Abstract

Wavefront control experiments in strong scintillation conditions (scintillation index, ≃1) over a 2.33 km, near-horizontal, atmospheric propagation path are presented. The adaptive-optics system used comprises a tracking and a fast-beam-steering mirror as well as a 132-actuator, microelectromechanical-system, piston-type deformable mirror with a VLSI controller that implements stochastic parallel gradient descent control optimization of a system performance metric. The experiments demonstrate mitigation of atmospheric distortions with a speckle beacon typical for directed energy and free-space laser communication applications.

© 2005 Optical Society of America

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References

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  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes, Vol. 16 of Oxford Series in Optical and Imaging Sciences (Oxford University, 1998).
  2. F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
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  3. 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]
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  5. “Report of the High Energy Laser Executive Review Panel,” Department of Defense Laser Master Plan (U.S. Department of Defense, 2000), Vol. 2.
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    [CrossRef]
  9. 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]
  10. 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]
  11. T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, G. Cauwenberghs, “Microscale adaptive optics: wavefront control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001).
    [CrossRef]
  12. A. Buffington, F. S. Crawford, R. A. Muller, A. J. Schwemin, R. G. Smits, “Correction of atmospheric distortion with an image-sharpening telescope,” J. Opt. Soc. Am. 67, 298–303 (1977).
    [CrossRef]
  13. S. L. McCall, T. R. Brown, A. Passner, “Improved optical stellar image using a real-time phase-correction system: initial results,” Astrophys. J. 211, 463–468 (1977).
    [CrossRef]
  14. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
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    [CrossRef]
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    [CrossRef]
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  19. T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).
  20. 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]
  21. T. Weyrauch, M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27, 751–753 (2002).
    [CrossRef]
  22. M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).
  23. M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).
  24. L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
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  26. T. G. Bifano, J. Perrault, R. Krishnamoorthy Mali, M. N. Horenstein, “Microelectromechanical deformable mirrors,” IEEE J. Sel. Top. Quantum Electron. 5, 83–89 (1999).
    [CrossRef]
  27. V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
    [CrossRef]
  28. J. C. Ricklin, F. M. Davidson, “Atmospheric optical communication with a Gaussian Schell beam,” J. Opt. Soc. Am. A 20, 856–866 (2003).
    [CrossRef]
  29. M. A. Vorontsov, G. W. Carhart, J. W. Gowens, J. C. Ricklin, “Adaptive correction of wavefront phase distortions in a free-space laser communication: system and method,” U.S. patent (pending).

2003 (1)

2002 (2)

2001 (1)

2000 (2)

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]

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

1999 (1)

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

1998 (3)

1997 (1)

1995 (1)

1993 (1)

1983 (1)

1978 (1)

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

1977 (4)

Andrews, L. C.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Banta, M.

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

Baranova, N. B.

Barclay, H. T.

Bierden, P. A.

T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).

Bifano, T. G.

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, G. Cauwenberghs, “Microscale adaptive optics: wavefront control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001).
[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).
[CrossRef]

T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).

Brown, T. R.

S. L. McCall, T. R. Brown, A. Passner, “Improved optical stellar image using a real-time phase-correction system: initial results,” Astrophys. J. 211, 463–468 (1977).
[CrossRef]

Bruno, T. L.

Buffington, A.

Carhart, G. W.

M. A. Vorontsov, G. W. Carhart, “Adaptive phase distortion correction in strong speckle-modulation conditions,” Opt. Lett. 27, 2155–2157 (2002).
[CrossRef]

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]

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]

R. T. Edward, 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, 1999), Chap. 16, pp. 359–382.

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

M. A. Vorontsov, G. W. Carhart, J. W. Gowens, J. C. Ricklin, “Adaptive correction of wavefront phase distortions in a free-space laser communication: system and method,” U.S. patent (pending).

Carrano, J. C.

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

Cauwenberghs, G.

Cohen, M.

Coudé du Foresto, V.

