Abstract

Recent progress has been made to compute efficiently the open-loop minimum-variance reconstructor (MVR) for multiconjugate adaptive optics systems by a combination of sparse matrix and iterative techniques. Using spectral analysis, I show that a closed-loop laser guide star multiconjugate adaptive optics control algorithm consisting of MVR cascaded with an integrator control law is unstable. To solve this problem, a computationally efficient pseudo-open-loop control (POLC) method was recently proposed. I give a theoretical proof of the stability of this method and demonstrate its superior performance and robustness against misregistration errors compared with conventional least-squares control. This can be accounted for by the fact that POLC incorporates turbulence statistics through its regularization term that can be interpreted as spatial filtering, yielding increased robustness to misregistration. For the Gemini-South 8-m telescope multiconjugate system and for median Cerro Pachon seeing, the performance of POLC in terms of rms wave-front error averaged over a 1-arc min field of view is approximately three times superior to that of a least-squares reconstructor. Performance degradation due to 30% translational misregistration on all three mirrors is approximately a 30% increased rms wave-front error, whereas a least-squares reconstructor is unstable at such a misregistration level.

© 2005 Optical Society of America

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  1. J. M. Beckers, “Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics,” in Proceedings of the ESO Conference and Workshop on Very Large Telescopes and their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), Vol. 30,pp. 693–703.
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  3. T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
    [Crossref]
  4. E. Diolaiti, R. Ragazzoni, M. Tordi, “Stability and optimality of a layer oriented MCAO system,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds., (European Southern Observatory, Garching, Germany, 2002), Vol. 58.
  5. E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
    [Crossref]
  6. F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations and performance of multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
    [Crossref]
  7. “The MCAO preliminary design review report,” , Gemini Observatory, Hilo, Hawaii, (2001), http://www.gemini.edu/documentation/webdocs/rev/mcao_pdr/mcao_pdr.html .
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  9. R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.
  10. M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4839, 578–587 (2002).
    [Crossref]
  11. N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.
  12. T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
    [Crossref]
  13. B. L. Ellerbroek, “Scaling multi-conjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
    [Crossref]
  14. B. L. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002).
    [Crossref]
  15. B. L. Ellerbroek, L. Gilles, C. R. Vogel, “Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes,” Appl. Opt. 42, 4811–4818 (2003).
    [Crossref] [PubMed]
  16. L. Gilles, “Order N sparse minimum variance open-loop reconstructor for extreme adaptive optics,” Opt. Lett. 28, 1927–1929 (2003).
    [Crossref] [PubMed]
  17. L. Gilles, B. L. Ellerbroek, C. R. Vogel, “Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics,” Appl. Opt. 42, 5233–5250 (2003).
    [Crossref] [PubMed]
  18. R. Flicker, F. J. Rigaut, B. L. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8 m telescope,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
    [Crossref]
  19. B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
    [Crossref]
  20. D. T. Gavel, W. Wiberg, “Towards strehl-optimizing adaptive optics controllers,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 890–901 (2002).
    [Crossref]
  21. B. L. Ellerbroek, “First-order performance evaluation of adaptive optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
    [Crossref]
  22. B. L. Ellerbroek, G. M. Cochran, “A wave optics propagation code for multi-conjugate adaptive optics,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 104–120 (2002).
    [Crossref]
  23. B. L. Ellerbroek, “A wave optics propagation code for multiconjugate adaptive optics,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.
  24. B. L. Ellerbroek, C. R. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 206–217 (2003).
    [Crossref]
  25. B. L. Ellerbroek, “Wavefront reconstruction algorithms and simulation results for multiconjugate adaptive optics on giant telescopes,” in Second Backaskog Workshop on Extremely Large Telescopes, A. L. Ardeberg, T. Andersen, eds., Proc. SPIE5382, 478–489 (2003).
    [Crossref]
  26. B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser guide star multiconjugate adaptive optics,” J. Opt. Soc. Am. 18, 2539–2547 (2001).
    [Crossref]
  27. E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
    [Crossref]
  28. G. A. Hyver, R. M. Blankinship, “ALI high power beam control,” in Guidance and Control, Vol. 88 of Advances in the Astronautical Sciences, R. D. Culp, J. D. Medbery, eds., (American Astronautical Society, Springfield, Va., 1995), pp. 445–460.

2003 (3)

2002 (1)

2001 (3)

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
[Crossref]

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser guide star multiconjugate adaptive optics,” J. Opt. Soc. Am. 18, 2539–2547 (2001).
[Crossref]

1994 (2)

1983 (1)

Angel, R.

