Abstract

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.

© 2002 Optical Society of America

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  1. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
    [CrossRef]
  2. J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
    [CrossRef]
  3. F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
    [CrossRef]
  4. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
    [CrossRef]
  5. F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  6. M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
    [CrossRef]
  7. R. Foy, A. Labeyrie, “Feasibility of adaptive optics telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).
  8. J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
    [CrossRef]
  9. R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).
  10. R. Ragazzoni, “Robust tilt determination from laser guide star using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).
  11. D. L. Fried, J. F. Belsher, “Analysis of fundamental limits to artificial guide star adaptive optics systems performance for astronomical imaging,” J. Opt. Soc. Am. A 11, 277–287 (1994).
    [CrossRef]
  12. C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
    [CrossRef]
  13. R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
    [CrossRef]
  14. R. Foy, “Laser Guide Star advanced concepts: the cone effect,” in Laser Guide Star Adaptive Optics for Astronomy, (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 25–57.
  15. 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 Muenchen, Germany, 1988), Vol. 2, pp. 693–703.
  16. D. C. Johnston, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
    [CrossRef]
  17. 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]
  18. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in E. Wolf, editor, Progress in Optics XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.
  19. A. T. Young, “Aperture filtering and saturation of scintillation,” J. Opt. Soc. Am. 60, 248–250 (1970).
    [CrossRef]
  20. M. Tallon, R. Foy, “Adaptive telescope with laser probe—isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).
  21. B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
    [CrossRef]
  22. M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing and multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei Muenchen, Germany, 1992), pp. 517–521.
  23. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999).
  24. C. Boyer, V. Michau, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the come-on project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–421 (1990).
    [CrossRef]
  25. B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multi-conjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2539–2547 (2001).
    [CrossRef]
  26. M. Le Louarn, “Multiconjugate adaptive optics with laser guide stars: performance in the infrared and the visible,” manuscript available from the author.
  27. R. Hudgin, “Wave-front compensation error due to finite corrector-element size,” J. Opt. Soc. Am. 67, 393–395 (1977).
    [CrossRef]
  28. R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).
  29. A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in a multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
    [CrossRef]
  30. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  31. R. J. Sasiela, “Wave-front correction by one or more synthetic beacons,” J. Opt. Soc. Am. A 11, 379–393 (1994).
    [CrossRef]
  32. G. A. Tyler, “Merging: a new method for tomography through random media,” J. Opt. Soc. Am. A 11, 409–424 (1994).
    [CrossRef]
  33. I. A. De La Rue, B. L. Ellerbroek, “A study of multiple guide stars to improve the performance of laser guide star adaptive optical systems,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 310–319 (1998).
    [CrossRef]
  34. R. R. Parenti, R. J. Sasiela, “Laser guide star systems for astronomical applications,” J. Opt. Soc. Am. A 11, 288–309 (1994).
    [CrossRef]
  35. D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
    [CrossRef]
  36. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
    [CrossRef]
  37. G. Wahba, J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Mon. Weather Rev. 108, 1122–1143 (1979).
    [CrossRef]
  38. G. A. Tyler, “Rapid evaluation of d0: the effective diameter of a laser-guide-star adaptive-optics system,” J. Opt. Soc. Am. A 11, 325–338 (1994).
    [CrossRef]
  39. V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
    [CrossRef]
  40. 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]
  41. M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
    [CrossRef]
  42. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  43. T. Fusco, “Correction partielle et anisoplanétisme en optique adaptative: traitement a posteriori et optique adaptative multiconjuguée,” Ph.D. thesis (Université de Nice Sophia-Antipolis, Nice, France, 2000).

2001 (1)

2000 (2)

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

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

1999 (1)

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

1998 (3)

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

1997 (2)

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

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

1995 (1)

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

1994 (8)

1992 (2)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

1990 (1)

M. Tallon, R. Foy, “Adaptive telescope with laser probe—isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

1987 (1)

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

1985 (1)

R. Foy, A. Labeyrie, “Feasibility of adaptive optics telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

1982 (1)

1980 (1)

1979 (1)

G. Wahba, J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Mon. Weather Rev. 108, 1122–1143 (1979).
[CrossRef]

1977 (1)

1970 (1)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Adcock, M. J.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

An, J.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Angel, J. R. P.

Arsenault, R.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Avicola, K.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[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 Muenchen, Germany, 1988), Vol. 2, pp. 693–703.

Beeman, B. V.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Belsher, J. F.

Beuzit, J.-L.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Biraben, F.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

Bissinger, H. D.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Boyer, C.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the come-on project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–421 (1990).
[CrossRef]

Brase, J. M.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Chazalet, F.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Conan, J.-M.

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]

Crampton, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Dainty, J. C.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Davies, R. I.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

De La Rue, I. A.

I. A. De La Rue, B. L. Ellerbroek, “A study of multiple guide stars to improve the performance of laser guide star adaptive optical systems,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 310–319 (1998).
[CrossRef]

Demailly, L.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Eckart, A.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Ellerbroek, B. L.

