G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).

[CrossRef]

M. C. Roggemann, V. M. Bright, S. R. Hick, W. D. Cowan, “Use of micro-electromechanical deformable mirrors to control aberrations in optical system,” Opt. Eng. 36, 1326–1338 (1997).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

G. W. Carhart, M. A. Vorontsov, “Synthetic imaging: non-adaptive anisoplanatic image correction in atmospheric turbulence,” Opt. Lett. 23, 745–747 (1998).

[CrossRef]

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. 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, 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]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent in algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).

[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. Bayoumi, eds. (Kluwer Academic, Boston, 1999), Chap. 1, pp. 359–382.

G. W. Carhart, M. A. Vorontsov, R. T. Edwards, M. Cohen, G. Cauwenberghs, “Adaptive wavefront control using a VLSI implementation of the parallel perturbation gradient descent algorithm,” in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. Gonglewski, M. Vorontsov, eds., Proc. SPIE3760, 61–66 (1999).

[CrossRef]

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

[CrossRef]

G. Cauwenberghs, “Analog VLSI recurrent neural network learning a continuous-time trajectory,” IEEE Trans. Neural Netw. 41, 827–829 (1994).

G. Cauwenberghs, “A learning analog neural network chip with continuous-recurrent dynamics,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds., (Morgan Kaufmann, San Mateo, Calif.1994), Vol. 6, pp. 858–865.

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. Bayoumi, eds. (Kluwer Academic, Boston, 1999), Chap. 1, pp. 359–382.

G. W. Carhart, M. A. Vorontsov, R. T. Edwards, M. Cohen, G. Cauwenberghs, “Adaptive wavefront control using a VLSI implementation of the parallel perturbation gradient descent algorithm,” in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. Gonglewski, M. Vorontsov, eds., Proc. SPIE3760, 61–66 (1999).

[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 Kaufmann, San Mateo, Calif, 1993), Vol. 5, pp. 244–251.

H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1978).

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. Bayoumi, eds. (Kluwer Academic, Boston, 1999), Chap. 1, pp. 359–382.

G. W. Carhart, M. A. Vorontsov, R. T. Edwards, M. Cohen, G. Cauwenberghs, “Adaptive wavefront control using a VLSI implementation of the parallel perturbation gradient descent algorithm,” in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. Gonglewski, M. Vorontsov, eds., Proc. SPIE3760, 61–66 (1999).

[CrossRef]

M. C. Roggemann, V. M. Bright, S. R. Hick, W. D. Cowan, “Use of micro-electromechanical deformable mirrors to control aberrations in optical system,” Opt. Eng. 36, 1326–1338 (1997).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

G. W. Carhart, M. A. Vorontsov, R. T. Edwards, M. Cohen, G. Cauwenberghs, “Adaptive wavefront control using a VLSI implementation of the parallel perturbation gradient descent algorithm,” in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. Gonglewski, M. Vorontsov, eds., Proc. SPIE3760, 61–66 (1999).

[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. Bayoumi, eds. (Kluwer Academic, Boston, 1999), Chap. 1, pp. 359–382.

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News (October1995), pp. 16–21.

B. Flower, M. Jabri, “Summed weight neuron perturbation: an O(n)improvement over weight perturbation,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufmann, San Meteo, Calif., 1993), Vol. 5, pp. 212–219.

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 5(6), 14–19 (1994).

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).

[CrossRef]

M. C. Roggemann, V. M. Bright, S. R. Hick, W. D. Cowan, “Use of micro-electromechanical deformable mirrors to control aberrations in optical system,” Opt. Eng. 36, 1326–1338 (1997).

[CrossRef]

B. Flower, M. Jabri, “Summed weight neuron perturbation: an O(n)improvement over weight perturbation,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufmann, San Meteo, Calif., 1993), Vol. 5, pp. 212–219.

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

H. J. Kushner, D. S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems (Springer-Verlag, New York, 1978).

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News (October1995), pp. 16–21.

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

[CrossRef]

J. E. Pearson, S. Hansen, “Experimental studies of a deformable-mirror adaptive optical system,” J. Opt. Soc. Am. 67, 325–333 (1977).

[CrossRef]

S. A. Kokorowski, M. E. Pedinoff, J. E. Pearson, “Analytical, experimental and computer simulation results on the interactive effects of speckle with multi-dither adaptive optics systems,” J. Opt. Soc. Am. 67, 333–345 (1977).

[CrossRef]

In the nonlinear-optics-based or dynamical-holography-based phase conjugation systems, we have true wave-front conjugation (both phase conjugation and amplitude correction); see, for example, B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[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]

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, 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]

G. B. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News (October1995), pp. 16–21.

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. 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, 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]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent in algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).

[CrossRef]

M. C. Roggemann, V. M. Bright, S. R. Hick, W. D. Cowan, “Use of micro-electromechanical deformable mirrors to control aberrations in optical system,” Opt. Eng. 36, 1326–1338 (1997).

[CrossRef]

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

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

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

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983).

[CrossRef]

In the nonlinear-optics-based or dynamical-holography-based phase conjugation systems, we have true wave-front conjugation (both phase conjugation and amplitude correction); see, for example, B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).

M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wavefront phase distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).

[CrossRef]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent in algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).

[CrossRef]

J. C. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,” IEEE Trans. Autom. Control 37, 332–341 (1992).

[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, New York, 1987), pp. 1161–1167.

J. C. Spall, “Adaptive stochastic approximation by the simultaneous perturbation method,” IEEE Trans. Autom. Control45 (to be published); in condensed form in Proceedings of the IEEE Conference on Decision and Control (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 3872–3879.

