Abstract

A new optimization technique, stochastic parallel-gradient descent, is applied for high-resolution adaptive wave-front correction. A performance criterion for parallel-perturbation-based algorithms is introduced and applied to optimize adaptive system architecture. We present numerical simulation results for an adaptive imaging system based on the stochastic parallel-perturbation technique, along with experimental results obtained for a white-light adaptive imaging system with 37 control channels. An adaptive system with a self-organized (adaptive) control channel hierarchy is introduced and analyzed.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
    [CrossRef]
  2. P. R. Barbier, G. Moddel, “Spatial light modulators: processing light in real time,” Opt. Photonics News 8, 16–21 (March1997).
    [CrossRef]
  3. U. Efron, ed., Spatial Light Modulator Technology: Materials, Devices, and Applications (Marcel Dekker, New York, 1995).
  4. M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
    [CrossRef]
  5. J. M. Younse, “Mirrors on a Chip,” IEEE Spectr. 30, 27–31 (November1993).
    [CrossRef]
  6. G. V. Vdovin, P. M. Sarro, “Flexible mirror micromachined in silicon,” Appl. Opt. 34, 2968–2972 (1995).
    [CrossRef] [PubMed]
  7. A. Dembo, T. Kailath, “Model-free distributed learning,” IEEE Trans. Neural Netw. 1, 58–70 (1990).
    [CrossRef] [PubMed]
  8. G. Cauwenberghs, “Analog VLSI stochastic perturbative learning architectures,” Int. J. Analog Integr. Circ. Signal Process. 13, 195–209 (1997).
    [CrossRef]
  9. G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 244–251.
  10. J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.
  11. D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.
  12. M. A. Vorontsov, G. W. Carhart, J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997); G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).
    [CrossRef] [PubMed]
  13. V. I. Polejaev, M. A. Vorontsov, “Adaptive active imaging system based on radiation focusing for extended targets,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 216–220 (1997).
    [CrossRef]
  14. Special issues on Atmospheric-Compensation Technology, J. Opt. Soc. Am. A 11(1) and (2), 255–451, 779–945 (1994).
  15. M. C. Roggemann, B. M. Welsh, Imaging Through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  16. J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993).
    [CrossRef]
  17. R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberration using phase diversity,” J. Opt. Soc. Am. A 9, 1072–1085 (1992).
    [CrossRef]
  18. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
  19. T. G. Alley, M. A. Kramer, D. R. Martinez, L. P. Schelonka, “Single-pass imaging through a thick dynamic distorter using four-wave mixing,” Opt. Lett. 15, 81–83 (1990).
    [CrossRef] [PubMed]
  20. V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
    [CrossRef]
  21. D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.
  22. M. Avriel, Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, N.J., 1976).
  23. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Adaptive imaging system for phase-distorted extended source/multiple distance objects,” Appl. Opt. 36, 3319–3328 (1997).
    [CrossRef] [PubMed]
  24. T. R. O’Meara, “The multidither principle in adaptive optics,” J. Opt. Soc. Am. 67, 315–325 (1977).
  25. R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991).
  26. H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1987).
  27. D. Lawrence, Genetic Algorithm and Stimulated Annealing (Morgan Kaufman, Los Altos, Calif., 1987).
  28. P. J. M. van Luarhoven, E. H. L. Aarts, Stimulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).
  29. U. Mahlab, J. Shamir, “Iterative optimization algorithms for filter generation in optical correlators: a comparison,” Appl. Opt. 31, 1117–1125 (1992).
    [CrossRef] [PubMed]
  30. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  31. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  32. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  33. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  34. D. P. Greenwood, D. L. Fried, “Power spectra requirements for wave-front-compensative systems,” J. Opt. Soc. Am. 66, 193–206 (1976).
    [CrossRef]
  35. M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Image quality criteria for an adaptive imaging system based on statistical analysis of the speckle field,” J. Opt. Soc. Am. A 13, 1456–1466 (1996).
    [CrossRef]
  36. R. Dou, D. V. Pruidze, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Coherent optical processor for image-quality metric measurement,” in Propagation and Imaging through the Atmosphere, L. Bissonnette, C. Dainty, eds., Proc. SPIE3125, 339–343 (1997).
    [CrossRef]
  37. M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase distorted imaging systems: nonlinear and adaptive approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
    [CrossRef]
  38. L. I. Goldfischer, “Autocorrelation function and power spectral density of laser-produced speckle patterns,” J. Opt. Soc. Am. 55, 247–252 (1965).
    [CrossRef]

