# Optical Interferometry, 2e

**By**

- P. Hariharan, School of Physics, University of Sydney, Sydney, Australia

When the first edition of "Optical Interferometry" was published, interferometry was regarded as a rather esoteric method of making measurements, largely confined to the laboratory. Today, however, besides its use in several fields of research, it has applications in fields as diverse as measurement of length and velocity, sensors for rotation, acceleration, vibration and electrical and magnetic fields, as well as in microscopy and nanotechnology. Most topics are discussed first at a level accessible to anyone with a basic knowledge of physical optics, then a more detailed treatment of the topic is undertaken, and finally each topic is supplemented by a reference list of more than 1000 selected original publications in total.

View full description### Audience

The primary market for the book would be scientists and engineers interested in precision measurements of a range of physical quantities in industry as well as researchers and students in universities.A secondary market would be members of organizations such as the Optical Society of America, SPIE and IEEE who are interested in possible applications in their work.

### Book information

- Published: September 2003
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-311630-7

### Table of Contents

Chapter 1Optical interferometry: its development 1.1 The wave theory of light1.2 Michelson"s experiment1.3 Measurement of the metre1.4 Coherence1.5 Interference filters1.6 Interference spectroscopy1.7 The development of the laser1.8 Electronic techniques1.9 Heterodyne techniques1.10 Holographic interferometry1.11 Speckle interferrometry1.12 Stellar interferometry1.13 Relativity and gravitational waves1.14 Fiber interferometers1.15 Nonlinear interferometers1.16 Quantum effects1.17 Future directionsChapter 2Two-beam interference 2.1 Complex representation of light waves2.2 Interference of two monochromatic waves2.3 Wavefront division2.4 Amplitude division2.4.1Interference in a plane-parallel plate2.4.2Fizeau fringes2.4.3Interference in a thin film2.5 Localization of fringes2.5.1Nonlocalized fringes2.5.2Localized fringes2.5.3Fringes in a plane-parallel plate2.5.4Fringes in a thin film2.6 Two-beam interferometers2.7 The Michelson interferometer2.7.1Nonlocalized fringes2.7.2Fringes of equal inclination2.7.3Fringes of equal thickness2.8 The Mach-Zehnder interferometer2.9 The Sagnac interferometer2.10 Interference with white light2.11Channeled spectra2.12 Achromatic fringes2.13 Interferential color photography Chapter 3Coherence 3.1 Quasi-monochromatic light3.2 Waves and wave groups3.3 Phase velocity and group velocity3.4 The mutual coherence function3.5 Spatial coherence3.6 Temporal coherence3.7 Coherence time and coherence length3.8 Combined spatial and temporal effects3.9 Application to a two-beam interferometer3.10 Source-size effects3.11 Spectral bandwidth effects3.12 Spectral coherence3.13 Polarization effectsChapter 4Multiple-beam interference 4.1 Fringes in a plane-parallel plate4.2 Fringes by reflection4.3 Fringes in a thin film: fringes of equal thickness4.4 Fringes of equal chromatic order4.5 Fringes of superposition4.6 Three-beam fringes4.7 Double-passed fringesChapter 5The laser as a light source 5.1 Gas lasers5.2 Laser modes5.2.1Modes of a confocal resonator5.2.2Generalized spherical resonator5.2.3Longitudinal modes5.2.4Single-frequency operation5.3 Comparison of laser frequencies5.4 Frequency stabilization5.4.1Polarization stabilized laser5.4.2Stabilized transverse Zeeman laser5.4.3Stabilization on the Lamb dip5.4.4Stabilization by saturated absorption5.4.5Stabilization by saturated fluorescence5.5 Semiconductor lasers5.6 Ruby and Nd:YAG lasers5.7 Dye lasers5.8 Laser beamsChapter 6Electronic techniques 6.1 Photoelectric setting methods6.2 Fringe counting6.3 Heterodyne interferometry6.4 Computer-aided fringe analysis6.4.1Fourier transform techniques6.5 Phase-shifting interferometry6.5.1Error-correcting algorithms6.6 Techniques of phase shifting6.6.1Frequency shifting6.6.2Polarization techniquesChapter 7Measurements of length 7.1 Line standards7.2 End standards7.3 The integral interference order7.4 Exact fractions7.5 The refractive index of air7.6 The international prototype metre7.7 The 86Kr standard7.8 Frequency measurements7.9 The definition of the metre7.10 Length measurements with lasers7.10.1Two-wavelength interferometry7.10.2Frequency-modulation interferometry7.11 Changes in lengthChapter 8Optical testing 8.1 The Fizeau interferometer8.2 The Twyman-Green interferometer8.3 Unequal-path interferometers8.4 Phase