Abstract

We investigate the performance of a general multiconjugate adaptive optics (MCAO) system in which signals from multiple reference beacons are used to drive several deformable mirrors in the optical beam train. Taking an analytic approach that yields a detailed view of the effects of low-order aberration modes defined over the metapupil, we show that in the geometrical optics approximation, N deformable mirrors conjugated to different ranges can be driven to correct these modes through order N with unlimited isoplanatic angle, regardless of the distribution of turbulence along the line of sight. We find, however, that the optimal deformable mirror shapes are functions of target range, so the best compensation for starlight is in general not the correction that minimizes the wave-front aberration in a laser guide beacon. This introduces focal anisoplanatism in the wave-front measurements that can be overcome only through the use of beacons at several ranges. We derive expressions for the number of beacons required to sense the aberration to arbitrary order and establish necessary and sufficient conditions on their geometry for both natural and laser guide stars. Finally, we derive an expression for the residual uncompensated error by mode as a function of field angle, target range, and MCAO system geometry.

© 2003 Optical Society of America

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  1. J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.
  2. J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds., Proc. SPIE4004, 282–289 (2000).
    [Crossref]
  3. P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds. Proc. SPIE4004, 290–299 (2000).
    [Crossref]
  4. J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei München, Germany, 1998), Vol. 2, pp. 693–703.
  5. I. De La Rue, B. L. Ellerbroek, “Multiconjugate adaptive optics with hybrid laser beacon systems,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 290–301 (2002).
    [Crossref]
  6. D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.
  7. M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 578–587 (2003).
    [Crossref]
  8. A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  17. 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]
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    [Crossref]
  19. R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).
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    [Crossref]
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    [Crossref]
  22. S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
    [Crossref]
  23. M. Lloyd-Hart, S. M. Jefferies, J. R. P. Angel, E. K. Hege, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
    [Crossref]
  24. G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, ed. F. Roddier (Oxford U. Press, New York, 1998), p. 118.
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    [Crossref]

2002 (2)

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
[Crossref]

2001 (4)

2000 (3)

1999 (2)

M. S. Belen’kii, S. J. Karis, J. M. Brown, R. Q. Fugate, “Experimental validation of a technique to measure tilt from a laser guide star,” Opt. Lett. 24, 637–639 (1999).
[Crossref]

R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).

1997 (1)

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

1976 (1)

Ageorges, N.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

Allaert, E.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Angel, J. R. P.

M. Lloyd-Hart, S. M. Jefferies, J. R. P. Angel, E. K. Hege, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
[Crossref]

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

Angel, R.

R. Angel, M. Lloyd-Hart, “Atmospheric tomography with Rayleigh laser beacons for correction of wide fields and 30-m-class telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 270–276 (2000).
[Crossref]

Avila, R.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

Beckers, J. M.

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei München, Germany, 1998), Vol. 2, pp. 693–703.

Belen’kii, M. S.

Bonaccini, D.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Brown, J. M.

Brunetto, E.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Buzzoni, B.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Conan, R.

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

Cullum, M.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Davies, R.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

De La Rue, I.

I. De La Rue, B. L. Ellerbroek, “Multiconjugate adaptive optics with hybrid laser beacon systems,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 290–301 (2002).
[Crossref]

di Chirico, C.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Dierickx, P.

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds. Proc. SPIE4004, 290–299 (2000).
[Crossref]

Dimmler, M.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Ellerbroek, B. L.

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

I. De La Rue, B. L. Ellerbroek, “Multiconjugate adaptive optics with hybrid laser beacon systems,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 290–301 (2002).
[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]

Esposito, S.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (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]

Flicker, R. C.

Foy, R.

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

Fugate, R. Q.

Gilmozzi, R.

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds. Proc. SPIE4004, 290–299 (2000).
[Crossref]

Gray, P.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Hackenberg, W.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Hege, E. K.

M. Lloyd-Hart, S. M. Jefferies, J. R. P. Angel, E. K. Hege, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
[Crossref]

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

Hill, J. M.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

Hippler, S.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Hubin, N.

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

Hubin, N. N.

E. Viard, N. N. Hubin, M. Le Louarn, “Adaptive optics with four laser guide stars: cone effect correction on large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 106–114 (2000).
[Crossref]

Jefferies, S. M.

Karis, S. J.

Koivunen, A. C.

Le Louarn, M.