1998 (1)

1997 (5)

M. A. Vorontsov, G. W. Carhart, J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997); G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).
[CrossRef] [PubMed]

P. R. Barbier, G. Moddel, “Spatial light modulators: processing light in real time,” Opt. Photonics News 8, 16–21 (March1997).
[CrossRef]

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

G. Cauwenberghs, “Analog VLSI stochastic perturbative learning architectures,” Int. J. Analog Integr. Circ. Signal Process. 13, 195–209 (1997).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Adaptive imaging system for phase-distorted extended source/multiple distance objects,” Appl. Opt. 36, 3319–3328 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (3)

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
[CrossRef]

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase distorted imaging systems: nonlinear and adaptive approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

G. V. Vdovin, P. M. Sarro, “Flexible mirror micromachined in silicon,” Appl. Opt. 34, 2968–2972 (1995).
[CrossRef] [PubMed]

1994 (1)

Special issues on Atmospheric-Compensation Technology, J. Opt. Soc. Am. A 11(1) and (2), 255–451, 779–945 (1994).

1993 (2)

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993).
[CrossRef]

J. M. Younse, “Mirrors on a Chip,” IEEE Spectr. 30, 27–31 (November1993).
[CrossRef]

1992 (2)

1990 (2)

1977 (1)

1976 (2)

1965 (2)

Aarts, E. H. L.

P. J. M. van Luarhoven, E. H. L. Aarts, Stimulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

Alley, T. G.

Alspector, J.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.

Avriel, M.

M. Avriel, Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, N.J., 1976).

Barbier, P. R.

P. R. Barbier, G. Moddel, “Spatial light modulators: processing light in real time,” Opt. Photonics News 8, 16–21 (March1997).
[CrossRef]

Barr, A. H.

D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.

Beckers, J. M.

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993).
[CrossRef]

Bright, V. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Carhart, G. W.

Cauwenberghs, G.

G. Cauwenberghs, “Analog VLSI stochastic perturbative learning architectures,” Int. J. Analog Integr. Circ. Signal Process. 13, 195–209 (1997).
[CrossRef]

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 244–251.

Clark, D. S.

H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1987).

Comtois, J. H.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Cowan, W. D.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Dembo, A.

A. Dembo, T. Kailath, “Model-free distributed learning,” IEEE Trans. Neural Netw. 1, 58–70 (1990).
[CrossRef] [PubMed]

Dou, R.

R. Dou, D. V. Pruidze, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Coherent optical processor for image-quality metric measurement,” in Propagation and Imaging through the Atmosphere, L. Bissonnette, C. Dainty, eds., Proc. SPIE3125, 339–343 (1997).
[CrossRef]

Fender, J. S.

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
[CrossRef]

Fienup, J. R.

Fleischer, K.

D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.

Fried, D. L.

Gaeta, C. J.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Goldfischer, L. I.

Goodman, J. W.

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

Greenwood, D. P.

Hick, S. R.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Jayakumar, A.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.

Kailath, T.

A. Dembo, T. Kailath, “Model-free distributed learning,” IEEE Trans. Neural Netw. 1, 58–70 (1990).
[CrossRef] [PubMed]

Kerns, D.

D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.

Kirk, D. B.

D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.

Kramer, M. A.

Kushner, H. J.

H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1987).

Lawrence, D.

D. Lawrence, Genetic Algorithm and Stimulated Annealing (Morgan Kaufman, Los Altos, Calif., 1987).

Love, G. B.

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
[CrossRef]

Mahlab, U.

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

Martinez, D. R.

Meir, R.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.

Mitchell, P. V.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Moddel, G.

