Abstract

We introduce beam-quality metrics for adaptive wave-front control that permit estimation of the degree of laser beam energy concentration on a remotely located extended object based upon the backscattered wave intensity distribution at the receiver. A 37-control-channel adaptive optics system with phase correction of the output wave capable of operating in the presence of speckle-field-induced strong intensity modulation is presented. System operation is based on optimization of the speckle-field-based metric by the stochastic parallel gradient descent technique. Results demonstrate that adaptive wave-front correction using speckle-field-based beam-quality metrics can significantly improve laser beam concentration on extended objects.

© 2002 Optical Society of America

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References

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  1. J. C. Dainty, ed., Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, Heidelberg, Germany, 1984).
  2. F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).
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  4. M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).
  5. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
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    [CrossRef] [PubMed]
  7. M. A. Vorontsov and V. P. Sivokon, J. Opt. Soc. Am. A 15, 2745 (1998).
    [CrossRef]
  8. M. A. Vorontsov, G. W. Carhart, M. Cohen, and G. Cauwenberghs, J. Opt. Soc. Am. A 17, 1440 (2000).
    [CrossRef]
  9. M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
    [CrossRef]
  10. V. I. Polejaev and M. A. Vorontsov, Proc. SPIE 3126, 216 (1997).
    [CrossRef]
  11. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and D. Voelz, J. Opt. Soc. Am. A 13, 1456 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
  13. R. A. Muller and A. Buffington, J. Opt. Soc. Am. 64, 1200 (1974).
  14. We consider here the rather typical scenario where speckle statistics (characteristic speckle size) does not significantly change due to propagation.

2000 (1)

1998 (1)

1997 (2)

1996 (1)

1995 (1)

1984 (1)

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
[CrossRef]

1977 (1)

1974 (1)

Bass, F. G.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Buffington, A.

Carhart, G. W.

Cauwenberghs, G.

Cohen, M.

Fuks, I. M.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Goodman, J. W.

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

Karnaukhov, V. N.

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
[CrossRef]

Kokorowski, S. A.

Kuz’minskii, A. L.

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
[CrossRef]

Muller, R. A.

Pearson, J. E.

Pedinoff, M. E.

Polejaev, V. I.

V. I. Polejaev and M. A. Vorontsov, Proc. SPIE 3126, 216 (1997).
[CrossRef]

Pruidze, D. V.

Ricklin, J. C.

Roggemann, M. C.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

Sarro, P.

Shmalhauzen, V. I.

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
[CrossRef]

Sivokon, V. P.

Vdovin, G.

Voelz, D.

Vorontsov, M. A.

Welsh, B. M.

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Proc. SPIE (1)

V. I. Polejaev and M. A. Vorontsov, Proc. SPIE 3126, 216 (1997).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz’minskii, and V. I. Shmalhauzen, Sov. J. Quantum Electron. 14, 761 (1984).
[CrossRef]

Other (5)

M. C. Roggemann and B. M. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

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

J. C. Dainty, ed., Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, Heidelberg, Germany, 1984).

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

We consider here the rather typical scenario where speckle statistics (characteristic speckle size) does not significantly change due to propagation.

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Figures (3)

Fig. 1
Fig. 1

Scheme of the target-in-the-loop adaptive system experimental setup. The photos at the bottom are a, objects used in the experiments [the distance between holes on the optical bench is 1 (2.54 cm)]; b, intensity distribution on the object surface with adaptive system feedback on; c, same as in b but for feedback off. The scales in b and c are the same. The diameter of the beam in photo c is 5 mm. BS, beam splitter.

Fig. 2
Fig. 2

a, b, Speckle-field intensity distributions registered by the optical receiver system camera and c, d, the corresponding edge maps. Speckle pattern a and edge map c correspond to the highly defocused beam on the object surface shown in Fig. 1c; speckle pattern b and edge map d correspond to the focused beam shown in Fig. 1b.

Fig. 3
Fig. 3

Averaged adaptation process evolution curves Js and J2 versus number of iterations n. The filled circles on the axes mark the iteration numbers corresponding to the introduction of random phase distortions. Vertical bars characterize the standard deviations σs=Js-Js21/2/Js and σ2=J2-J221/2/J2.

Equations (3)

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Jstn=Enrd2r, where Enr=2signInr-I¯n.
ujn+1=ujn+γnδJnsignδJnsignδujn m=0,,,
J2tn=Inor2d2r.

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