Abstract

The problem of determining the phase ϕ of the complex degree of coherence γ of a light beam from measurements of its modulus |γ| is considered. If a reference beam of light with an exactly known complex degree of coherence is available, then the phase ϕ may be determined from an additional experiment in which the two beams are superimposed.

© 1968 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press Ltd., Oxford, England, 1965), Ch. X.
  2. See for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
    [CrossRef]
  3. A. A. Michelson, Phil. Mag. 31, 338 (1891); Phil. Mag. 34, 280 (1892).
  4. E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
    [CrossRef]
  5. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. (Clarendon Press, Oxford, England, 1948), p. 128.
  6. P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
    [CrossRef]
  7. A. Walther, Optica Acta 10, 41 (1963).
    [CrossRef]
  8. H. M. Nussenzveig, J. Math. Phys. 8, 561 (1967).
    [CrossRef]
  9. H. Gamo, J. Appl. Phys. 34, 875 (1963); Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 252. The idea of superposing incident beam with a coherent background has also been suggested by Gamo in this latter reference. However, in our method the reference source need not be coherent.
    [CrossRef]
  10. C. L. Mehta, Nuovo Cimento 36, 202 (1965).
    [CrossRef]
  11. D. Dialetis and E. Wolf, Nuovo Cimento 47, 113 (1967); D. Dialetis, J. Math. Phys. 8, 1641 (1967).
    [CrossRef]
  12. A. A. Michelson, Astrophys. J.,  51, 257 (1920).
    [CrossRef]
  13. R. Hanbury Brown and R. Q. Twiss, Proc. Roy. Soc. (London) A248, 199 (1958).

1967 (2)

H. M. Nussenzveig, J. Math. Phys. 8, 561 (1967).
[CrossRef]

D. Dialetis and E. Wolf, Nuovo Cimento 47, 113 (1967); D. Dialetis, J. Math. Phys. 8, 1641 (1967).
[CrossRef]

1965 (2)

C. L. Mehta, Nuovo Cimento 36, 202 (1965).
[CrossRef]

See for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[CrossRef]

1963 (3)

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[CrossRef]

A. Walther, Optica Acta 10, 41 (1963).
[CrossRef]

H. Gamo, J. Appl. Phys. 34, 875 (1963); Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 252. The idea of superposing incident beam with a coherent background has also been suggested by Gamo in this latter reference. However, in our method the reference source need not be coherent.
[CrossRef]

1962 (1)

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[CrossRef]

1958 (1)

R. Hanbury Brown and R. Q. Twiss, Proc. Roy. Soc. (London) A248, 199 (1958).

1920 (1)

A. A. Michelson, Astrophys. J.,  51, 257 (1920).
[CrossRef]

1891 (1)

A. A. Michelson, Phil. Mag. 31, 338 (1891); Phil. Mag. 34, 280 (1892).

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press Ltd., Oxford, England, 1965), Ch. X.

Dialetis, D.

D. Dialetis and E. Wolf, Nuovo Cimento 47, 113 (1967); D. Dialetis, J. Math. Phys. 8, 1641 (1967).
[CrossRef]

Gamo, H.

H. Gamo, J. Appl. Phys. 34, 875 (1963); Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 252. The idea of superposing incident beam with a coherent background has also been suggested by Gamo in this latter reference. However, in our method the reference source need not be coherent.
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown and R. Q. Twiss, Proc. Roy. Soc. (London) A248, 199 (1958).

Mandel, L.

See for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[CrossRef]

Marathay, A. S.

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[CrossRef]

Mehta, C. L.

C. L. Mehta, Nuovo Cimento 36, 202 (1965).
[CrossRef]

Michelson, A. A.

A. A. Michelson, Astrophys. J.,  51, 257 (1920).
[CrossRef]

A. A. Michelson, Phil. Mag. 31, 338 (1891); Phil. Mag. 34, 280 (1892).

Nussenzveig, H. M.

H. M. Nussenzveig, J. Math. Phys. 8, 561 (1967).
[CrossRef]

Roman, P.

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[CrossRef]

Titchmarsh, E. C.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. (Clarendon Press, Oxford, England, 1948), p. 128.

Twiss, R. Q.

R. Hanbury Brown and R. Q. Twiss, Proc. Roy. Soc. (London) A248, 199 (1958).

Walther, A.

A. Walther, Optica Acta 10, 41 (1963).
[CrossRef]

Wolf, E.

D. Dialetis and E. Wolf, Nuovo Cimento 47, 113 (1967); D. Dialetis, J. Math. Phys. 8, 1641 (1967).
[CrossRef]

See for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[CrossRef]

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press Ltd., Oxford, England, 1965), Ch. X.

Astrophys. J. (1)

A. A. Michelson, Astrophys. J.,  51, 257 (1920).
[CrossRef]

J. Appl. Phys. (1)

H. Gamo, J. Appl. Phys. 34, 875 (1963); Advances in Quantum Electronics, J. R. Singer, Ed. (Columbia University Press, New York, 1961), p. 252. The idea of superposing incident beam with a coherent background has also been suggested by Gamo in this latter reference. However, in our method the reference source need not be coherent.
[CrossRef]

J. Math. Phys. (1)

H. M. Nussenzveig, J. Math. Phys. 8, 561 (1967).
[CrossRef]

Nuovo Cimento (3)

C. L. Mehta, Nuovo Cimento 36, 202 (1965).
[CrossRef]

D. Dialetis and E. Wolf, Nuovo Cimento 47, 113 (1967); D. Dialetis, J. Math. Phys. 8, 1641 (1967).
[CrossRef]

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[CrossRef]

Optica Acta (1)

A. Walther, Optica Acta 10, 41 (1963).
[CrossRef]

Phil. Mag. (1)

A. A. Michelson, Phil. Mag. 31, 338 (1891); Phil. Mag. 34, 280 (1892).

Proc. Phys. Soc. (London) (1)

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[CrossRef]

Proc. Roy. Soc. (London) (1)

R. Hanbury Brown and R. Q. Twiss, Proc. Roy. Soc. (London) A248, 199 (1958).

Rev. Mod. Phys. (1)

See for example, L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon Press Ltd., Oxford, England, 1965), Ch. X.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. (Clarendon Press, Oxford, England, 1948), p. 128.

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Equations (5)

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γ ( τ ) = 0 g ( ν ) e - 2 π i ν τ d ν .
g ˜ ( ν ) = g ( ν ) + g 0 ( ν ) .
γ ˜ ( τ ) = γ ( τ ) + γ 0 ( τ ) ,
γ ˜ ( τ ) 2 = γ ( τ ) 2 + γ 0 ( τ ) 2 + 2 γ ( τ ) γ 0 ( τ ) cos [ ϕ ( τ ) - ϕ 0 ( τ ) ] ,
Γ ˜ ( P 1 , P 2 , τ ) = Γ ( P 1 , P 2 , τ ) + Γ 0 ( P 1 , P 2 , τ ) .