R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.

Beckers, J. M.

J. M. Beckers, “Increasing the size of the isoplanatic patch with multi-conjugate adaptive optics,” in Proceedings of the ESO Conference and Workshop on Very Large Telescopes and their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), Vol. 30,pp. 693–703.

Blankinship, R. M.

G. A. Hyver, R. M. Blankinship, “ALI high power beam control,” in Guidance and Control, Vol. 88 of Advances in the Astronautical Sciences, R. D. Culp, J. D. Medbery, eds., (American Astronautical Society, Springfield, Va., 1995), pp. 445–460.

Cheng, A.

N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.

Cochran, G. M.

B. L. Ellerbroek, G. M. Cochran, “A wave optics propagation code for multi-conjugate adaptive optics,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 104–120 (2002).
[Crossref]

Conan, J. M.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[Crossref]

Diolaiti, E.

E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
[Crossref]

E. Diolaiti, R. Ragazzoni, M. Tordi, “Stability and optimality of a layer oriented MCAO system,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds., (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Ellerbroek, B. L.

B. L. Ellerbroek, L. Gilles, C. R. Vogel, “Numerical simulations of multiconjugate adaptive optics wave-front reconstruction on giant telescopes,” Appl. Opt. 42, 4811–4818 (2003).
[Crossref] [PubMed]

L. Gilles, B. L. Ellerbroek, C. R. Vogel, “Preconditioned conjugate gradient wave-front reconstructors for multiconjugate adaptive optics,” Appl. Opt. 42, 5233–5250 (2003).
[Crossref] [PubMed]

B. L. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1803–1816 (2002).
[Crossref]

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser guide star multiconjugate adaptive optics,” J. Opt. Soc. Am. 18, 2539–2547 (2001).
[Crossref]

B. L. Ellerbroek, “First-order performance evaluation of adaptive optics systems for atmospheric turbulence compensation in extended-field-of-view astronomical telescopes,” J. Opt. Soc. Am. A 11, 783–805 (1994).
[Crossref]

B. L. Ellerbroek, “Wavefront reconstruction algorithms and simulation results for multiconjugate adaptive optics on giant telescopes,” in Second Backaskog Workshop on Extremely Large Telescopes, A. L. Ardeberg, T. Andersen, eds., Proc. SPIE5382, 478–489 (2003).
[Crossref]

B. L. Ellerbroek, G. M. Cochran, “A wave optics propagation code for multi-conjugate adaptive optics,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 104–120 (2002).
[Crossref]

B. L. Ellerbroek, “A wave optics propagation code for multiconjugate adaptive optics,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

B. L. Ellerbroek, C. R. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 206–217 (2003).
[Crossref]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations and performance of multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[Crossref]

B. L. Ellerbroek, “Scaling multi-conjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[Crossref]

R. Flicker, F. J. Rigaut, B. L. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8 m telescope,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[Crossref]

Flicker, R.

R. Flicker, F. J. Rigaut, B. L. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8 m telescope,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[Crossref]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations and performance of multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[Crossref]

Fusco, T.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[Crossref]

Gavel, D. T.

D. T. Gavel, W. Wiberg, “Towards strehl-optimizing adaptive optics controllers,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 890–901 (2002).
[Crossref]

Georges, J. A.

N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.

Gilles, L.

Hege, K.

R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Hyver, G. A.

G. A. Hyver, R. M. Blankinship, “ALI high power beam control,” in Guidance and Control, Vol. 88 of Advances in the Astronautical Sciences, R. D. Culp, J. D. Medbery, eds., (American Astronautical Society, Springfield, Va., 1995), pp. 445–460.

Johnston, D. C.

Kulcsar, C.

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

Le Roux, B.

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

Lloyd-Hart, M.

N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.

M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4839, 578–587 (2002).
[Crossref]

R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Michau, V.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[Crossref]

Milton, N. M.

M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, J. R. P. Angel, R. Gilmozzi, eds., Proc. SPIE4839, 578–587 (2002).
[Crossref]

N. M. Milton, M. Lloyd-Hart, A. Cheng, J. A. Georges, R. Angel, “Design and expected performance of an MCAO system for the Giant Magellan Telescope,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 238–249.

Mugnier, L. M.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[Crossref]

Peng, C.

R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Ragazzoni, R.

E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
[Crossref]

E. Diolaiti, R. Ragazzoni, M. Tordi, “Stability and optimality of a layer oriented MCAO system,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds., (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Raynaud, H.-F.

