B. Hatfield and S. Enguehard, Adaptive Optics (Perseus, 2005).

M. A. Vorontsov and V. V. Kolosov, "Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing," J. Opt. Soc. Am. A 21, 126-141 (2005).

[CrossRef]

Phase Conjugate Laser Optics, A.Brignon and J.P.Huignard, eds., Wiley Series in Lasers and Applications (Wiley, 2004).

S. Haykin, Neural Networks: A Comprehensive Foundation2nd ed. (Prentice Hall, 1999).

M. I. Charnotskii, "Imaging in turbulence beyond the diffraction limit," Proc. SPIE 2534, 289-293 (1995).

[CrossRef]

F. Yu. Kanev and V. P. Lukin, "Amplitude phase beam control with the help of a two-mirror adaptive system," Atmosph. Opt. 4, 878-881 (1991).

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

V. V. Kolosov and S. I. Sysoev, "Minimization of angular characteristics of partially coherent optical radiation," Atmosph. Opt. 2, 297-301 (1989).

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics IV: Wave Propagation through Random Media (Springer, 1989).

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

B. Ya. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).

M. A. Vorontsov and V. I. Shmal'hauzen, Principles of Adaptive Optics, (Nauka, Moscow, 1985).

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

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

Optical Phase Conjugation, R.A.Fisher, ed. (Academic, 1983).

V. V. Kolosov and A. V. Kuzikovskii, "Phase compensation for refractive distortions of partially coherent beam," Sov. J. Quantum Electron. 11, 301-303 (1981).

[CrossRef]

M. A. Vorontsov and V. I. Shmal'hauzen, "Interference criteria for the light focusing problem," Sov. J. Quantum Electron. 10, 285-289 (1980).

[CrossRef]

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

J. C. Dunn, "Convergence rates for conditional gradient sequences generated by implicit length rules," SIAM J. Control Optim. 18, 473-487 (1980).

[CrossRef]

M. A. Vorontsov, "Phase conjugation method for thermal blooming compensation of light beams," Sov. J. Quantum Electron. 9, 1221-1233 (1979).

[CrossRef]

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

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

[CrossRef]

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

[CrossRef]

S. A. Kokorowski, M. E. Pedinoff, and 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]

C. L. Hayes, R. A. Brandewie, W. C. Davis, and G. E. Mevers, "Experimental test of an infrared phase conjugation adaptive array," J. Opt. Soc. Am. 67, 269-277 (1977).

[CrossRef]

E. Polak, "An historical survey of computational methods in optimal control," SIAM Rev. 15, 553-584 (1973).

[CrossRef]

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

M. A. Vorontsov and G. W. Carhart, "Adaptive phase distortion correction in strong speckle-modulation conditions," Opt. Lett. 27, 2155-2157 (2002).

[CrossRef]

M. A. Vorontsov and G. W. Carhart, "Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images," J. Opt. Soc. Am. A 18, 1312-1324 (2001).

[CrossRef]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and 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]

J. C. Dunn, "Convergence rates for conditional gradient sequences generated by implicit length rules," SIAM J. Control Optim. 18, 473-487 (1980).

[CrossRef]

B. Hatfield and S. Enguehard, Adaptive Optics (Perseus, 2005).

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

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

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

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

[CrossRef]

B. Hatfield and S. Enguehard, Adaptive Optics (Perseus, 2005).

S. Haykin, Neural Networks: A Comprehensive Foundation2nd ed. (Prentice Hall, 1999).

F. Yu. Kanev and V. P. Lukin, "Amplitude phase beam control with the help of a two-mirror adaptive system," Atmosph. Opt. 4, 878-881 (1991).

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

V. V. Dudorov, M. A. Vorontsov, and V. V. Kolosov, "Speckle-field propagation in 'frozen' turbulence: brightness function approach," J. Opt. Soc. Am. A 23, 1924-1936 (2006).

[CrossRef]

M. A. Vorontsov and V. V. Kolosov, "Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing," J. Opt. Soc. Am. A 21, 126-141 (2005).

[CrossRef]

V. V. Kolosov and S. I. Sysoev, "Analysis of some algorithms for minimizing angular divergence of partially coherent optical radiation," Atmosph. Opt. 3, 70-76 (1990).

V. V. Kolosov and S. I. Sysoev, "Minimization of angular characteristics of partially coherent optical radiation," Atmosph. Opt. 2, 297-301 (1989).

V. V. Kolosov and A. V. Kuzikovskii, "Phase compensation for refractive distortions of partially coherent beam," Sov. J. Quantum Electron. 11, 301-303 (1981).

[CrossRef]

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics IV: Wave Propagation through Random Media (Springer, 1989).

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

V. V. Kolosov and A. V. Kuzikovskii, "Phase compensation for refractive distortions of partially coherent beam," Sov. J. Quantum Electron. 11, 301-303 (1981).

