LIMITED OFFER

## Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code needed.

Skip to main content# Optical Interferometry, 2e

## Purchase options

## Save 50% on book bundles

## Institutional subscription on ScienceDirect

Request a sales quote### P. Hariharan

- 1st Edition - September 22, 2003
- Author: P. Hariharan
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 3 9 9 5 6 1 - 2
- Hardback ISBN:9 7 8 - 0 - 1 2 - 3 1 1 6 3 0 - 7
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 7 3 6 4 - 2

When the first edition of Optical Interferometry was published, interferometry was regarded as a rather esoteric method of making measurements, largely confined to the laborator… Read more

LIMITED OFFER

Immediately download your ebook while waiting for your print delivery. No promo code needed.

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.

- 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.

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

Coherence

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

Holography

F.1 The off-axis hologram

F.2 Volume holograms

F.3 Computer-generated holograms

Appendix G

Speckle

G.1 Speckle statistics

G.2 Second-order statistics

G.3 Image speckle

G.4 Young"s fringes

G.5 Addition of speckle patterns

Bibliography

References

Author index

Subject index

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

Coherence

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

Holography

F.1 The off-axis hologram

F.2 Volume holograms

F.3 Computer-generated holograms

Appendix G

Speckle

G.1 Speckle statistics

G.2 Second-order statistics

G.3 Image speckle

G.4 Young"s fringes

G.5 Addition of speckle patterns

Bibliography

References

Author index

Subject index

- No. of pages: 352
- Language: English
- Edition: 1
- Published: September 22, 2003
- Imprint: Academic Press
- Paperback ISBN: 9780123995612
- Hardback ISBN: 9780123116307
- eBook ISBN: 9780080473642

PH

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, AustraliaRead *Optical Interferometry, 2e* on ScienceDirect