B. Le Roux, J. M. Conan, C. Kulcsar, H.-F. Raynaud, L. M. Mugnier, T. Fusco, “Optimal control law for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 878–889 (2002).
[Crossref]

Rigaut, F.

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser guide star multiconjugate adaptive optics,” J. Opt. Soc. Am. 18, 2539–2547 (2001).
[Crossref]

Rigaut, F. J.

R. Flicker, F. J. Rigaut, B. L. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8 m telescope,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1032–1043 (2000).
[Crossref]

F. J. Rigaut, B. L. Ellerbroek, R. Flicker, “Principles, limitations and performance of multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1022–1031 (2000).
[Crossref]

Rousset, G.

T. Fusco, J. M. Conan, G. Rousset, L. M. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
[Crossref]

T. Fusco, J. M. Conan, V. Michau, L. M. Mugnier, G. Rousset, “Phase estimation for large field of view: application to multiconjugate adaptive optics,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[Crossref]

Sarlot, R.

R. Angel, M. Lloyd-Hart, K. Hege, R. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Tordi, M.

E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
[Crossref]

E. Diolaiti, R. Ragazzoni, M. Tordi, “Stability and optimality of a layer oriented MCAO system,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds., (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

Vogel, C. R.

Wallner, E. P.

Welsh, B. M.

Wiberg, W.

D. T. Gavel, W. Wiberg, “Towards strehl-optimizing adaptive optics controllers,” in Adaptive Optical Systems Technology II, P. L. Wizinowich, ed., Proc. SPIE4839, 890–901 (2002).
[Crossref]

Appl. Opt. (2)

Astron. Astrophys. (1)

E. Diolaiti, R. Ragazzoni, M. Tordi, “Closed loop performance of a layer-oriented multiconjugate adaptive optics system,” Astron. Astrophys. 372, 710–718 (2001).
[Crossref]

J. Opt. Soc. Am. (2)

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser guide star multiconjugate adaptive optics,” J. Opt. Soc. Am. 18, 2539–2547 (2001).
[Crossref]

E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
[Crossref]

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

Opt. Lett. (1)

Other (18)

G. A. Hyver, R. M. Blankinship, “ALI high power beam control,” in Guidance and Control, Vol. 88 of Advances in the Astronautical Sciences, R. D. Culp, J. D. Medbery, eds., (American Astronautical Society, Springfield, Va., 1995), pp. 445–460.

B. L. Ellerbroek, G. M. Cochran, “A wave optics propagation code for multi-conjugate adaptive optics,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 104–120 (2002).
[Crossref]

B. L. Ellerbroek, “A wave optics propagation code for multiconjugate adaptive optics,” in Proceedings of the ESO Conference and Workshop Beyond Conventional Adaptive Optics, R. Ragazzoni, N. Hubin, S. Esposito, E. Vernet, eds. (European Southern Observatory, Garching, Germany, 2002), Vol. 58.

B. L. Ellerbroek, C. R. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 206–217 (2003).
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B. L. Ellerbroek, “Wavefront reconstruction algorithms and simulation results for multiconjugate adaptive optics on giant telescopes,” in Second Backaskog Workshop on Extremely Large Telescopes, A. L. Ardeberg, T. Andersen, eds., Proc. SPIE5382, 478–489 (2003).
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Figures (8)

Fig. 1
Fig. 1

Generic multi-input, multi-output control feedback loops of AO systems. (a) Displays generic input, error, and output signals and an open-loop transfer matrix HOL(z). In AO, these signals are, respectively, the open-loop sensor measurements s0(z), the residual sensor measurements s(z), and the slope change Δs(z) produced by the DMs. (b) Displays the classical LSR scheme. A least-squares reconstruction matrix R is applied to the closed-loop slope data s(z) to produce an estimate of the residual error êa(z) at all actuator locations; this error is then temporally filtered by a scalar filter g(z) to produce an actual phase value â(z) at all actuators. (c) The MVR scheme, where R = FE is split into estimation and fitting steps. The product of the interaction and fitting matrices is denoted as x ^. (d) The POLC scheme that incorporates two additional nested feedback loops probing signal on the estimated turbulence profile G x ˜ = G a F.