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

Crawford, F. S.

Davidson, F. M.

Dimas, C. E.

T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).

Edward, R. T.

R. T. Edward, 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, 1999), Chap. 16, pp. 359–382.

Faucherre, M.

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

Fried, D. L.

Gitton, P.

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

Gowens, J.

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

Gowens, J. W.

M. A. Vorontsov, G. W. Carhart, J. W. Gowens, J. C. Ricklin, “Adaptive correction of wavefront phase distortions in a free-space laser communication: system and method,” U.S. patent (pending).

Gravecha, M. E.

M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).

Gurvich, A. S.

M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).

Hammer, J. A.

Hansen, S.

Hardy, J. W.

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

J. W. Hardy, Adaptive Optics for Astronomical Telescopes, Vol. 16 of Oxford Series in Optical and Imaging Sciences (Oxford University, 1998).

Herrmann, J.

Hopen, C. Y.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[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).
[CrossRef]

Hubin, N.

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

Humphreys, R. A.

Jankevics, A.

Kashkarov, S. S.

M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).

Kravtsov, Y. A.

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).
[CrossRef]

Landers, F.

Levine, B. M.

Mamaev, A. V.

Martinsen, E. A.

McCall, S. L.

S. L. McCall, T. R. Brown, A. Passner, “Improved optical stellar image using a real-time phase-correction system: initial results,” Astrophys. J. 211, 463–468 (1977).
[CrossRef]

Muller, R. A.

O’Meara, T. R.

Passner, A.

S. L. McCall, T. R. Brown, A. Passner, “Improved optical stellar image using a real-time phase-correction system: initial results,” Astrophys. J. 211, 463–468 (1977).
[CrossRef]

Pearson, J. E.

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).
[CrossRef]

Perreault, J. A.

T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).

Phillips, R. L.

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

Pilipetsky, N. F.

Pokasov, V. L. V.

M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).

Price, T. R.

Primmerman, C. A.

Ricklin, J. C.

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
[CrossRef]

Schwemin, A. J.

Shkunov, V. V.

Sivokon, V. P.

Smits, R. G.

Spall, J. C.

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003).
[CrossRef]

Toledo-Quinones, M.

Vorontsov, M. A.

M. A. Vorontsov, G. W. Carhart, “Adaptive phase distortion correction in strong speckle-modulation conditions,” Opt. Lett. 27, 2155–2157 (2002).
[CrossRef]

T. Weyrauch, M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27, 751–753 (2002).
[CrossRef]

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, G. Cauwenberghs, “Microscale adaptive optics: wavefront control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001).
[CrossRef]

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]

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]

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, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

R. T. Edward, 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, 1999), Chap. 16, pp. 359–382.

M. A. Vorontsov, G. W. Carhart, J. W. Gowens, J. C. Ricklin, “Adaptive correction of wavefront phase distortions in a free-space laser communication: system and method,” U.S. patent (pending).

Weyrauch, T.

T. Weyrauch, M. A. Vorontsov, “Dynamic wave-front distortion compensation with a 134-control-channel submillisecond adaptive system,” Opt. Lett. 27, 751–753 (2002).
[CrossRef]

T. Weyrauch, M. A. Vorontsov, T. G. Bifano, J. A. Hammer, M. Cohen, G. Cauwenberghs, “Microscale adaptive optics: wavefront control with a μ-mirror array and a VLSI stochastic gradient descent controller,” Appl. Opt. 40, 4243–4253 (2001).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

Wirth, A.

Zeldovich, B. Y.

Zollars, B. G.