M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
[Crossref]

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
[Crossref]

E. Viard, N. N. Hubin, M. Le Louarn, “Adaptive optics with four laser guide stars: cone effect correction on large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 106–114 (2000).
[Crossref]

Lloyd-Hart, M.

M. Lloyd-Hart, S. M. Jefferies, J. R. P. Angel, E. K. Hege, “Wave-front sensing with time-of-flight phase diversity,” Opt. Lett. 26, 402–404 (2001).
[Crossref]

R. Angel, M. Lloyd-Hart, “Atmospheric tomography with Rayleigh laser beacons for correction of wide fields and 30-m-class telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 270–276 (2000).
[Crossref]

M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 578–587 (2003).
[Crossref]

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

Marchetti, E.

R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).

McKenna, D. L.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[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, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 578–587 (2003).
[Crossref]

Nelson, J. E.

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds., Proc. SPIE4004, 282–289 (2000).
[Crossref]

Neumann, U.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Noethe, L.

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

Noll, R. J.

O’Sullivan, C.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

Ott, T.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Peng, C.

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

Pique, J.-P.

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

Quattri, M.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Rabien, S.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Ragazzoni, R.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

Redfern, M.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

Riccardi, A.

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

Rigaut, F.

R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).

Rigaut, F. J.

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

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]

Roggemann, M. C.

Rousset, G.

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, ed. F. Roddier (Oxford U. Press, New York, 1998), p. 118.

Salinari, P.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

Sarazin, M.

Sarlot, R. J.

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

Schöck, M.

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

Stanton, P. C.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

Tallon, M.

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

M. Le Louarn, M. Tallon, “Analysis of modes and behavior of a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 19, 912–925 (2002).
[Crossref]

Tarenghi, M.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Tokovinin, A.

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
[Crossref]

van Kesteren, A.

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

Viard, E.

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

E. Viard, N. N. Hubin, M. Le Louarn, “Adaptive optics with four laser guide stars: cone effect correction on large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 106–114 (2000).
[Crossref]

Weiss, R.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

Astron. Astrophys. (3)

A. Tokovinin, M. Le Louarn, E. Viard, N. Hubin, R. Conan, “Optimized modal tomography in adaptive optics,” Astron. Astrophys. 378, 710–721 (2001).
[Crossref]

R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

Exp. Astron. (1)

S. Esposito, R. Ragazzoni, A. Riccardi, C. O’Sullivan, N. Ageorges, M. Redfern, R. Davies, “Absolute tilt from a laser guide star: a first experiment,” Exp. Astron. 10, 135–145 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

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

Mon. Not. R. Astron. Soc. (1)

M. Schöck, R. Foy, M. Tallon, L. Noethe, J.-P. Pique, “Performance analysis of polychromatic laser guide stars used for wavefront tilt sensing,” Mon. Not. R. Astron. Soc. 337, 910–920 (2002).
[Crossref]

Opt. Lett. (3)

Other (13)

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, ed. F. Roddier (Oxford U. Press, New York, 1998), p. 118.

D. L. McKenna, R. Avila, J. M. Hill, S. Hippler, P. Salinari, P. C. Stanton, R. Weiss, “LBT facility SCIDAR: recent results,” in Adaptive Optical Systems Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 825–836 (2003).
[Crossref]

J. R. P. Angel, M. Lloyd-Hart, E. K. Hege, R. J. Sarlot, C. Peng, “The 20/20 telescope: MCAO imaging at the individual and combined foci,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/angel_pap.pdf , 2001.

J. E. Nelson, “Design concepts for the California Extremely Large Telescope (CELT),” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds., Proc. SPIE4004, 282–289 (2000).
[Crossref]

P. Dierickx, R. Gilmozzi, “Progress of the OWL 100-m telescope conceptual design,” in Telescope Structures, Enclosures, Controls, Assembly/Integration/Validation, and Commissioning, T. A. Sebring, T. Andersen, eds. Proc. SPIE4004, 290–299 (2000).
[Crossref]

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in ESO Conference on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei München, Germany, 1998), Vol. 2, pp. 693–703.