unwrapping8.5 Analysis of wavefront aberrations8.5.1Zernike polynomials8.5.2Wavefront fitting8.6 Shearing interferometers8.6.1Lateral shearing interferometers8.6.2Interpretation of interferograms8.6.3Rotational and radial shearing8.7 Grating interferometers8.8 The scatter-plate interferometer8.9 The point-diffraction interferometer8.10 Computerized test methods8.10.1Absolute tests for flatness8.10.2Small-scale irregularities8.10.3Sources of error8.10.4Subaperture testing8.10.5Testing aspheric surfaces8.10.6Computer-generated holograms8.11 Testing of rough surfaces8.12 The optical transfer functionChapter 9Interference microscopy 9.1 The Mirau interferometer9.2 Common-path interference microscopes9.3 Polarization interferometers9.3.1Lateral shear9.3.2Radial shear9.4 The Nomarski interferometer9.5 Electronic phase measurements9.5.1Phase-shifting techniques9.6 Surface profiling with white light9.6.1Achromatic phase-shifting9.6.2Spectrally resolved interferometryChapter 10Interferometric sensors 10.1 Rotation sensing10.1.1Ring lasers10.1.2Ring interferometers10.2 Laser-feedback interferometers10.2.1Diode-laser interferometers10.3 Fiber interferometers10.4 Multiplexed fiber-optic sensors10.5 Doppler interferometry10.5.1Laser-Doppler velocimetry10.5.2Measurements of surface velocities10.6 Vibration measurements10.7 Magnetic fields10.8 Adaptive optical systemsChapter 11Interference spectroscopy 11.1 Etendue of an interferometer11.2 The Fabry-Perot interferometer11.3 The scanning Fabry-Perot interferometer11.4 The spherical-mirror Fabry-Perot interferometer11.5 The multiple Fabry-Perot interferometer11.6 The multiple-pass Fabry-Perot interferometer11.7 Holographic filters11.8 Birefringent filters11.9 Wavelength meters11.9.1Dynamic wavelength meters11.9.2Static wavelength meters11.10 Heterodyne techniques11.11 Measurements of laser linewidthsChapter 12Fourier-transform spectroscopy 12.1 The etendue and multiplex advantages12.2 Theory12.3 Resolution and apodization12.4 Sampling12.5 Effect of source and detector size12.6 Field widening12.7 Phase correction12.8 Noise12.9 Pre-filtering12.10 Interferometers for Fourier-transform spectroscopy12.11 Computation of the spectrum12.12 ApplicationsChapter 13Nonlinear interferometers 13.1 Interferometry with pulsed lasers13.2 Second-harmonic interferometers13.2.1Critical phase matching13.3 Phase-conjugate interferometers13.3.1Phase-conjugating mirrors13.4 Interferometers using active elements13.5 Photorefractive oscillators13.6 Measurements of nonlinear susceptibilitiesChapter 14Stellar interferometry 14.1 Michelson"s stellar interferometer14.2 The intensity interferometer14.3 Heterodyne stellar interferometry14.3.1Large heterodyne interferometer14.4 Long-baseline interferometers14.5 Stellar speckle interferometry14.6 Telescope arraysChapter 15Space-time and gravitation 15.1 The Michelson-Morley experiment15.2 Gravitational waves15.3 Gravitational-wave detectors15.4 LIGO15.5 The standard quantum limit15.6 Squeezed states of light15.7 Interferometry below the SQLChapter 16Single-photon interferometry 16.1 Interferometry at the "single-photon" level16.2 Interference - the quantum picture16.3 Sources of nonclassical light16.3.1Parametric down-conversion16.4 The beam splitter16.5 Interference with single-photon states16.6 The geometric phase16.6.1Observations at the "single-photon" level16.6.2Observations with single-photon states16.7 Interference with independent sources16.7.1Observations at the "single-photon" level16.7.2Observations in the time domain16.8 Superposition statesChapter 17Fourth-order interference 17.1 Nonclassical fourth-order interference17.2 Interference in separated interferometers17.3 The geometric phaseChapter 18Two-photon interferometry 18.1 Interferometric tests of Bell"s inequality18.2 Tests using unbalanced interferometers18.3 Two-photon interference18.4 The quantum eraser18.5 Single-photon tunneling18.5.1Dispersion cancellation18.5.2Measurements of tunneling time18.6 ConclusionsAppendix ATwo-dimensional linear systems A.1 The Fourier transformA.2 Convolution and correlationA.3 The Dirac delta functionA.4 Random functionsAppendix BThe Fresnel-Kirchhoff integral Appendix CReflection and transmission at a surface C.1 The Fresnel transformC.2 The Stokes relationsAppendix DThe Jones calculus Appendix EThe geometric phase E.1 The Poincare sphereE.2 The Pancharatnam phaseAppendix FHolography F.1 The off-axis hologramF.2 Volume hologramsF.3 Computer-generated hologramsAppendix GSpeckle G.1 Speckle statisticsG.2 Second-order statisticsG.3 Image speckleG.4 Young"s fringesG.5 Addition of speckle patternsBibliography References Author index Subject index