Appl. Opt. (4)

Astron. Astrophys. Suppl. Ser. (1)

V. Coudé du Foresto, M. Faucherre, N. Hubin, P. Gitton, “Using single-mode fibers to monitor fast Strehl ratio fluctuations,” Astron. Astrophys. Suppl. Ser. 145, 305–310 (2000).
[CrossRef]

Astrophys. J. (1)

S. L. McCall, T. R. Brown, A. Passner, “Improved optical stellar image using a real-time phase-correction system: initial results,” Astrophys. J. 211, 463–468 (1977).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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

J. Opt. Soc. Am. (4)

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

Opt. Lett. (3)

Proc. IEEE (1)

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

Other (10)

J. C. Spall, Introduction to Stochastic Search and Optimization (Wiley, 2003).
[CrossRef]

R. T. Edward, 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, 1999), Chap. 16, pp. 359–382.

T. G. Bifano, J. A. Perreault, P. A. Bierden, C. E. Dimas, “Micromachined deformable mirrors for adaptive optics,” in High-Resolution Wavefront Control: Methods, Devices, and Applications IV, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, S. R. Restaino, R. K. Tyson, eds., Proc. SPIE4825, 10–13 (2002).

M. A. Vorontsov, G. W. Carhart, M. Banta, T. Weyrauch, J. Gowens, J. C. Carrano, “Atmospheric laser optics testbed (A_LOT): atmospheric propagation characterization, beam control and imaging results,” in Advanced Wavefront Control: Methods, Devices, and Applications, J. D. Gonglewski, M. A. Vorontsov, M. T. Gruneisen, eds., Proc. SPIE5162, 37–48 (2003).

M. E. Gravecha, A. S. Gurvich, S. S. Kashkarov, V. L. V. Pokasov, “Similarity relations and their experimental verification for strong intensity fluctuations of laser radiation,” in Laser Beam Propagation in the Atmosphere, J. Strohbehn, ed. (Springer-Verlag, 1978).

L. C. Andrews, R. L. Phillips, C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, 2001).
[CrossRef]

M. A. Vorontsov, G. W. Carhart, J. W. Gowens, J. C. Ricklin, “Adaptive correction of wavefront phase distortions in a free-space laser communication: system and method,” U.S. patent (pending).

J. W. Hardy, Adaptive Optics for Astronomical Telescopes, Vol. 16 of Oxford Series in Optical and Imaging Sciences (Oxford University, 1998).

F. Roddier, Adaptive Optics in Astronomy (Cambridge University, 1999).
[CrossRef]

“Report of the High Energy Laser Executive Review Panel,” Department of Defense Laser Master Plan (U.S. Department of Defense, 2000), Vol. 2.

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Figures (14)

Fig. 1
Fig. 1

Schematic of the experimental setup with an adaptive receiver: The light from lasercom transceiver modules (DL, Dominion Lasercom; TL, Terralink 1000), used as speckle beacons and mounted on top of a 73 m high water tower, propagated 2.33 km through the atmosphere. A 45° mirror inside a shed on the roof of the laboratory building redirected the light through a 8 m long pipe onto an optical table inside the laboratory, where the transceiver telescope (with a 15 cm aperture) and the AO subsystems were located. The light passed first through the beam-steering system with the tracking mirror, TM, for correction of large-amplitude but slow wavefront tilts and the fast-steering mirror, FSM, for correction of atmospheric-turbulence-induced tilts and jitter. Higher-order wavefront distortions were compensated with the MEMS deformable mirror, μDM, driven by the SPGD controller. (The active mirrors of the AO subsystems are depicted as transmissive elements to simplify the schematic.) The fast digital camera, FDC, in image plane ′ of the entrance pupil was used for recording irradiance fluctuations (scintillations).

Fig. 2
Fig. 2

Results from measurement of the irradiance distributions in the receiver telescope’s pupil plane, : (a) Probability density function p(I) of measured irradiance values I for three different atmospheric conditions (Cn2 = 1 × 10−15, 5 × 10−15, and 5 × 10−14 m−2/3), which correspond to Rytov variances σR2 = 0.2, 1, and 10, respectively. The insets show sample, short-exposure irradiance distributions for each condition. (The areas on the photos correspond to 11 × 11 cm2 in .) The time dependence of the irradiance at a sample pixel is shown for σR2 equals (b) 0.2, (c) 1, and (d) 10. (e) The average temporal spectra 〈sI(f)〉 of the irradiance fluctuations in individual pixels for the three different turbulence conditions. (f) The contents spectra wI(f) = fsI(f)〉 reveal the main spectral contributions on the logarithmic frequency scale.