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

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

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, “High-resolution adaptive phase distortion compensation using a diffractive-feedback system: experimental results,” J. Opt. Soc. Am. A 16, 2567–2573 (1999).

[CrossRef]

M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wavefront phase distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).

[CrossRef]

G. W. Carhart, M. A. Vorontsov, “Synthetic imaging: non-adaptive anisoplanatic image correction in atmospheric turbulence,” Opt. Lett. 23, 745–747 (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).

[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]

G. W. Carhart, J. C. Ricklin, V. P. Sivokon, M. A. Vorontsov, “Parallel perturbation gradient descent in algorithm for adaptive wavefront correction,” in Adaptive Optics and Applications, R. Tyson, R. Fugate, eds., Proc. SPIE3126, 221–227 (1997).

[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. Bayoumi, eds. (Kluwer Academic, Boston, 1999), Chap. 1, pp. 359–382.

G. W. Carhart, M. A. Vorontsov, R. T. Edwards, M. Cohen, G. Cauwenberghs, “Adaptive wavefront control using a VLSI implementation of the parallel perturbation gradient descent algorithm,” in High-Resolution Wavefront Control: Methods, Devices, and Applications, J. Gonglewski, M. Vorontsov, eds., Proc. SPIE3760, 61–66 (1999).

[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]

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

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

In the nonlinear-optics-based or dynamical-holography-based phase conjugation systems, we have true wave-front conjugation (both phase conjugation and amplitude correction); see, for example, B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).

G. Andreou, K. A. Boahen, “Translinear circuits in subthreshold MOS,” Analog Integr. Circuits Signal Process. 9, 141–166 (1996).

[CrossRef]

L. Zhu, P. Sun, D. 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]

C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).

[CrossRef]
[PubMed]

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]

J. C. Spall, “Multivariate stochastic approximation using a simultaneous perturbation gradient approximation,” IEEE Trans. Autom. Control 37, 332–341 (1992).

[CrossRef]

Special issue on partial differential equations and geometry-driven diffusion in image processing and analysis, IEEE Trans. Image Process. 7 (1998).

G. Cauwenberghs, “Analog VLSI recurrent neural network learning a continuous-time trajectory,” IEEE Trans. Neural Netw. 41, 827–829 (1994).

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

[CrossRef]

T. R. O’Meara, “The multi-dither principle in adaptive optics,” J. Opt. Soc. Am. 67, 306–315 (1977).

[CrossRef]

J. E. Pearson, S. Hansen, “Experimental studies of a deformable-mirror adaptive optical system,” J. Opt. Soc. Am. 67, 325–333 (1977).

[CrossRef]

S. A. Kokorowski, M. E. Pedinoff, J. E. Pearson, “Analytical, experimental and computer simulation results on the interactive effects of speckle with multi-dither adaptive optics systems,” J. Opt. Soc. Am. 67, 333–345 (1977).

[CrossRef]

R. A. Muller, A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).

[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983).

[CrossRef]

J. H. Shapiro, “Reciprocity of the turbulent atmosphere,” J. Opt. Soc. Am. 61, 492–495 (1971).

[CrossRef]

D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998).

[CrossRef]

M. A. Vorontsov, V. P. Sivokon, “Stochastic parallel gradient descent technique for high-resolution wavefront phase distortion correction,” J. Opt. Soc. Am. A 15, 2745–2758 (1998).

[CrossRef]

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, “High-resolution adaptive phase distortion compensation using a diffractive-feedback system: experimental results,” J. Opt. Soc. Am. A 16, 2567–2573 (1999).

[CrossRef]

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

[CrossRef]

M. C. Roggemann, V. M. Bright, S. R. Hick, W. D. Cowan, “Use of micro-electromechanical deformable mirrors to control aberrations in optical system,” Opt. Eng. 36, 1326–1338 (1997).

[CrossRef]

R. Q. Fugate, “Laser beacon adaptive optics,” Opt. Photon. News 5(6), 14–19 (1994).

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).

[CrossRef]

In the nonlinear-optics-based or dynamical-holography-based phase conjugation systems, we have true wave-front conjugation (both phase conjugation and amplitude correction); see, for example, B. Y. Zeldovich, N. V. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences (Springer-Verlag, Berlin, 1985).

B. M. Levine, A. Wirth, H. DaSilva, F. M. Landers, S. Kahalas, T. L. Bruno, P. R. Barbier, D. W. Rush, P. Polak-Dingels, G. L. Burdge, D. P. Looze, “Active compensation for horizontal line-of-sight turbulence over near-ground paths,” in Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, ed., Proc. SPIE3233, 221–232 (1998).

[CrossRef]

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

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

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, New York, 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 Kaufmann, San Mateo, Calif, 1993), Vol. 5, pp. 244–251.

J. C. Spall, “Adaptive stochastic approximation by the simultaneous perturbation method,” IEEE Trans. Autom. Control45 (to be published); in condensed form in Proceedings of the IEEE Conference on Decision and Control (Institute of Electrical and Electronics Engineers, New York, 1998), pp. 3872–3879.

B. Flower, M. Jabri, “Summed weight neuron perturbation: an O(n)improvement over weight perturbation,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds. (Morgan Kaufmann, San Meteo, Calif., 1993), Vol. 5, pp. 212–219.

G. Cauwenberghs, “A learning analog neural network chip with continuous-recurrent dynamics,” in Advances in Neural Information Processing Systems, S. J. Hanson, J. D. Cowan, C. L. Giles, eds., (Morgan Kaufmann, San Mateo, Calif.1994), Vol. 6, pp. 858–865.

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This is not necessarily true if the division form J˜j′=δJj/δujis used.

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