[CrossRef]

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

F. Yu. Kanev and V. P. Lukin, "Amplitude phase beam control with the help of a two-mirror adaptive system," Atmosph. Opt. 4, 878-881 (1991).

S. A. Kokorowski, M. E. Pedinoff, and 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]

J. E. Pearson, S. A. Kokorovski, and M. E. Pedinoff, "Effects of speckles in adaptive optical systems," J. Opt. Soc. Am. 66, 1261-1267 (1976).

[CrossRef]

S. A. Kokorowski, M. E. Pedinoff, and 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]

J. E. Pearson, S. A. Kokorovski, and M. E. Pedinoff, "Effects of speckles in adaptive optical systems," J. Opt. Soc. Am. 66, 1261-1267 (1976).

[CrossRef]

B. Ya. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).

E. Polak, "An historical survey of computational methods in optimal control," SIAM Rev. 15, 553-584 (1973).

[CrossRef]

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics IV: Wave Propagation through Random Media (Springer, 1989).

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

B. Ya. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

M. A. Vorontsov and V. I. Shmal'hauzen, Principles of Adaptive Optics, (Nauka, Moscow, 1985).

M. A. Vorontsov and V. I. Shmal'hauzen, "Interference criteria for the light focusing problem," Sov. J. Quantum Electron. 10, 285-289 (1980).

[CrossRef]

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

V. V. Kolosov and S. I. Sysoev, "Analysis of some algorithms for minimizing angular divergence of partially coherent optical radiation," Atmosph. Opt. 3, 70-76 (1990).

V. V. Kolosov and S. I. Sysoev, "Minimization of angular characteristics of partially coherent optical radiation," Atmosph. Opt. 2, 297-301 (1989).

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics IV: Wave Propagation through Random Media (Springer, 1989).

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

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

V. V. Dudorov, M. A. Vorontsov, and V. V. Kolosov, "Speckle-field propagation in 'frozen' turbulence: brightness function approach," J. Opt. Soc. Am. A 23, 1924-1936 (2006).

[CrossRef]

M. A. Vorontsov and V. V. Kolosov, "Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing," J. Opt. Soc. Am. A 21, 126-141 (2005).

[CrossRef]

M. A. Vorontsov and G. W. Carhart, "Adaptive phase distortion correction in strong speckle-modulation conditions," Opt. Lett. 27, 2155-2157 (2002).

[CrossRef]

T. Weyrauch and M. A. Vorontsov, "Dynamic wave-front distortion compensation with 134-control-channel sub-millisecond adaptive system," Opt. Lett. 27, 751-753 (2002).

[CrossRef]

M. A. Vorontsov and G. W. Carhart, "Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images," J. Opt. Soc. Am. A 18, 1312-1324 (2001).

[CrossRef]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and 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]

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

M. A. Vorontsov and V. I. Shmal'hauzen, Principles of Adaptive Optics, (Nauka, Moscow, 1985).

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

M. A. Vorontsov and V. I. Shmal'hauzen, "Interference criteria for the light focusing problem," Sov. J. Quantum Electron. 10, 285-289 (1980).

[CrossRef]

M. A. Vorontsov, "Phase conjugation method for thermal blooming compensation of light beams," Sov. J. Quantum Electron. 9, 1221-1233 (1979).

[CrossRef]

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

B. Ya. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).

V. V. Kolosov and S. I. Sysoev, "Minimization of angular characteristics of partially coherent optical radiation," Atmosph. Opt. 2, 297-301 (1989).

F. Yu. Kanev and V. P. Lukin, "Amplitude phase beam control with the help of a two-mirror adaptive system," Atmosph. Opt. 4, 878-881 (1991).

V. V. Kolosov and S. I. Sysoev, "Analysis of some algorithms for minimizing angular divergence of partially coherent optical radiation," Atmosph. Opt. 3, 70-76 (1990).

N. V. Vysotina, N. N. Rozanov, V. E. Semenov, and V. A. Smirnov, "Amplitude-phase adaptive control over optically inhomogeneous paths with deformable mirrors," Izv. Vyssh. Uchebn. Zaved. Fiz. 11, 42-50 (1985).

J. E. Pearson, S. A. Kokorovski, and M. E. Pedinoff, "Effects of speckles in adaptive optical systems," J. Opt. Soc. Am. 66, 1261-1267 (1976).

[CrossRef]

R. A. Miller and A. Buffington, "Real-time correction of atmospherically degraded telescope images through image sharpening," J. Opt. Soc. Am. 64, 1200-1210 (1974).

[CrossRef]

J. H. Shapiro, "Reciprocity of the turbulent atmosphere," J. Opt. Soc. Am. 61, 492-495 (1971).

[CrossRef]

S. A. Kokorowski, M. E. Pedinoff, and 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]

C. L. Hayes, R. A. Brandewie, W. C. Davis, and G. E. Mevers, "Experimental test of an infrared phase conjugation adaptive array," J. Opt. Soc. Am. 67, 269-277 (1977).