Fig. 3
Fig. 3

Schematics of the AO setup that consist of a beam-steering subsystem, dashed box, with subsystems for slow tracking and fast beam steering and a higher-resolution, wavefront correction subsystem with a MEMS mirror and a SPGD controller. The pupil plane, , is imaged by the transceiver telescope, L1, L2, onto the plane of the tracking mirror, TM, and subsequently by an optical relay, L3, L4, onto the plane of the fast steering mirror, FSM. Part of the light is coupled out by beam splitter BS1 and focused by lens L5 onto the position sensitive detector, PSD, to provide feedback signals Vx, Vy to the fast-steering controller. The tracking controller monitors the FSM control voltages (Ux, Uy) and keeps them in the center of their dynamic range by applying correction signals (Ũx, Ũy) to TM. The optical relay, L6, L7, which images the pupil onto the plane of the MEMS deformable mirror, μDM, connects the beam-steering subsystem with the MEMS SPGD subsystem μAO (dotted box). After reflection from μDM and beam splitter BS2, part of the received light is coupled by lens L8 into the single-mode fiber, SM1 (~5.5 μm), in focal plane ′. The optical power in the fiber, measured by photomultiplier PM, is used as feedback signal J for the SPGD controller. Another part of the received light is transmitted by BS2 and BS3 and focused by L10 onto the camera, CCD, in focal plane ‴ (the image of the far-field intensity distribution). For adaptive transmission the light emerging from SM2 is collimated by L9 and propagates after reflection from beam splitter BS3 in the opposite direction through the AO system’s optical train.

Fig. 4
Fig. 4

Efficiency of beam steering with the fast-steering mirror with controlled (sinusoidal) tilt aberrations: The error suppression factor η(f) = 〈θon2(f)〉1/2/〈θoff2(f)〉1/2 after compensation (closed-loop) as a function of the frequency f of the introduced tip/tilt aberration is shown. Dashed line, the 3 dB bandwidth of ~330 Hz.

Fig. 5
Fig. 5

(a) Probability density function pθ for tilt angle θx in the receiver pupil plane, , after 2.33 km of atmospheric propagation with the feedback off and with tip/tilt correction (the feedback on). The left inset shows the trajectory of tip/tilt angles acquired during a 2 s period in open-loop conditions; the right inset is the corresponding measurement with a closed feedback loop. (b) Temporal spectra sθ(f) for the tilt angle θx without tip/tilt correction (feedback off) and for the residual tilt angle with the beam-steering system operation (feedback on).

Fig. 6
Fig. 6

(a) Schematic of the setup for BER measurements for a closed-loop, free-space optical communication link with a single adaptive transmitter. The bit pattern generator modulates the light transmitted by adaptive transmitter A. The transceiver, B, on the water tower receives and retransmits the optical bit stream, which is received by the nonadaptive receiver, C, and sent to the BER analyzer. The telescopes for A and C are separated by distance, h = 2 m, to introduce spatial diversity. (b) Schematic of the adaptive transmitter with tracking mirror TM and fast-beam-steering mirror FS. It uses light from transceiver B as a beacon for tip/tilt correction. (c) Bit error rates measured during a 600 s period with the beam steering turned on and off alternatively for 60 s intervals each. Horizontal lines, the average BER for each 60 s period.

Fig. 7
Fig. 7

Average metric evolution curves 〈J(t)〉 for (a) self-induced minimization of the performance metric and (b) the subsequent metric maximization process. The insets in (a) and (b) are focal-plane intensity distributions at the end of the minimization and maximization process, respectively.

