Abstract

The performance of adaptive systems that consist of microscale on-chip elements [microelectromechanical mirror (µ-mirror) arrays and a VLSI stochastic gradient descent microelectronic control system] is analyzed. The µ-mirror arrays with 5 × 5 and 6 × 6 actuators were driven with a control system composed of two mixed-mode VLSI chips implementing model-free beam-quality metric optimization by the stochastic parallel perturbative gradient descent technique. The adaptation rate achieved was near 6000 iterations/s. A secondary (learning) feedback loop was used to control system parameters during the adaptation process, further increasing the adaptation rate.

© 2001 Optical Society of America

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  1. N. Maluf, An Introduction to Microelectromechanical Systems Engineering (Artech House, Norwood, Mass., 2000).
  2. M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
    [CrossRef]
  3. R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
    [CrossRef]
  4. T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).
  5. T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
  6. J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.
  7. M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright, M. C. Roggemann, “Aberration-correction results from a segmented microelectromechanical deformable mirror and refractive lenslet array,” Opt. Lett. 23, 645–647 (1998).
    [CrossRef]
  8. G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
    [CrossRef]
  9. J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
    [CrossRef]
  10. J. Mansell, R. L. Byer, “Micromachined silicon deformable mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 896–901 (1998).
    [CrossRef]
  11. J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1987), pp. 1161–1167.
  12. G. Cauwenberghs, “A fast stochastic error-descent algorithm for supervised learning and optimization,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufman, San Mateo, Calif., 1993), Vol. 5, pp. 244–251.
  13. 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).
    [CrossRef] [PubMed]
  14. M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wave-front phase distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).
    [CrossRef]
  15. R. T. Edwards, M. Cohen, G. Cauwenberghs, M. A. Vorontsov, G. W. Carhart, “Analog VLSI parallel stochastic optimization for adaptive optics,” in Learning on Silicon, G. Cauwenberghs, M. A. Bazoumi, eds. (Kluwer Academic, Boston, Mass., 1999), pp. 359–382.
  16. M. A. Vorontsov, G. W. Carhart, M. Cohen, G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
    [CrossRef]
  17. A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
    [CrossRef]
  18. 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. 36, 1326–1338 (1997).
    [CrossRef]
  19. L. Zhu, P.-C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
    [CrossRef]
  20. S. Grossberg, “Nonlinear neural networks: principles, mechanisms, and architectures,” Neural Networks 1, 17–61 (1988).
    [CrossRef]

2000

1999

L. Zhu, P.-C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainman, “Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
[CrossRef]

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

1998

1997

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).
[CrossRef] [PubMed]

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[CrossRef]

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[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. 36, 1326–1338 (1997).
[CrossRef]

1988

S. Grossberg, “Nonlinear neural networks: principles, mechanisms, and architectures,” Neural Networks 1, 17–61 (1988).
[CrossRef]

Anderson, R. B.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Bartsch, D.-U.

Bifano, T. G.

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Bright, V. M.

M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright, M. C. Roggemann, “Aberration-correction results from a segmented microelectromechanical deformable mirror and refractive lenslet array,” Opt. Lett. 23, 645–647 (1998).
[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. 36, 1326–1338 (1997).
[CrossRef]

A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
[CrossRef]

J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
[CrossRef]

Brown, D. M.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Byer, R. L.

J. Mansell, R. L. Byer, “Micromachined silicon deformable mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 896–901 (1998).
[CrossRef]

Carhart, G. W.

Castañon, D. A.

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Cauwenberghs, G.

M. A. Vorontsov, G. W. Carhart, M. Cohen, G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
[CrossRef]

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

R. T. Edwards, M. Cohen, G. Cauwenberghs, M. A. Vorontsov, G. W. Carhart, “Analog VLSI parallel stochastic optimization for adaptive optics,” in Learning on Silicon, G. Cauwenberghs, M. A. Bazoumi, eds. (Kluwer Academic, Boston, Mass., 1999), pp. 359–382.

