Abstract

Off-axis aberrations in a beam-scanning multiphoton confocal microscope are corrected with a deformable mirror. The optimal mirror shape for each pixel is determined by a genetic learning algorithm, in which the second-harmonic or two-photon fluorescence signal from a reference sample is maximized. The speed of the convergence is improved by use of a Zernike polynomial basis for the deformable mirror shape. This adaptive optical correction scheme is implemented in an all-reflective system by use of extremely short (10-fs) optical pulses, and it is shown that the scanning area of an f:1 off-axis parabola can be increased by nine times with this technique.

© 2000 Optical Society of America

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References

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  1. W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. F. Druon, G. Cheriaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, J. C. Chanteloup, and G. Vdovin, Opt. Lett. 23, 1043 (1998).
    [CrossRef]
  6. D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
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    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1997).
  9. B. M. Levine, A. Wirth, and C. Standley, “Flexible configuration of wavefront sensor and reconstructors for OA systems,” presented at the International Workshop on Adaptive Optics for Industry and Medicine, Durham, UK, July 12–16, 1999.

1998 (2)

1997 (1)

G. Vdovin, S. Middelhoek, and P. Sarro, Opt. Eng. 35, 1382 (1997).
[CrossRef]

1995 (1)

1993 (1)

T. Baeck and H.-P. Schwefel, Evol. Computation 1, 1 (1993).
[CrossRef]

1990 (1)

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Baeck, T.

T. Baeck and H.-P. Schwefel, Evol. Computation 1, 1 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1997).

Brakenhoff, G. J.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, J. Microsc. 191, 266 (1998).
[CrossRef]

Chanteloup, J. C.

Cheriaux, G.

Denk, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Druon, F.

Faure, J.

Goldberg, D.

D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Krausz, F.

Lenzner, M.

Levine, B. M.

B. M. Levine, A. Wirth, and C. Standley, “Flexible configuration of wavefront sensor and reconstructors for OA systems,” presented at the International Workshop on Adaptive Optics for Industry and Medicine, Durham, UK, July 12–16, 1999.

Maksimchuk, A.

Middelhoek, S.

G. Vdovin, S. Middelhoek, and P. Sarro, Opt. Eng. 35, 1382 (1997).
[CrossRef]

Muller, M.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, J. Microsc. 191, 266 (1998).
[CrossRef]

Nantel, M.

Nees, J.

Sarro, P.

G. Vdovin, S. Middelhoek, and P. Sarro, Opt. Eng. 35, 1382 (1997).
[CrossRef]

Schwefel, H.-P.

T. Baeck and H.-P. Schwefel, Evol. Computation 1, 1 (1993).
[CrossRef]

Spielmann, Ch.

Squier, J.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, J. Microsc. 191, 266 (1998).
[CrossRef]

Standley, C.

B. M. Levine, A. Wirth, and C. Standley, “Flexible configuration of wavefront sensor and reconstructors for OA systems,” presented at the International Workshop on Adaptive Optics for Industry and Medicine, Durham, UK, July 12–16, 1999.

Stingl, A.

Strickler, J.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Szipöcsand, R.

Vdovin, G.

Webb, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Wilson, K. R.

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, J. Microsc. 191, 266 (1998).
[CrossRef]

Wirth, A.

B. M. Levine, A. Wirth, and C. Standley, “Flexible configuration of wavefront sensor and reconstructors for OA systems,” presented at the International Workshop on Adaptive Optics for Industry and Medicine, Durham, UK, July 12–16, 1999.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1997).

Evol. Computation (1)

T. Baeck and H.-P. Schwefel, Evol. Computation 1, 1 (1993).
[CrossRef]

J. Microsc. (1)

M. Muller, J. Squier, K. R. Wilson, and G. J. Brakenhoff, J. Microsc. 191, 266 (1998).
[CrossRef]

Opt. Eng. (1)

G. Vdovin, S. Middelhoek, and P. Sarro, Opt. Eng. 35, 1382 (1997).
[CrossRef]

Opt. Lett. (2)

Science (1)

W. Denk, J. Strickler, and W. Webb, Science 248, 73 (1990).
[CrossRef] [PubMed]

Other (3)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1997).

B. M. Levine, A. Wirth, and C. Standley, “Flexible configuration of wavefront sensor and reconstructors for OA systems,” presented at the International Workshop on Adaptive Optics for Industry and Medicine, Durham, UK, July 12–16, 1999.

D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: PMT, photomultiplier-tube; osc., oscillator.

Fig. 2
Fig. 2

Genetic algorithm improvement of the average fitness function with generations for two different populations. The first population is composed of 100 individuals with deformable mirror actuator chromosomes. The second is composed of the same number of individuals with Zernike polynomial amplitude chromosomes.

Fig. 3
Fig. 3

Inverted images of the focus spot on axis, for a right scanning of 70 µm and a down scanning of 50 µm. The off-axis spots are displayed uncorrected and corrected. The uncorrected spots have been brightened to improved visibility in the figure. All the corrected spots and the centered one correspond to Airy patterns.

Fig. 4
Fig. 4

Strehl ratio measured for the horizontal scanning. The adaptive wave-front correction allows the scanning area to be extended. The asymmetry of the plot is due to the use of an off-axis 60° parabola.

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