 E.l The Pancharatnam Phase 183 E.2 Achromatic Phase Shifters 183 E.3 Switchable Achromatic Phase Shifters 185

Contents The Twyman-Green Interf erometer: Initial Adjustment 187 The Mach-Zehnder Interferometer: Initial Adjustment 191 Fourier Transf orms and Correlation 193 H.l Fourier Transforms 193 H.

10 Contents The Twyman-Green Interf erometer: Initial Adjustment 187 The Mach-Zehnder Interferometer: Initial Adjustment 191 Fourier Transf orms and Correlation 193 H.l Fourier Transforms 193 H.2 Correlation 194 Coherence 195 LI Quasi-Monochromatic Light The Mutual Coherence Function Complex Degree of Coherence Visibility of the Interference Fringes Spatial Coherence Temporal Coherence Coherence Length 199 Heterodyne Interferometry 201 Laser Frequency Shifting 203

Evaluation of Shearing Interferograms 205 L. 1 Lateral Shearing Interferometers 205 L.2 Radial Shearing Interferometers 205 Phase-Shifting Interferometry 209 M.

11 Evaluation of Shearing Interferograms 205 L. 1 Lateral Shearing Interferometers 205 L.2 Radial Shearing Interferometers 205 Phase-Shifting Interferometry 209 M.l Error-Correcting Algorithms 210 Holographie Imaging 211 N.l Hologram Recording 211 N.2 Image Reconstruction 212 Laser Speckle 215 Laser Frequency Modulation 219 Index 221

Basics of INTERFEROMETRY

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