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Optical Interferometry, 2e - 1st Edition - ISBN: 9780123116307, 9780080473642

Optical Interferometry, 2e

1st Edition

Author: P. Hariharan
eBook ISBN: 9780080473642
Hardcover ISBN: 9780123116307
Imprint: Academic Press
Published Date: 22nd September 2003
Page Count: 352
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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


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© Academic Press 2003
22nd September 2003
Academic Press
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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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