P. R. Barbier, G. Moddel, “Spatial light modulators: processing light in real time,” Opt. Photonics News 8, 16–21 (March1997).
[CrossRef]

Noll, R. J.

O’Meara, T. R.

Paxman, R. G.

Pepper, D. M.

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Polejaev, V. I.

V. I. Polejaev, M. A. Vorontsov, “Adaptive active imaging system based on radiation focusing for extended targets,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 216–220 (1997).
[CrossRef]

Pruidze, D. V.

Restaino, S. R.

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
[CrossRef]

Ricklin, J. C.

Roberts, P. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Roggeman, M. C.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

Roggemann, M. C.

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

Sarro, P. M.

Schelonka, L. P.

Schulz, T. J.

Shamir, J.

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Sivokon, V. P.

V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
[CrossRef]

R. Dou, D. V. Pruidze, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Coherent optical processor for image-quality metric measurement,” in Propagation and Imaging through the Atmosphere, L. Bissonnette, C. Dainty, eds., Proc. SPIE3125, 339–343 (1997).
[CrossRef]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991).

van Luarhoven, P. J. M.

P. J. M. van Luarhoven, E. H. L. Aarts, Stimulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

Vdovin, G. V.

Voelz, D. G.

Vorontsov, M. A.

V. P. Sivokon, M. A. Vorontsov, “High-resolution adaptive phase distortion suppression based solely on intensity information,” J. Opt. Soc. Am. A 15, 234–247 (1998).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Adaptive imaging system for phase-distorted extended source/multiple distance objects,” Appl. Opt. 36, 3319–3328 (1997).
[CrossRef] [PubMed]

M. A. Vorontsov, G. W. Carhart, J. C. Ricklin, “Adaptive phase-distortion correction based on parallel gradient-descent optimization,” Opt. Lett. 22, 907–909 (1997); G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).
[CrossRef] [PubMed]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, D. G. Voelz, “Image quality criteria for an adaptive imaging system based on statistical analysis of the speckle field,” J. Opt. Soc. Am. A 13, 1456–1466 (1996).
[CrossRef]

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase distorted imaging systems: nonlinear and adaptive approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

V. I. Polejaev, M. A. Vorontsov, “Adaptive active imaging system based on radiation focusing for extended targets,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 216–220 (1997).
[CrossRef]

R. Dou, D. V. Pruidze, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Coherent optical processor for image-quality metric measurement,” in Propagation and Imaging through the Atmosphere, L. Bissonnette, C. Dainty, eds., Proc. SPIE3125, 339–343 (1997).
[CrossRef]

Welsh, B. M.

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

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

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

Younse, J. M.

J. M. Younse, “Mirrors on a Chip,” IEEE Spectr. 30, 27–31 (November1993).
[CrossRef]

Yuhas, B.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Annu. Rev. Astron. Astrophys. (1)

J. M. Beckers, “Adaptive optics for astronomy: principles, performance, and applications,” Annu. Rev. Astron. Astrophys. 31, 13–62 (1993).
[CrossRef]

Appl. Opt. (3)

IEEE Spectr. (1)

J. M. Younse, “Mirrors on a Chip,” IEEE Spectr. 30, 27–31 (November1993).
[CrossRef]

IEEE Trans. Neural Netw. (1)

A. Dembo, T. Kailath, “Model-free distributed learning,” IEEE Trans. Neural Netw. 1, 58–70 (1990).
[CrossRef] [PubMed]

Int. J. Analog Integr. Circ. Signal Process. (1)

G. Cauwenberghs, “Analog VLSI stochastic perturbative learning architectures,” Int. J. Analog Integr. Circ. Signal Process. 13, 195–209 (1997).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (4)

Opt. Eng. (Bellingham) (2)

M. C. Roggeman, V. M. Bright, B. M. Welsh, S. R. Hick, P. C. Roberts, W. D. Cowan, J. H. Comtois, “Use of micro-electro-mechanical deformable mirrors to control aberrations in optical systems: theoretical and experimental results,” Opt. Eng. (Bellingham) 36, 1326–1338 (1997).
[CrossRef]