[CrossRef]

D. L. Fried, "Statistics of a geometric representation of wavefront distortion," J. Opt. Soc. Am. 55, 1427-1435 (1965).

[CrossRef]

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

[CrossRef]

M. A. Vorontsov, G. W. Carhart, D. V. Pruidze, J. C. Ricklin, and 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 and G. W. Carhart, "Anisoplanatic imaging through turbulent media: image recovery by local information fusion from a set of short-exposure images," J. Opt. Soc. Am. A 18, 1312-1324 (2001).

[CrossRef]

V. V. Dudorov, M. A. Vorontsov, and V. V. Kolosov, "Speckle-field propagation in 'frozen' turbulence: brightness function approach," J. Opt. Soc. Am. A 23, 1924-1936 (2006).

[CrossRef]

M. I. Charnotskii, V. A. Myakinin, and V. Zavorotnyy, "Observation of superresolution in nonisoplanatic imaging through turbulence," J. Opt. Soc. Am. A 7, 1345-1350 (1990).

[CrossRef]

J. D. Barchers, "Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations," J. Opt. Soc. Am. A 19, 926-945 (2002).

[CrossRef]

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

[CrossRef]

M. C. Roggemann and A. C. Koivunen, "Branch-point reconstruction in laser beam projection through turbulence with finite-degree-of-freedom phase-only wave-front correction," J. Opt. Soc. Am. A 17, 53-62 (2000).

[CrossRef]

M. A. Vorontsov and V. V. Kolosov, "Target-in-the-loop beam control: basic considerations for analysis and wavefront sensing," J. Opt. Soc. Am. A 21, 126-141 (2005).

[CrossRef]

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

[CrossRef]

M. I. Charnotskii, "Imaging in turbulence beyond the diffraction limit," Proc. SPIE 2534, 289-293 (1995).

[CrossRef]

J. C. Dunn, "Convergence rates for conditional gradient sequences generated by implicit length rules," SIAM J. Control Optim. 18, 473-487 (1980).

[CrossRef]

E. Polak, "An historical survey of computational methods in optimal control," SIAM Rev. 15, 553-584 (1973).

[CrossRef]

V. V. Kolosov and A. V. Kuzikovskii, "Phase compensation for refractive distortions of partially coherent beam," Sov. J. Quantum Electron. 11, 301-303 (1981).

[CrossRef]

M. A. Vorontsov and V. I. Shmal'hauzen, "Interference criteria for the light focusing problem," Sov. J. Quantum Electron. 10, 285-289 (1980).

[CrossRef]

M. A. Vorontsov, "Phase conjugation method for thermal blooming compensation of light beams," Sov. J. Quantum Electron. 9, 1221-1233 (1979).

[CrossRef]

A. A. Vasil'ev, M. A. Vorontsov, I. A. Kudryashov, and V. I. Shmalhauzen, "Adaptive focusing of radiation on a diffusely scattering reflector under nonlinear refraction conditions," Sov. J. Quantum Electron. 17, 1106-1115 (1987).

[CrossRef]

M. A. Vorontsov, V. N. Karnaukhov, A. L. Kuz'minskii, and V. I. Shmalhauzen, "Speckle effects in adaptive optical systems," Sov. J. Quantum Electron. 14, 761-766 (1984).

[CrossRef]

The time delay ΔtC includes time required for wavefront phase measurement and the outgoing beam phase control.

In the case of a point-source target, the pupil-plane phase screen and an outgoing beam with spatially uniform intensity distribution (flat-top beam), phase and field conjugation are equivalent.

This implies that measurement of phase φ(r,t) is performed over a time τph (sensor's photo-receiver integration time) shorter than the characteristic times τs and τat for target surface roughness and propagation medium refractive index realization update (τph<min{τs,τat}).

S. Haykin, Neural Networks: A Comprehensive Foundation2nd ed. (Prentice Hall, 1999).

For a nearly diffraction-limited hit-spot size, the speckle size (radius) asp≃a0 for a Gaussian beam. The speckle size is 1.22π times smaller for a flat-top beam.

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, 1979).

Optical Phase Conjugation, R.A.Fisher, ed. (Academic, 1983).

B. Ya. Zeldovich, N. F. Pilipetsky, and V. V. Shkunov, Principles of Phase Conjugation (Springer, 1985).

M. A. Vorontsov and V. I. Shmal'hauzen, Principles of Adaptive Optics, (Nauka, Moscow, 1985).

Phase Conjugate Laser Optics, A.Brignon and J.P.Huignard, eds., Wiley Series in Lasers and Applications (Wiley, 2004).

B. Hatfield and S. Enguehard, Adaptive Optics (Perseus, 2005).

M. C. Rytov, Yu A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics IV: Wave Propagation through Random Media (Springer, 1989).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

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

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

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