Abstract

We describe an adaptive wavefront control technique based on a parallel stochastic perturbation method that can be applied to a general class of adaptive-optical system. The efficiency of this approach is analyzed numerically and experimentally by use of a white-light adaptive-imaging system with an extended source. To create and compensate for static phase distortions, we use 127-element liquid-crystal phase modulators. Results demonstrate that adaptive wavefront correction by a parallel-perturbation technique can significantly improve image quality.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).
  2. A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemin, and R. G. Smits, J. Opt. Soc. Am. 67, 298 (1977).
    [CrossRef]
  3. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and D. G. Voelz, J. Opt. Soc. Am. A 13, 1456 (1996).
    [CrossRef]
  4. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and D. G. Voelz, Appl. Opt. 36, 3319 (1997).
    [CrossRef] [PubMed]
  5. T. R. O’Meara, J. Opt. Soc. Am. 67, 315 (1977).
    [CrossRef]
  6. A. Dembo and T. Kailath, IEEE Trans. Neural Networks 1, 58 (1990).
    [CrossRef]
  7. G. Cauwenberghs, J. Analog Integ. Circ. Signal Process. 1, 14 (1996).
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

1997

1996

1990

A. Dembo and T. Kailath, IEEE Trans. Neural Networks 1, 58 (1990).
[CrossRef]

1977

Buffington, A.

Carhart, G. W.

Cauwenberghs, G.

G. Cauwenberghs, J. Analog Integ. Circ. Signal Process. 1, 14 (1996).

Crawford, F. S.

Dembo, A.

A. Dembo and T. Kailath, IEEE Trans. Neural Networks 1, 58 (1990).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Kailath, T.

A. Dembo and T. Kailath, IEEE Trans. Neural Networks 1, 58 (1990).
[CrossRef]

Muller, R. A.

O’Meara, T. R.

Pruidze, D. V.

Ricklin, J. C.

Schwemin, A. J.

Smits, R. G.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

Voelz, D. G.

Vorontsov, M. A.

Appl. Opt.

IEEE Trans. Neural Networks

A. Dembo and T. Kailath, IEEE Trans. Neural Networks 1, 58 (1990).
[CrossRef]

J. Analog Integ. Circ. Signal Process.

G. Cauwenberghs, J. Analog Integ. Circ. Signal Process. 1, 14 (1996).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

General schematic for the adaptive-imaging system; the wavefront-corrector electrode geometry used in the experiment is at the bottom left.

Fig. 2
Fig. 2

Evolution curves Jph versus iterations n for three numbers of control channels N: a–d correspond to marked points on the evolution curve for N=256. The algorithm parameters are δu=0.004, γ=4.0×10-5, and α=1. An undistorted image corresponds to the point Jph=1.0. The dashed curve corresponds to conventional gradient-descent optimization.

Fig. 3
Fig. 3

Introduced (a, b) and residual (c, d) phase distortions in a gray-scale representation of amplitude 2π. Distorted (e) and corrected (f) images resulted from phase maps b and d, respectively. Image f corresponds to n=10, 000  iterations. Phase-screen parameters are a, σW=0.56π, and b, σW=0.56π.

Fig. 4
Fig. 4

Correction of a phase-distorted image with Eq.  (3): phase-distortion standard deviation σW=0.4π, α=1 (curve  1), and α=3 (curve  2). Curve  1, system with a single LC phase modulator, with a, undistorted, b, distorted, and c, corrected images. Corrected image c, obtained after n=750 iterations, corresponds to phase map d of amplitude 0.4π. Curve  2, system with two LC phase modulators.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ujn+1=ujn-γδJ/δuj,
J=Jph=FexpiαIr4d2q
ujn+1=1-βujn+βNnbl=1Nnbuln-γδJδuj-1Nl=1Nuln-u0,

Metrics