Clark, R. L.

J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Cohen, M.

M. A. Vorontsov, G. W. Carhart, M. Cohen, G. Cauwenberghs, “Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration,” J. Opt. Soc. Am. A 17, 1440–1453 (2000).
[CrossRef]

R. T. Edwards, M. Cohen, G. Cauwenberghs, M. A. Vorontsov, G. W. Carhart, “Analog VLSI parallel stochastic optimization for adaptive optics,” in Learning on Silicon, G. Cauwenberghs, M. A. Bazoumi, eds. (Kluwer Academic, Boston, Mass., 1999), pp. 359–382.

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. 36, 1326–1338 (1997).
[CrossRef]

J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
[CrossRef]

Cowan, W. D.

M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright, M. C. Roggemann, “Aberration-correction results from a segmented microelectromechanical deformable mirror and refractive lenslet array,” Opt. Lett. 23, 645–647 (1998).
[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. 36, 1326–1338 (1997).
[CrossRef]

Dorton, J. K.

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Edwards, R. T.

R. T. Edwards, M. Cohen, G. Cauwenberghs, M. A. Vorontsov, G. W. Carhart, “Analog VLSI parallel stochastic optimization for adaptive optics,” in Learning on Silicon, G. Cauwenberghs, M. A. Bazoumi, eds. (Kluwer Academic, Boston, Mass., 1999), pp. 359–382.

Fainman, Y.

Freeman, W. R.

Grossberg, S.

S. Grossberg, “Nonlinear neural networks: principles, mechanisms, and architectures,” Neural Networks 1, 17–61 (1988).
[CrossRef]

Gustafson, S. C.

J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
[CrossRef]

Hammer, J. A.

J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

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. 36, 1326–1338 (1997).
[CrossRef]

Horenstein, M. N.

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Karpinisky, J. R.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Karpinsky, J.

J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.

Krishnamoorthy Mali, R.

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Lee, M. K.

Lee, Y. C.

A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
[CrossRef]

Lindsey, R.

J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.

Lindsey, R. L.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Maluf, N.

N. Maluf, An Introduction to Microelectromechanical Systems Engineering (Artech House, Norwood, Mass., 2000).

Mansell, J.

J. Mansell, R. L. Byer, “Micromachined silicon deformable mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 896–901 (1998).
[CrossRef]

Merritt, P. H.

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

Michalicek, M. A.

J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
[CrossRef]

Middelhoek, S.

G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Perrault, J.

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

Perreault, J.

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

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. 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. 36, 1326–1338 (1997).
[CrossRef]

Roggemann, M. C.

Sarro, P. M.

G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Sivokon, V. P.

Spall, J. C.

J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1987), pp. 1161–1167.

Sun, P.-C.

Tuantranont, A.

A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
[CrossRef]

Vandelli, N.

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

Vdovin, G.

G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Vorontsov, M. A.

Welsh, B. M.

M. K. Lee, W. D. Cowan, B. M. Welsh, V. M. Bright, M. C. Roggemann, “Aberration-correction results from a segmented microelectromechanical deformable mirror and refractive lenslet array,” Opt. Lett. 23, 645–647 (1998).
[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. 36, 1326–1338 (1997).
[CrossRef]

Wu, M. C.

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[CrossRef]

Zhang, W.

A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
[CrossRef]

Zhu, L.

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).

J. Opt. Soc. Am. A

Neural Networks

S. Grossberg, “Nonlinear neural networks: principles, mechanisms, and architectures,” Neural Networks 1, 17–61 (1988).
[CrossRef]

Opt. Eng.

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. 36, 1326–1338 (1997).
[CrossRef]

T. G. Bifano, R. Krishnamoorthy Mali, J. K. Dorton, J. Perreault, N. Vandelli, M. N. Horenstein, D. A. Castañon, “Continuous-membrane surface-micromachined silicon deformable mirror,” Opt. Eng.36, 1354–1360 (1997).