M. A. Vorontsov, J. C. Ricklin, G. W. Carhart, “Optical simulation of phase distorted imaging systems: nonlinear and adaptive approach,” Opt. Eng. (Bellingham) 34, 3229–3238 (1995).
[CrossRef]

Opt. Lett. (2)

Opt. Photonics News (2)

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photonics News 6, 16–21 (October1995).
[CrossRef]

P. R. Barbier, G. Moddel, “Spatial light modulators: processing light in real time,” Opt. Photonics News 8, 16–21 (March1997).
[CrossRef]

Other (16)

U. Efron, ed., Spatial Light Modulator Technology: Materials, Devices, and Applications (Marcel Dekker, New York, 1995).

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

G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 244–251.

J. Alspector, R. Meir, B. Yuhas, A. Jayakumar, “A parallel gradient descent method for learning in analog VLSI neural networks,” in Advances in Neural Information Processing Systems, J. D. Cowan, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 836–844.

D. B. Kirk, D. Kerns, K. Fleischer, A. H. Barr, “Analog VLSI implementation of multidimensional gradient descent,” in Advances in Neural Information Processing Systems, C. L. Giles, ed. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 789–796.

V. I. Polejaev, M. A. Vorontsov, “Adaptive active imaging system based on radiation focusing for extended targets,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 216–220 (1997).
[CrossRef]

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

D. M. Pepper, C. J. Gaeta, P. V. Mitchell, “Real-time holography, innovative adaptive optics, and compensated optical processors using spatial light modulators,” in Spatial Light Modulator Technology: Materials, Devices, and Applications, U. Efron, ed. (Marcel Dekker, New York, 1995), pp. 585–654.

M. Avriel, Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, N.J., 1976).

R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, 1991).

H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1987).

D. Lawrence, Genetic Algorithm and Stimulated Annealing (Morgan Kaufman, Los Altos, Calif., 1987).

P. J. M. van Luarhoven, E. H. L. Aarts, Stimulated Annealing: Theory and Applications (Reidel, Dordrecht, The Netherlands, 1987).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).

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

R. Dou, D. V. Pruidze, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Coherent optical processor for image-quality metric measurement,” in Propagation and Imaging through the Atmosphere, L. Bissonnette, C. Dainty, eds., Proc. SPIE3125, 339–343 (1997).
[CrossRef]

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 (11)

Fig. 1
Fig. 1

(a) Coefficients θN,M and νN,M and (b) the ratio χM versus number of compensated aberrations M for different values N of the number of control channels.

Fig. 2
Fig. 2

General schematic for an adaptive imaging system based on image-quality-metric optimization with use of the parallel-perturbation technique.

Fig. 3
Fig. 3

Evolution curves (J versus iteration number m) for algorithms (I)–(III): (a) phase-distortion realization (σφ=1.8 rad, St=0.11), (b) distorted image, (c)–(e) random perturbation realizations corresponding to algorithms (I)–(III).

Fig. 4
Fig. 4

Images obtained after (a)–(c) 200 and (d)–(f) 2000 iterations for algorithms (I)–(III): (a), (d) conventional stochastic parallel-gradient-descent algorithm (I); (b), (e) algorithm with modal control (II); (c), (f) algorithm with global coupling (III).

Fig. 5
Fig. 5

Experimental setup for an adaptive imaging system based on parallel-gradient-descent optimization.

Fig. 6
Fig. 6

Evolution curve of the adaptation process for a white-light adaptive imaging system. Points n0, n1, and n2 indicate the moment at which phase distortions were introduced: (a) distorted image (σφ2.2π rad) for n=n1, (b) corrected image.

Fig. 7
Fig. 7

Optical scheme for generation of wave-front perturbation.

Fig. 8
Fig. 8

Schematic for high-resolution adaptive imaging system with self-organized perturbation statistics: (a) phase-distortion realization for D/r0=20 (σφ3.5 rad, St=0.002), (b) distorted image.