B. L. Ellerbroek, F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multi-conjugate adaptive optics,” J. Opt. Soc. Am. A 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, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

I. A. De La Rue, B. L. Ellerbroek, “A study of multiple guide stars to improve the performance of laser guide star adaptive optical systems,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 310–319 (1998).
[CrossRef]

Erbert, G. V.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Fletcher, J. M.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Foy, R.

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

M. Tallon, R. Foy, “Adaptive telescope with laser probe—isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

R. Foy, A. Labeyrie, “Feasibility of adaptive optics telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing and multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei Muenchen, Germany, 1992), pp. 517–521.

R. Foy, “Laser Guide Star advanced concepts: the cone effect,” in Laser Guide Star Adaptive Optics for Astronomy, (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 25–57.

Fried, D. L.

Friedman, H. W.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Fusco, T.

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]

T. Fusco, “Correction partielle et anisoplanétisme en optique adaptative: traitement a posteriori et optique adaptative multiconjuguée,” Ph.D. thesis (Université de Nice Sophia-Antipolis, Nice, France, 2000).

Gavel, D. T.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Gendron, E.

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Gigan, P.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Glindemann, A.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Grynberg, G.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

Hackenberg, W.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Holstenberg, H.-C.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Hubin, N.

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Hudgin, R.

Jagourel, P.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Johnston, D. C.

Kanz, K.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Kasper, M.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Klückers, V. A.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

Labeyrie, A.

R. Foy, A. Labeyrie, “Feasibility of adaptive optics telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Lacombe, F.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Lai, O.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Lane, R. G.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Le Louarn, M.

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

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

Liu, M. C.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Lloyd-Hart, M.

Macintosh, B.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Marchetti, E.

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

Max, C. E.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

McCarthy, D.

McCullough, P. R.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

Michau, V.

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the come-on project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–421 (1990).
[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]

Migus, A.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

Mugnier, L. M.

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]

Munro, I.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

Neeb, K. P.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Nicholls, T. W.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

Olivier, S. S.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Ott, T.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Parenti, R. R.

Patience, J.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Pilkington, J. D. H.

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Quirrenbach, A.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Rabaud, D.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

Rabien, S.

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

Ragazzoni, R.

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 star using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

Rigaut, F.

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

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

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

Rigaut, F. J.

B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in E. Wolf, editor, Progress in Optics XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.

Rouan, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Rousset, G.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the come-on project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–421 (1990).
[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]

Salmon, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Sandler, D. G.

Sarazin, M.

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

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Sasiela, R. J.

Southwell, W. H.

Stahl, S.

Stilburn, J.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Tallon, M.

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

M. Tallon, R. Foy, “Adaptive telescope with laser probe—isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing and multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei Muenchen, Germany, 1992), pp. 517–521.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Thomas, J.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Tokovinin, A.

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

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Tyler, G. A.

Véran, J. P.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Vernin, J.

M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing and multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei Muenchen, Germany, 1992), pp. 517–521.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Wahba, G.

G. Wahba, J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Mon. Weather Rev. 108, 1122–1143 (1979).
[CrossRef]

Waltjen, K. E.

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Welsh, B. M.

Wendelberger, J.

G. Wahba, J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Mon. Weather Rev. 108, 1122–1143 (1979).
[CrossRef]

Wooder, N. J.

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

Young, A. T.

Astron. Astrophys. (5)

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

R. Foy, A. Labeyrie, “Feasibility of adaptive optics telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

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

M. Tallon, R. Foy, “Adaptive telescope with laser probe—isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

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

Astron. Astrophys. Suppl. Ser. (2)

V. A. Klückers, N. J. Wooder, T. W. Nicholls, M. J. Adcock, I. Munro, J. C. Dainty, “Profiling of atmospheric turbulence strength and velocity using a generalised SCIDAR technique,” Astron. Astrophys. Suppl. Ser. 130, 141–155 (1998).
[CrossRef]

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. Suppl. Ser. 111, 569–578 (1995).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (10)

G. A. Tyler, “Rapid evaluation of d0: the effective diameter of a laser-guide-star adaptive-optics system,” J. Opt. Soc. Am. A 11, 325–338 (1994).
[CrossRef]

R. J. Sasiela, “Wave-front correction by one or more synthetic beacons,” J. Opt. Soc. Am. A 11, 379–393 (1994).
[CrossRef]

G. A. Tyler, “Merging: a new method for tomography through random media,” J. Opt. Soc. Am. A 11, 409–424 (1994).
[CrossRef]

R. R. Parenti, R. J. Sasiela, “Laser guide star systems for astronomical applications,” J. Opt. Soc. Am. A 11, 288–309 (1994).
[CrossRef]

D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–945 (1994).
[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]

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

D. C. Johnston, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
[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]