Fig. 8
Fig. 8

(a) Two sample time series of the metric J(t) after 2.33 km atmospheric propagation. The Cn2 values were identical for both measurements, but the wind speed was considerably higher for measurement 2. The beam-steering system was on; hence J(t) is proportional to the instantaneous tilt-corrected Strehl ratio St(t). (b) The corresponding (average) power spectra 〈sJ(f)〉 and, (c) the contents spectra wJ(f) = fsJ(f)〉 reveal the difference in the main spectral components (f, frequency). Note the frequency shift of the maxima of wJ(f) by a factor of 5.

Fig. 9
Fig. 9

Three sample pdf’s p(J) for metric values, demonstrating the range of the metric variance σJ2 = 〈I2〉/〈I2 − 1 observed in various atmospheric conditions. The J values are normalized by their corresponding mean value 〈J〉.

Fig. 10
Fig. 10

Method for evaluating the performance of the AO system: Metric values J are recorded for a trial with five phases of different operation conditions for the adaptive systems (as indicated) and subsequently saved before the next trial is started. Data evaluation (e.g., calculation of the average metric evolution curves) are performed on data sets of 1000 or more recorded trials.

Fig. 11
Fig. 11

Probability density functions pi(J) of metric values J for three different operation conditions of the AO system: No adaptation (i = 1, BS and μAO off), beam steering only (i = 2, BS on, μAO off), and beam steering together with high-resolution SPGD AO control (i = 3, BS and μAO on) are shown. Deep fading (the occurrence of low J values) is strongly reduced with wavefront correction.

Fig. 12
Fig. 12

Results from an experiment for mitigation of atmospheric-turbulence-induced wavefront distortions with the SPGD AO system (μAO): Evolution curve in (a) improvement in the average metric 〈J(t)〉 after μAO is switched on at t = 0 and its decrease after feedback is switched off at t ≈ 550 ms. The beam-steering system is always on during the experiment. Curve in (b) corresponding improvement in the normalized metric variance σJ2 = 〈J2〉/〈J2 − 1; curves in (c) measured average metric values for the rising and the decay process (gray dots) on a logarithmic time scale together with fit curves (lines) describing a biexponential process.

Fig. 13
Fig. 13

Long-exposure distributions of the irradiance I(r) measured with the camera, CCD, in focal plane ″ (in Fig. 3) and the corresponding three-dimensional plots recorded while the SPGD AO system, μAO, was (a) off and (b) on. (The wavefront-tilt control with the beam-steering system was on in both cases.) (c) The corresponding two-dimensional beam profiles were rescaled to the dimensions in focal plane ′ of the receiver fiber, SM1. The mode-field diameter of SM1 (5.5 μm) is indicated by the gray circle. For comparison the profile obtained with a single-mode fiber source located in focal plane is also shown, which demonstrates the optical system quality obtained for a point source without atmospheric propagation.

Fig. 14
Fig. 14

Results from an experiment in which an adaptive-transceiver configuration is used: Curve 〈J(t)〉 describes the evolution of the local metric (from the beam received at the laboratory with the AO setup) that was used as a feedback signal for the SPGD controller. The SPGD AO system, μAO, was turned on at t = 0 and off at t = 550 ms while the beam steering, BSS, was continuously working. The curve of the remote receiver metric J2, which describes the irradiance at the beacon location at the water tower, demonstrates that the SPGD AO system improves the outgoing beam simultaneously with optimization of the incoming beam.

Equations (3)

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U x ( n ) = U x ( n - 1 ) + k P , x e x ( n ) + k I , x S x ( n ) + k D , x [ e x ( n ) - e x ( n - 1 ) ] .
J ± ( n ) = J [ u 1 ( n ) ± δ u 1 ( n ) , , u j ( n ) ± δ u j ( n ) , , u N ( n ) ± δ u N ( n ) ] .
u J ( n + 1 ) = u j ( n ) + γ [ J + ( n ) - J - ( n ) ] sign [ δ u j ( n ) ] ,

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