Optical Interferometry, 2e

Optical Interferometry, 2e

1st Edition - September 22, 2003

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  • Author: P. Hariharan
  • eBook ISBN: 9780080473642
  • Hardcover ISBN: 9780123116307

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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.

Key Features

  • Historical development of interferometry
  • The laser as a light source
  • Two-beam interference
  • Techniques for frequency stabilization
  • Coherence
  • Electronic phase measurements
  • Multiple-beam interference
  • Quantum effects in optical interference
  • Extensive coverage of the applications of interferometry, such as measurements of length, optical testing, interference microscopy, interference spectroscopy, Fourier-transform spectroscopy, interferometric sensors, nonlinear interferometers, stellar interferometry, and studies of space-time and gravitation


scientists and engineers interested in precision measurements of a range of physical quantities in industry as well as researchers and students in universities, members of organizations such as the Optical Society of America, SPIE and IEEE who are interested in possible applications in their work.

Table of Contents

  • Chapter 1
    Optical interferometry: its development
    1.1 The wave theory of light
    1.2 Michelson"s experiment
    1.3 Measurement of the metre
    1.4 Coherence
    1.5 Interference filters
    1.6 Interference spectroscopy
    1.7 The development of the laser
    1.8 Electronic techniques
    1.9 Heterodyne techniques
    1.10 Holographic interferometry
    1.11 Speckle interferrometry
    1.12 Stellar interferometry
    1.13 Relativity and gravitational waves
    1.14 Fiber interferometers
    1.15 Nonlinear interferometers
    1.16 Quantum effects
    1.17 Future directions

    Chapter 2
    Two-beam interference
    2.1 Complex representation of light waves
    2.2 Interference of two monochromatic waves
    2.3 Wavefront division
    2.4 Amplitude division
    2.4.1Interference in a plane-parallel plate
    2.4.2Fizeau fringes
    2.4.3Interference in a thin film
    2.5 Localization of fringes
    2.5.1Nonlocalized fringes
    2.5.2Localized fringes
    2.5.3Fringes in a plane-parallel plate
    2.5.4Fringes in a thin film
    2.6 Two-beam interferometers
    2.7 The Michelson interferometer
    2.7.1Nonlocalized fringes
    2.7.2Fringes of equal inclination
    2.7.3Fringes of equal thickness
    2.8 The Mach-Zehnder interferometer
    2.9 The Sagnac interferometer
    2.10 Interference with white light
    2.11Channeled spectra
    2.12 Achromatic fringes
    2.13 Interferential color photography

    Chapter 3
    3.1 Quasi-monochromatic light
    3.2 Waves and wave groups
    3.3 Phase velocity and group velocity
    3.4 The mutual coherence function
    3.5 Spatial coherence
    3.6 Temporal coherence
    3.7 Coherence time and coherence length
    3.8 Combined spatial and temporal effects
    3.9 Application to a two-beam interferometer
    3.10 Source-size effects
    3.11 Spectral bandwidth effects
    3.12 Spectral coherence
    3.13 Polarization effects

    Chapter 4
    Multiple-beam interference
    4.1 Fringes in a plane-parallel plate
    4.2 Fringes by reflection
    4.3 Fringes in a thin film: fringes of equal thickness
    4.4 Fringes of equal chromatic order
    4.5 Fringes of superposition
    4.6 Three-beam fringes
    4.7 Double-passed fringes

    Chapter 5
    The laser as a light source
    5.1 Gas lasers
    5.2 Laser modes
    5.2.1Modes of a confocal resonator
    5.2.2Generalized spherical resonator
    5.2.3Longitudinal modes
    5.2.4Single-frequency operation
    5.3 Comparison of laser frequencies
    5.4 Frequency stabilization
    5.4.1Polarization stabilized laser
    5.4.2Stabilized transverse Zeeman laser
    5.4.3Stabilization on the Lamb dip
    5.4.4Stabilization by saturated absorption
    5.4.5Stabilization by saturated fluorescence
    5.5 Semiconductor lasers
    5.6 Ruby and Nd:YAG lasers
    5.7 Dye lasers
    5.8 Laser beams