Fig. 2
Fig. 2

Left panel: representative FIR g(n) given by Eq. (13) with α = β = 0.495 and δ = 1/2. Right panel: open-loop power spectrum |g|2, closed-loop power spectrum |g|2/|1 + g|2, and error rejection (closed-loop relative to open-loop) power spectrum 1/|1 + g|2 for a perfectly registered LSR control scheme (i.e., Ga′ = Ga and all eigenvalues of RGa are equal to one). The −3-dB (50% reduction) disturbance rejection bandwidth is around νcs ≈ 1/25. For a temporal sampling rate of νs = 800 Hz, this rejection bandwidth is νc = 32 Hz. If the seeing is λ/r0 ≃ 0.65 arc sec at λ = 550 nm, the system can then compensate an average wind speed of <||v||> ≃ 12 m/s. The closed-loop −3-dB bandwidth is around νcs ≈ 1/9, which for a sampling rate of 800 Hz is ≈88 Hz. The gain margin is approximately −6 dB, and the phase margin is 63 deg at ν/νs ≈ 1/16 (0-dB open-loop bandwidth).

Fig. 3
Fig. 3

Equivalent representation of the POLC control scheme, where the estimation matrix E is followed by a nondiagonal temporal filtering matrix T(z), with T(z) = [I + g(z)M]−1g(z) and M = I - E G x ˜.

Fig. 4
Fig. 4

Evaluation directions with their associated Simpson weights and GS locations.

Fig. 5
Fig. 5

DM phase screens, reconstructed turbulent phase screens (PS), and LGS beam prints.

Fig. 6
Fig. 6

Upper panels: eigenvalues of RGa for the least-squares reconstructor R obtained from the truncated singular value of the interaction matrix Ga, together with the poles of the eigenvalues of the error rejection matrix Qa(z). Lower panels: eigenvalues of E G x ˜, where E is the estimation matrix of the MVR, together with the poles of the eigenvalues of the error rejection matrix Qx(z).

Fig. 7
Fig. 7

Eigenvalues and poles of LSR and POLC for 30% translational misregistration on all three DMs in three random directions.

Fig. 8
Fig. 8

Monte Carlo results comparing LSR and POLC for 0% and 30% translational misregistration on all three DMs in directions at 30 deg, 150 deg, and 300 deg, respectively, for 30-mas rms LGS WFS noise per subaperture and 0.5-mas rms TT NGS noise.

Equations (28)

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ψ e ( z ) = ψ in ( z ) - ψ out ( z ) ,
ψ out ( z ) = H OL ( z ) ψ e ( z ) .
ψ e ( z ) = H REJ ( z ) ψ in ,
H REJ ( z ) = [ I + H OL ( z ) ] - 1 ,
ψ out ( z ) = H CL ( z ) ψ in ( z ) ,
H CL ( z ) = H OL ( z ) [ I + H OL ( z ) ] - 1 = H OL ( z ) H REJ ( z ) ,
R = ( G a T G a + P a ) - 1 G a T ,
E = ( G x T C η - 1 G x + C x - 1 ) - 1 G x T C η - 1 .
F = H a H x ,
H a = ( H a T W H a + P a ) - 1 H a T W .
u ^ = x ^ + e ^ x = E s ^ 0 ,
g ( z ) = δ / ( z 2 - α z - β ) ,
g ( n ) = δ / ( α 2 + 4 β ) 1 / 2 [ ( c + ) n - 1 - ( c - ) n - 1 ] Θ ( n - 1 ) ,
c ± = α / 2 ± ( α 2 + 4 β ) 1 / 2 / 2 ,
H CL ( z ) = [ I + G a R g ( z ) ] - 1 G a R g ( z ) .
H CL ( z ) = G a Q a ( z ) R g ( z ) ,
Q a ( z ) = [ I + R G a g ( z ) ] - 1 .
H CL ( z ) = G a ( I - P a ) R g ( z ) 1 + g ( z ) + G a P a R g ( z ) .
H CL ( z ) = G x ˜ Q x ( z ) E g ( z ) ,
Q x ( z ) = [ I + E G x ˜ g ( z ) ] - 1 ,
H CL ( z ) = G x ˜ T ( z ) E [ I + G x ˜ T ( z ) E ] - 1 ,
= G x ˜ T ( z ) [ I + E G x ˜ T ( z ) ] - 1 E ,
= G x ˜ Q x ( z ) E g ( z ) ,
Q x ( z ) = [ I + ( E G x ˜ + M ) g ( z ) ] - 1 ,
E G x ˜ + M = I + E ( G x ˜ - G x ˜ ) .
s ^ 0 ( n ) = s ( n ) + G x ˜ x ^ ( n ) ,
e ^ x ( n ) = E s ^ 0 ( n ) - x ^ ( n ) ,
x ^ ( n + 1 ) = α x ^ ( n ) + β x ^ ( n - 1 ) + δ e ^ x ( n - 1 ) ,

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