Abstract

Many partially coherent beams are made up of a superposition of mutually uncorrelated Hermite–Gaussian modes. We prove that knowledge of the transverse intensity profile of such a beam is sufficient for evaluating the weights of the modes in an exact way. Simulations indicate that the proposed method resists noise well.

© 1998 Optical Society of America

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References

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  6. F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.
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  8. Y. Champagne, J. Opt. Soc. Am. A 12, 1707 (1995).
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  9. J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
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  10. E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
    [CrossRef]
  11. B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
    [CrossRef]
  12. A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
    [CrossRef]
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    [CrossRef]

1998 (1)

1996 (1)

1995 (2)

1993 (2)

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

1992 (1)

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

1989 (2)

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef] [PubMed]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

1984 (1)

1982 (2)

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Agarwal, G. S.

Ambrosini, D.

Bagini, V.

Borghi, R.

Cai, B.

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

Champagne, Y.

Cutolo, A.

Friberg, A. T.

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef] [PubMed]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Gori, F.

V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, M. Santarsiero, D. Ambrosini, and G. Schirripa Spagnolo, J. Opt. Soc. Am. A 13, 1385 (1996).
[CrossRef]

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

Isernia, T.

Izzo, I.

Lü, B.

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

Martínez-Herrero, R.

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

Mejías, P. M.

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

Pacileo, A. M.

Pierri, R.

Santarsiero, M.

Schirripa Spagnolo, G.

Siegman, A. E.

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Starikov, A.

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Tervonen, E.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef] [PubMed]

Townsend, S. W.

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

Turunen, J.

J. Turunen, E. Tervonen, and A. T. Friberg, Opt. Lett. 14, 627 (1989).
[CrossRef] [PubMed]

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Wolf, E.

Yang, C.

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

Zeni, L.

Zhang, B.

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. E. Siegman and S. W. Townsend, IEEE J. Quantum Electron. 29, 1212 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Opt. Commun. (2)

R. Martínez-Herrero and P. M. Mejías, Opt. Commun. 94, 197 (1992).
[CrossRef]

B. Lü, B. Zhang, B. Cai, and C. Yang, Opt. Commun. 101, 49 (1993).
[CrossRef]

Opt. Lett. (2)

Other (4)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, New York, 1995).
[CrossRef]

F. Gori, in Coherence and Quantum Optics, L. Mandel and E. Wolf, eds. (Plenum, New York, 1984), p. 363.

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Figures (1)

Fig. 1
Fig. 1

(a) Intensity flat-top distributions in the presence of additive noise. (b) Real part of the expansion coefficients. N=20.

Equations (8)

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Gnx;v0=2πv021/412nn!Hnx2v0exp-x2v02,
-+Gn2x;v0dx=1,  n=0,1,2,.
Ix=n=0cnGn2x;v0,
FGn2x;v0p=Ψnπ2v02p2,
Ψnt=Lntexp-t2
0ΨntΨmtdt=δn,m,
I˜p=n=0cnΨnπ2v02p2,
cn=2π2v020I˜pΨnπ2v02p2pdp.

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