G. Vdovin, S. Middelhoek, P. M. Sarro, “Technology and applications of micromachined silicon adaptive mirrors,” Opt. Eng. 36, 1382–1390 (1997).
[CrossRef]

Opt. Lett.

Proc. IEEE

M. C. Wu, “Micromachining for optical and optoelectronic systems,” Proc. IEEE 85, 1833–1856 (1997).
[CrossRef]

Other

R. L. Clark, J. R. Karpinisky, J. A. Hammer, R. B. Anderson, R. L. Lindsey, D. M. Brown, P. H. Merritt, “Micro-opto-electro-mechanical (MOEM) adaptive optic system,” in Miniaturized Systems with Micro-Optics and Micromechanics II, M. E. Motamedi, L. J. Hornbeck, K. S. Pister, eds., Proc. SPIE3008, 12–24 (1997).
[CrossRef]

N. Maluf, An Introduction to Microelectromechanical Systems Engineering (Artech House, Norwood, Mass., 2000).

J. H. Comtois, V. M. Bright, S. C. Gustafson, M. A. Michalicek, “Implementation of hexagonal micromirror arrays as phase-mostly spatial light modulator,” in Microelectronic Structures and Microelectromechanical Devices for Optical Processing and Multimedia Applications, W. Bailey, M. E. Motamedi, F.-C. Luo, eds., Proc. SPIE2641, 76–87 (1995).
[CrossRef]

J. Mansell, R. L. Byer, “Micromachined silicon deformable mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 896–901 (1998).
[CrossRef]

J. C. Spall, “A stochastic approximation technique for generating maximum likelihood parameter estimates,” in Proceedings of the American Control Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1987), pp. 1161–1167.

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

R. T. Edwards, M. Cohen, G. Cauwenberghs, M. A. Vorontsov, G. W. Carhart, “Analog VLSI parallel stochastic optimization for adaptive optics,” in Learning on Silicon, G. Cauwenberghs, M. A. Bazoumi, eds. (Kluwer Academic, Boston, Mass., 1999), pp. 359–382.

A. Tuantranont, V. M. Bright, W. Zhang, Y. C. Lee, “Flip chip integration of lenslet arrays on segmented deformable micromirrors,” in Design, Test, and Microfabrication of MEMS and MOEMS, B. Courtois, S. B. Crary, W. Ehrfeld, H. Fujita, J.-M. Karam, K. W. Markus, eds., Proc. SPIE3680, 668–678 (1999).
[CrossRef]

J. A. Hammer, J. Karpinsky, R. L. Clark, R. Lindsey, “Micro mirrors in adaptive optics systems,” in Proceedings of the World Automation Congress (WAC ’98), M. Jamshidi, C. W. de Silva, eds., Vol. 6 of TSI Press Series (TSI, Albuquerque, N.M., 1998), pp. 575–581.

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Figures (14)

Fig. 1
Fig. 1

Microphotographs of micromachined mirror arrays used in the experiments: (a) BUtt segmented membrane tip-tilt mirror with 4 × 4 elements (5 × 5 actuators),5 (b) MO z piston-type mirror array with zig-zag spring, (c) MO s piston-type mirror array with spiral spring,6 (d) BU12 12 × 12 actuator tip-tilt mirror array, (e) UC piston-type 12 × 12 mirror array,7,17 (f) OKO continuous-membrane mirror.8 MO and UC mirrors are shown without lenslet arrays. Photographs of magnified mirror elements are shown at the bottom right in (a)–(e). Mirror array structural elements are marked by capital letters: M, mirror elements; S, spring (flexure); and P, actuator post. Both BUtt and BU12 are made without a metallic reflecting coating and thus the polysilicon membrane surface is partially transparent.

Fig. 2
Fig. 2

(a), (c), (e) Mirror surface interference patterns and (b), (d), (f) corresponding far-field intensity distributions with no applied voltages for (a), (b) the BUtt mirror, (c), (d) the BU12 mirror, and (e), (f) the MO s mirror with a diffractive lenslet array (e, f).