    Chapter 6
    Electronic techniques
    6.1 Photoelectric setting methods
    6.2 Fringe counting
    6.3 Heterodyne interferometry
    6.4 Computer-aided fringe analysis
    6.4.1Fourier transform techniques
    6.5 Phase-shifting interferometry
    6.5.1Error-correcting algorithms
    6.6 Techniques of phase shifting
    6.6.1Frequency shifting
    6.6.2Polarization techniques

    Chapter 7
    Measurements of length
    7.1 Line standards
    7.2 End standards
    7.3 The integral interference order
    7.4 Exact fractions
    7.5 The refractive index of air
    7.6 The international prototype metre
    7.7 The 86Kr standard
    7.8 Frequency measurements
    7.9 The definition of the metre
    7.10 Length measurements with lasers
    7.10.1Two-wavelength interferometry
    7.10.2Frequency-modulation interferometry
    7.11 Changes in length

    Chapter 8
    Optical testing
    8.1 The Fizeau interferometer
    8.2 The Twyman-Green interferometer
    8.3 Unequal-path interferometers
    8.4 Phase unwrapping
    8.5 Analysis of wavefront aberrations
    8.5.1Zernike polynomials
    8.5.2Wavefront fitting
    8.6 Shearing interferometers
    8.6.1Lateral shearing interferometers
    8.6.2Interpretation of interferograms
    8.6.3Rotational and radial shearing
    8.7 Grating interferometers
    8.8 The scatter-plate interferometer
    8.9 The point-diffraction interferometer
    8.10 Computerized test methods
    8.10.1Absolute tests for flatness
    8.10.2Small-scale irregularities
    8.10.3Sources of error
    8.10.4Subaperture testing
    8.10.5Testing aspheric surfaces
    8.10.6Computer-generated holograms
    8.11 Testing of rough surfaces
    8.12 The optical transfer function

    Chapter 9
    Interference microscopy
    9.1 The Mirau interferometer
    9.2 Common-path interference microscopes
    9.3 Polarization interferometers
    9.3.1Lateral shear
    9.3.2Radial shear
    9.4 The Nomarski interferometer
    9.5 Electronic phase measurements
    9.5.1Phase-shifting techniques
    9.6 Surface profiling with white light
    9.6.1Achromatic phase-shifting
    9.6.2Spectrally resolved interferometry

    Chapter 10
    Interferometric sensors
    10.1 Rotation sensing
    10.1.1Ring lasers
    10.1.2Ring interferometers
    10.2 Laser-feedback interferometers
    10.2.1Diode-laser interferometers
    10.3 Fiber interferometers
    10.4 Multiplexed fiber-optic sensors
    10.5 Doppler interferometry
    10.5.1Laser-Doppler velocimetry
    10.5.2Measurements of surface velocities
    10.6 Vibration measurements
    10.7 Magnetic fields
    10.8 Adaptive optical systems

    Chapter 11
    Interference spectroscopy
    11.1 Etendue of an interferometer
    11.2 The Fabry-Perot interferometer
    11.3 The scanning Fabry-Perot interferometer
    11.4 The spherical-mirror Fabry-Perot interferometer
    11.5 The multiple Fabry-Perot interferometer
    11.6 The multiple-pass Fabry-Perot interferometer
    11.7 Holographic filters
    11.8 Birefringent filters
    11.9 Wavelength meters
    11.9.1Dynamic wavelength meters
    11.9.2Static wavelength meters
    11.10 Heterodyne techniques
    11.11 Measurements of laser linewidths

    Chapter 12
    Fourier-transform spectroscopy
    12.1 The etendue and multiplex advantages
    12.2 Theory
    12.3 Resolution and apodization
    12.4 Sampling
    12.5 Effect of source and detector size
    12.6 Field widening
    12.7 Phase correction
    12.8 Noise
    12.9 Pre-filtering
    12.10 Interferometers for Fourier-transform spectroscopy
    12.11 Computation of the spectrum
    12.12 Applications