I. De La Rue, B. L. Ellerbroek, “Multiconjugate adaptive optics with hybrid laser beacon systems,” in Adaptive Optics Systems and Technology II, R. K. Tyson, D. Bonaccini, M. C. Roggemann, eds., Proc. SPIE4494, 290–301 (2002).
[Crossref]

D. Bonaccini, W. Hackenberg, R. Davies, M. Cullum, S. Rabien, E. Brunetto, T. Ott, M. Quattri, S. Hippler, E. Allaert, M. Dimmler, M. Tarenghi, A. van Kesteren, C. di Chirico, B. Buzzoni, P. Gray, U. Neumann, “VLT Laser Guide Star Facility: from one to many LGS,” in Beyond Conventional Adaptive Optics, R. Ragazonni, ed. (Astronomical Observatory and Department of Astronomy, Padova, Italy, 2001). Available on line at http://www.adaopt.it/venice2001/proceedings/pdf/bonaccini_pap.pdf , 2001.

M. Lloyd-Hart, N. M. Milton, “Design and expected performance of the 6.5 m MMT MCAO system,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 578–587 (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]

R. Angel, M. Lloyd-Hart, “Atmospheric tomography with Rayleigh laser beacons for correction of wide fields and 30-m-class telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 270–276 (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]

E. Viard, N. N. Hubin, M. Le Louarn, “Adaptive optics with four laser guide stars: cone effect correction on large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 106–114 (2000).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Geometry of an example in which two DMs are able to correct quadratic aberration in wave fronts of objects at a particular range and anywhere in the field of view.

Fig. 2
Fig. 2

Contributions to the residual rms wave-front error from modes over the metapupil for stellar sources (solid curves) and sources at 95-km range (dashed curves). For the star, orders 1 and 2 are perfectly corrected, and the plots are coincident with the x axis. The remaining curves, from bottom to top, plot the cumulative contribution from orders 3–5, 13, and 30. For the 95-km objects, tilt introduces 180-nm error, second order is perfectly corrected, and third order is very well corrected below 50 arc sec. The curves plot the contributions from orders 1 and 2, 3, 4, 5, 13, and 30. For both sources, higher orders rapidly degrade the wave front at field angles above ∼50 arc sec.

Tables (1)

Tables Icon

Table 1 Details of the Model Atmosphere

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

ϕ(ρ, θ)=n=0m=0nζnmZnm(ρ, θ).
ϕn=0Nm=0nζnmZnmi=0Nj=0N-iαijxiyj,
Φ*(x, y; ξ, v)=0i=0j=0αij(h)XiYjdh.
Φ*N(x, y; ξ, v)=0i=0Nj=0N-iαij(h)XiYjdh.
Φ*N(x, y; ξ, v)=i=0Nk=0iikxi-kξkj=0N-il=0jjlyj-lvl0αijhˆk+ldh,
=k=0Nl=0N-kxkyli=kN-likξi-kj=lN-ijlvj-l×0αijhˆi+j-k-ldh,
ψm(x, y)=i=0Nmj=0Nm-iβij,mxiyj.
Ψ(x, y; ξ, v)=m=1Mψm(x+ξHˆm, y+vHˆm).
Ψ(x, y; ξ, v)=k=0Nl=0N-kxkyli=kN-likξi-kj=lN-ijl×vj-lm=1Mβij,mHˆmi+j-k-l.
m=1Mβij,mHˆmn=0αijhˆndh,
0ni+j.
n=0N(N-n)(n+1)=16 N(N+1)(N+2).
Φb(x, y; ξb, vb)=0hbi=0j=0αij(h)XbiYbjdh,
Ψb(x, y; ξb, vb)=m=1Mψm[x(1-Hm/hb)+ξbHˆm,y(1-Hm/hb)+vbHˆm].
0hbαij(1-h/hb)i+j-nhˆndh=m=1Mβij,m(1-Hm/hb)i+j-nHˆmn,
0ni+j.
β2,1=α2(1-hA/H2)(1-hA/hb), β2,2=α2hA(hb-hA)/H2(hb-H2).
Ψb(x, y; ξb, vb)=k=0Nl=0N-kγkl,bxkyl.
γkl,b=i=kN-likξbi-kj=lN-ijlvbj-l×m=1Mβij,m(1-Hm/hb)k+lHˆmi+j-k-l.
γk,b=i=kNikξbi-km=1Mβi,mHˆmi-k,
γ1,b=a10+a11ξb+a12ξb2++a1(N-1)ξbN-1,γ2,b=a20+a21ξb++a2(N-2)ξbN-2,  γN,b=aN0,
apq=p+qqm=1Mβp+q,mHˆmq.
n=1Nn+1=12 N(N+3),
i=0N-1j=0N-i-1cijξbivbj0
i=0N-2j=0N-i-2cijξbivbj0.
E(h)=AS(h)-MS(h)RAW,
(h)=diag(EVET),

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