Fig. 9
Fig. 9

Evolution curves of the adaptation process for image-quality-metric average values 〈J〉: (I) conventional stochastic parallel-gradient descent, algorithm (II) algorithm with global coupling, (III) algorithm with perturbations having Kolmogorov statistics (D/r0=20), (IV) algorithm with self-organized speckle-based perturbations. (a) Average distorted image.

Fig. 10
Fig. 10

Average images obtained after 500 (left row) and 2000 iterations (right row) for algorithms (I)–(IV).

Fig. 11
Fig. 11

Evolution of perturbation characteristic size ds during the adaptation process for different coefficients αs. Gray-scale images of the perturbation realizations corresponding to αs=2π for (a) m=0, (b) m=500, and (c) m=1500.

Tables (1)

Tables Icon

Table 1 Coefficients βj2 and θN for Kolmogorov Turbulence Model

Equations (47)

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

δJ=j=1N Jujδuj+12j,lN 2Jujuiδujδui+.
δJδul=Jul(δul)2+ψl,
ψl=jlN Jujδujδul+12j,iN 2Jujuiδujδuiδul+.
δJδul=Jul(δul)2+ψl,
ψl=jlN Jujδujδul+12j,iN 2Jujuiδujδuiδul+.
ul(m+1)=ul(m)-μδJ(m)δul(m),l=0, 1,, N.
ΔJi=1N Jui(-μδJδui)=-μi=1N JuiJui(δui)2+ψi-μi=1NJuiδui2-μi,jiN JuiJujδuiδuj.
ΔJ=-μσ2i=1NJui2+O(μσ4).
u(r)=j=1NujSj(r)
J=1sϕ2(r)d2r,
1sδu2(r)d2rP2
δJ=1sδu2(r)d2r+2δu(r)ϕ(r)d2r
δJδJmax=P2+2smaxδ(r)δu(r)ϕ(r)d2r.
δu(r)=αϕ(r),
δu(r)ϕ(r)=αϕ2(r),
δJ=δJmax2P(J)1/2.
1sSj(r)Si(r)d2r=δji,δu(r)=j=1NδujSj(r).
ηNη=1sδu(r)ϕ(r)d2r=j=1Nbjδuj,
ϕ(r)=j=1bjSj(r),bj=1sϕ(r)Sj(r)d2r.
ηN=αj=1Nbj2.
α0=Pj=1Nbj2-1/2.
ηN=Pj=1Nbj21/2,
δJ2α0j=1Nbj2=2Pj=1Nbj21/2.
G(q)=(0.023/r05/3)q-11/3,
δJδJZ2Pj=2NδJj1/2=2PθN(D/r0)5/6,
δJ2j=M+1Nbjδuj=2α0j=M+1Nbj2=2α0j=M+1Nβj2(D/r0)5/3.
δJδJM2Pj=M+1Nβj2j=2Nβj2-1/2(D/r0)5/6=2PνN,M(D/r0)5/6,
δuj=0,δujδui=αM2bj2δji,
whereαM=Pj=M+1Nbj2-1/2.
δJδJ02Pj=M+1Nβj21/2(D/r0)5/6
=2PθN,M(D/r0)5/6.
δJδJP2P0.141N-5/12(D/r0)5/6.
u(r)=j=1NvjSj(r)+k=2MakWk(r),
u(r)=j=1NvjSj(r)+k=2MakZˆk(r).
Zˆk(r)=j=1Nck,jSj(r),
ck,j=1a2Zk(r)Sj(r)d2r,
k=2,, M.
u(r)=j=1NujSj(r),uj=vj+k=2Mckjak,
vj(m+1)=vj(m)-μδJδvj, j=1,, N,
ak(m+1)=ak(m)-μδJδak,k=2,, M.
δvjδal=0,δvjδvl=σ2δjl,
δajδai=α02aj2δji,
δujδul=σ2δjl+k=2Mckjcklak2=σ2δjl+α02k=2Mckjcklβk2(D/r0)5/3.
δJδujJujσ2+κk=2M(ckj2βk2)+κljN Julk=2M(ckjcklβk2),
J=|F{exp[iγI(r)]}|4d2q.
u(m+1)(r)=u(m)(r)-μδJ(m)δu(m)(r),
m=0, 1,,

Metrics