Fig. 3
Fig. 3

Schematic of the experimental setup for Strehl ratio measurements.

Fig. 4
Fig. 4

Dependence of Strehl ratio on voltage applied to a single actuator for (a) the MO s and (b) the BUtt mirrors. Strehl ratio sensitivity curves 1, 2, and 3 correspond to three actuator locations within the mirror array, as shown at the bottom left (M is a mirror element; P is an actuator post).

Fig. 5
Fig. 5

Strehl ratio resonance curves for the micromachined mirrors examined. Resonance curves for OKO, UC, MO s , and MO z mirrors are shown in linear scales and the BU mirror on a logarithmic frequency scale.

Fig. 6
Fig. 6

Schematic of the microscale adaptive-optics system based on the AdOpt VLSI controller and micromachined mirrors used in the experiments.

Fig. 7
Fig. 7

Photograph of the key elements (VLSI controller board, µ mirror, and photodetector) of the microscale adaptive-optics system based on stochastic parallel gradient descent optimization. The VLSI controller board comprises 7 AdOpt chips and can provide control of as many as 133 channels. The U.S. quarter coin at the bottom right is used to indicate the scale.

Fig. 8
Fig. 8

Simplified timing diagrams for a single iteration cycle of the AdOpt system: sequence of external clock signals supplied to the AdOpt chips (top), clock signals used for beam-quality metric measurements (middle), corresponding sequence of changes in beam-quality metric J (bottom).

Fig. 9
Fig. 9

Experimental results of self-induced phase-distortion compensation in an adaptive system with the BUtt mirror: adaptation evolution curves for optimization of the beam-quality metric (a) for a single trial and (b) after averaging over 500 trials. Photographs correspond to focal-plane intensity distributions at the end of minimization (left) and maximization (right). The transition process (∼60 iteration long) is shown in (b) as an inset.

Fig. 10
Fig. 10

Beam-quality metric evolution curves averaged over 500 maximization trials 〈J(t)〉 for the following µ-mirror arrays: BUtt, MO s , and MO z . Photographs show typical snapshots of focal-plane intensity distributions for the MO s mirror at (left) t = 0 and (right) t = 200 ms.

Fig. 11
Fig. 11

Adaptation evolution curves for beam-quality metric (a) minimization and (b) maximization for a tip-tilt mirror array (BUtt) adaptive system. Curves correspond to four adaptation trials.

Fig. 12
Fig. 12

Probability-density distributions of beam-quality metrics p max and p min obtained during 500 adaptation trials: (a) adaptive system with the MO s and BUtt µ mirrors and fixed update coefficient γ = 60 and (b) probability distribution p max for the adaptive system with the BUtt µ mirror for three values of the update coefficient γ. Beam-quality metric J is normalized by its maximum value J max.

Fig. 13
Fig. 13

Convergence rate n c max of the adaptation process relative to update coefficient γ for maximization of the beam-quality metric in an adaptive system with the BUtt mirror. The metric fluctuation level is characterized by the normalized standard-deviation values σ̅ J shown in parentheses. The diamond represents results obtained in the system with a change in the adaptive update coefficient. The fluctuation level in the system without adaptation was near 0.01.

Fig. 14
Fig. 14

Adaptive system with a change in the adaptive update parameter through learning rule (4): (a) beam-quality metric evolution curve averaged over 1000 trials and (b) corresponding evolution curve for update coefficient γ. The value γ0 = 180 was used in the experiments, with fixed γ.

Tables (1)

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Table 1 Parameters of the µ-Mirror Chips Used in the Experiments

Equations (5)

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ujn+1=ujn+γ|δJn|signδJnsignδujn,
H1n=|signΔJ+n-signΔJ-n|, H2n=|δJn|, H3n=l=1L |Jn-Jn-l|.
H¯in=1M1m=0M1 Hin-m,  i=1, 2, 3.
τ dγdt=γ0-γ+ε0H¯t,
γn+1=γn+αγ0-γn+εH¯1nH¯2nH¯3n,

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