Abstract

The physical conditions for observing the longitudinal spatial coherence of light of an extended thermal source in interference experiments are defined. For experimental verification of these conditions a Michelson interferometer with a longitudinal scanning mirror was used. The influence of the longitudinal spatial coherence of thermal light on a fringe envelope is demonstrated experimentally.

© 2004 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  3. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  4. L. M. Soroko, Principles of Holography and Coherence Optics (Nauka, Moscow, 1971; in Russian).
  5. J. Rosen and A. Yariv, Opt. Commun. 117, 8 (1995).
    [CrossRef]
  6. J. Rosen and M. Takeda, Appl. Opt. 39, 4107 (2000).
    [CrossRef]
  7. M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).
  8. W. Wang, H. Kozaki, J. Rosen, and M. Takeda, Appl. Opt. 41, 1962 (2002).
    [CrossRef] [PubMed]
  9. C. W. McCutchen, J. Opt. Soc. Am.56, 727 (1966).
  10. M. Françon, La Granularite Laser (Speckle) et Ses Applications en Optique (Masson, Paris, 1978).
  11. V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

2003 (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).

2002 (1)

2000 (1)

1998 (1)

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

1995 (1)

J. Rosen and A. Yariv, Opt. Commun. 117, 8 (1995).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

Duan, Z.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).

Françon, M.

M. Françon, La Granularite Laser (Speckle) et Ses Applications en Optique (Masson, Paris, 1978).

Gokhler, M.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Khomutov, V. L.

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

Konstantinov, K. V.

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

Kozaki, H.

Lyakin, D. V.

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

McCutchen, C. W.

C. W. McCutchen, J. Opt. Soc. Am.56, 727 (1966).

Rosen, J.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, Appl. Opt. 41, 1962 (2002).
[CrossRef] [PubMed]

J. Rosen and M. Takeda, Appl. Opt. 39, 4107 (2000).
[CrossRef]

J. Rosen and A. Yariv, Opt. Commun. 117, 8 (1995).
[CrossRef]

Ryabukho, V. P.

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

Soroko, L. M.

L. M. Soroko, Principles of Holography and Coherence Optics (Nauka, Moscow, 1971; in Russian).

Takeda, M.

Wang, W.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

Yariv, A.

J. Rosen and A. Yariv, Opt. Commun. 117, 8 (1995).
[CrossRef]

Appl. Opt. (2)

Opt. Commun. (1)

J. Rosen and A. Yariv, Opt. Commun. 117, 8 (1995).
[CrossRef]

Opt. Eng. (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, Opt. Eng. 42, 1 (2003).

Tech. Phys. Lett. (1)

V. P. Ryabukho, V. L. Khomutov, D. V. Lyakin, and K. V. Konstantinov, Tech. Phys. Lett. 24, 132 (1998).
[CrossRef]

Other (7)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

C. W. McCutchen, J. Opt. Soc. Am.56, 727 (1966).

M. Françon, La Granularite Laser (Speckle) et Ses Applications en Optique (Masson, Paris, 1978).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, 1st ed. (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

L. M. Soroko, Principles of Holography and Coherence Optics (Nauka, Moscow, 1971; in Russian).

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Figures (3)

Fig. 1
Fig. 1

Scanning Michelson interferometer setup for observing longitudinal spatial coherence. Notation defined in text.

Fig. 2
Fig. 2

(a)–(c) Interference signals obtained when the photodetector was placed on an optical axis at the following angle apertures 2θ of the interfering fields: (a) 2θ=0.08, (b) 2θ=0.13, (c) 2θ=0.21. (d) Photodetector aperture placed at the periphery of the optical axis at angle distance ρ/L=0.2, 2θ=0.21.

Fig. 3
Fig. 3

Interference signals obtained (a) in the focal plane of a lens, 2θ=0.24 and (b), (c) in two planes of image space: (b) 2θ=0.32, m=0.5; (c) 2θ=0.13, m=7.2. The photodetector was placed on the optical axis.

Equations (3)

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I=I1+I2+2ΓΔρ,Δz,Δt×cos2πλ02ΔzM+Δφ12ρ,ΔzM+ψ,
ΓΔzexpi2πλ0Δz-+I0α×exp-iπλ0Δzα2dα,
ΓΔzΓ0=sinπθ2Δz/2λπθ2Δz/2λexpi2πλΔz1-θ22,

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