    Chapter 13
    Nonlinear interferometers
    13.1 Interferometry with pulsed lasers
    13.2 Second-harmonic interferometers
    13.2.1Critical phase matching
    13.3 Phase-conjugate interferometers
    13.3.1Phase-conjugating mirrors
    13.4 Interferometers using active elements
    13.5 Photorefractive oscillators
    13.6 Measurements of nonlinear susceptibilities

    Chapter 14
    Stellar interferometry
    14.1 Michelson"s stellar interferometer
    14.2 The intensity interferometer
    14.3 Heterodyne stellar interferometry
    14.3.1Large heterodyne interferometer
    14.4 Long-baseline interferometers
    14.5 Stellar speckle interferometry
    14.6 Telescope arrays

    Chapter 15
    Space-time and gravitation
    15.1 The Michelson-Morley experiment
    15.2 Gravitational waves
    15.3 Gravitational-wave detectors
    15.4 LIGO
    15.5 The standard quantum limit
    15.6 Squeezed states of light
    15.7 Interferometry below the SQL

    Chapter 16
    Single-photon interferometry
    16.1 Interferometry at the "single-photon" level
    16.2 Interference - the quantum picture
    16.3 Sources of nonclassical light
    16.3.1Parametric down-conversion
    16.4 The beam splitter
    16.5 Interference with single-photon states
    16.6 The geometric phase
    16.6.1Observations at the "single-photon" level
    16.6.2Observations with single-photon states
    16.7 Interference with independent sources
    16.7.1Observations at the "single-photon" level
    16.7.2Observations in the time domain
    16.8 Superposition states

    Chapter 17
    Fourth-order interference
    17.1 Nonclassical fourth-order interference
    17.2 Interference in separated interferometers
    17.3 The geometric phase

    Chapter 18
    Two-photon interferometry
    18.1 Interferometric tests of Bell"s inequality
    18.2 Tests using unbalanced interferometers
    18.3 Two-photon interference
    18.4 The quantum eraser
    18.5 Single-photon tunneling
    18.5.1Dispersion cancellation
    18.5.2Measurements of tunneling time
    18.6 Conclusions

    Appendix A
    Two-dimensional linear systems
    A.1 The Fourier transform
    A.2 Convolution and correlation
    A.3 The Dirac delta function
    A.4 Random functions
    Appendix B
    The Fresnel-Kirchhoff integral

    Appendix C
    Reflection and transmission at a surface
    C.1 The Fresnel transform
    C.2 The Stokes relations

    Appendix D
    The Jones calculus

    Appendix E
    The geometric phase
    E.1 The Poincare sphere
    E.2 The Pancharatnam phase

    Appendix F
    F.1 The off-axis hologram
    F.2 Volume holograms
    F.3 Computer-generated holograms

    Appendix G
    G.1 Speckle statistics
    G.2 Second-order statistics
    G.3 Image speckle
    G.4 Young"s fringes
    G.5 Addition of speckle patterns

    Author index
    Subject index

Product details

  • No. of pages: 352
  • Language: English
  • Copyright: © Academic Press 2003
  • Published: September 22, 2003
  • Imprint: Academic Press
  • eBook ISBN: 9780080473642
  • Hardcover ISBN: 9780123116307

About the Author

P. Hariharan

Professor P. Hariharan is a Research Fellow in the Division of Telecommunications and Industrial Physics of CSIRO in Sydney and a Visiting Professor at the University of Sydney. His main research interests are interferometry and holography. He is a Fellow of SPIE (The International Society for Optical Engineering), the Optical Society of America (OSA), the Institute of Physics, London, and the Royal Photographic Society. He was a vice-president and then the treasurer of the International Commission of Optics, as well as a director of SPIE. Honors he has received include OSA’s Joseph Fraunhofer Award, the Henderson Medal of the Royal Photographic Society, the Thomas Young Medal of the Institute of Physics, London, SPIE’s Dennis Gabor Award and, most recently, SPIE’s highest award, the Gold Medal.

Affiliations and Expertise

School of Physics, University of Sydney, Sydney, Australia

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