Basics of INTERFEROMETRY
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1 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
2 Contents Preface Acknowledgments xv xvii 1 Introduction 1 2 Interference: A Primer Light Waves Intensity in an Interference Pattern Visibility of Interference Fringes Interference with a Point Source Localization of Fringes Summary Problems 10 3 Two-Beam Interferometers Wavefront Division Amplitude Division The Rayleigh Interferometer The Michelson Interferometer Fringes Formed with a Point Source Fringes Formed with an Extended Source 20 vn
3 viii CONTENTS Pringes Formed with CoUimated Light Applications The Mach-Zehnder Interferometer The Sagnac Interferometer Summary Problems 23 4 Light Sources Coherence Source-Size Effects Slit Source Circular Pinhole Spectral Effects Polarization Effects White-Light Fringes Channeled Spectra Summary Problems 33 5 Multiple-Beam Interference Multiple-Beam Fringes by Transmission Multiple-Beam Pringes by Reflection Multiple-Beam Pringes of Equal Thickness Fringes of Equal Chromatic Order (FECO Fringes) The Fabry-Perot Interferometer Summary Problems 43 6 The Laser as a Light Source Lasers for Interferometry Laser Modes Single-Wavelength Operation of Lasers 49
4 CONTENTS ix 6.4 Polarization of Laser Beams Wavelength Stabilization of Lasers Laser Beam Expansion Problems with Laser Sources Laser Safety Summary Problems 53 7 Detectors Photomultipliers Photodiodes Charge-Coupled Detector Arrays Linear CCD Sensors Area CCD Sensors Frame-Transfer CCD Sensors Photoconductive Detectors Pyroelectric Detectors Summary Problems 64 8 Measurements of Length The Definition of the Metre Length Measurements The Fractional-Fringe Method Fringe Counting Heterodyne Techniques Synthetic Long-Wavelength Signals Laser Frequency Modulation Environmental Effects Measurement of Changes in Length Phase Compensation 73
5 x CONTENTS Heterodyne Methods Summary Problems 74 9 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 Summary Problems Digital Techniques Digital Fringe Analysis Digital Phase Measurements Testing Aspheric Surfaces Direct Measurements of Surface Shape Long-Wavelength Tests Tests with Shearing Interferometers Tests with Computer-Generated Holograms Summary Problems Macro- and Micro-Interferometry Interferometry of Refractive Index Fields The Mach-Zehnder Interferometer Interference Microscopy Multiple-Beam Interference 108
6 CONTENTS xi 11.5 Two-Beam Interference Microscopes The Nomarski Interferometer Summary Problems Holographie 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 Interferometric Sensors Laser-Doppler Interferometry Measurements of Vibration Amplitudes Fiber Interferometers Rotation Sensing Summary Problems Interference Spectroscopy Resolving Power and Etendue The Fabry-Perot Interferometer The Scanning Fabry-Perot Interferometer The Confocal Fabry-Perot Interferometer The Multiple-Pass Fabry-Perot Interferometer Interference Filters Birefringent Filters 143
7 xii CONTENTS 14.5 Interference Wavelength Meters Summary Problems Fourier-Transform Spectroscopy The Multiplex Advantage Theory of Fourier-Transform Spectroscopy Practical Aspects of Fourier-Transform Spectroscopy Computation of the Spectrum Applications of Fourier-Transform Spectroscopy Summary Problems 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
8 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
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