D. L. Fried, J. F. Belsher, “Analysis of fundamental limits to artificial guide star adaptive optics systems performance for astronomical imaging,” J. Opt. Soc. Am. A 11, 277–287 (1994).
[CrossRef]

Mon. Not. R. Astron. Soc. (2)

M. Le Louarn, R. Foy, N. Hubin, M. Tallon, “Laser guide star for 3.6m and 8m telescopes: performance and astrophysical implications,” Mon. Not. R. Astron. Soc. 295, 756 (1998).
[CrossRef]

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Mon. Weather Rev. (1)

G. Wahba, J. Wendelberger, “Some new mathematical methods for variational objective analysis using splines and cross validation,” Mon. Weather Rev. 108, 1122–1143 (1979).
[CrossRef]

Nature (London) (1)

J. D. H. Pilkington, “Artificial guide stars for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Publ. Astron. Soc. Pac. (2)

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada–France–Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236 (1953).
[CrossRef]

Science (1)

C. E. Max, S. S. Olivier, H. W. Friedman, J. An, K. Avicola, B. V. Beeman, H. D. Bissinger, J. M. Brase, G. V. Erbert, D. T. Gavel, K. Kanz, B. Macintosh, K. P. Neeb, K. E. Waltjen, M. C. Liu, J. Patience, “Image improvement from sodium layer laser guide star adaptive optics system,” Science 277, 1649–1652 (1997).
[CrossRef]

Waves Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Other (14)

I. A. De La Rue, B. L. Ellerbroek, “A study of multiple guide stars to improve the performance of laser guide star adaptive optical systems,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 310–319 (1998).
[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]

M. Le Louarn, “Multiconjugate adaptive optics with laser guide stars: performance in the infrared and the visible,” manuscript available from the author.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN—The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

B. L. Ellerbroek, F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 1088–1099 (2000).
[CrossRef]

M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing and multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching bei Muenchen, Germany, 1992), pp. 517–521.

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999).

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the come-on project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–421 (1990).
[CrossRef]

R. I. Davies, W. Hackenberg, T. Ott, A. Eckart, H.-C. Holstenberg, S. Rabien, A. Quirrenbach, M. Kasper, “Alfa: first operational experience of the MPE/MPIA laser guide star system for adaptive optics,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 116–124 (1998).
[CrossRef]

R. Foy, “Laser Guide Star advanced concepts: the cone effect,” in Laser Guide Star Adaptive Optics for Astronomy, (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 25–57.

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 Muenchen, Germany, 1988), Vol. 2, pp. 693–703.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in E. Wolf, editor, Progress in Optics XIX, E. Wolf, ed. (North-Holland, Amsterdam, 1981), pp. 281–376.

J.-L. Beuzit, N. Hubin, E. Gendron, L. Demailly, P. Gigan, F. Lacombe, F. Chazalet, D. Rabaud, G. Rousset, “Adonis: a user-friendly adaptive optics system for the ESO 3.6 m telescope,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 955–960 (1994).
[CrossRef]

T. Fusco, “Correction partielle et anisoplanétisme en optique adaptative: traitement a posteriori et optique adaptative multiconjuguée,” Ph.D. thesis (Université de Nice Sophia-Antipolis, Nice, France, 2000).

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Figures (19)

Fig. 1
Fig. 1

Limits on the FOV in a square geometry. The bottom horizontal axis gives the angular distance (arcseconds) between each of the four LGSs and the center of the FOV. The top horizontal axis is the corresponding unvignetted fully corrected FOV. The horizontal line is the number of measurements brought by four LGSs, while the vertical one shows the geometrical limit computed from relation 9. The three curves show the number of unknowns, from top to bottom, for four, three, and two DMs, whose heights are, respectively, (1 m, 1 km, 5 km, 10 km), (1 m, 1 km, 10 km), and (1 m, 10 km).

Fig. 2
Fig. 2

EVs for a system that can measure piston and tilt from the LGSs (top curve), can measure tilt but not piston from the LGSs (middle curve), and cannot measure tilt or piston (bottom curve). The values have been scaled to the highest singular value, and the middle and top curves have been multiplied by a constant (10 and 100, respectively). Note the increasing number of modes having zero EV from the top to the bottom curve.

Fig. 3
Fig. 3

First eigenmodes in the case where tilt and piston cannot be measured from the LGS, with their number (top row) and associated EVs (normalized to the highest EV, bottom row) (top line, lowest DM; bottom line, highest DM). We can see, among others, modes resembling defocus (mode 1), coma (modes 2 and 3), and astigmatism (mode 4).

Fig. 4
Fig. 4

Last singular modes when piston and tilt can be measured from the LGS (top line, lowest DM; bottom line, highest DM). The numbers are the EVs associated with each mode. The solid black squares correspond to an odd piston.

Fig. 5
Fig. 5

Last singular modes when tilt can be measured from the LGS (top line, lowest DM; bottom line, highest DM). The numbers are the EVs associated with each mode. The solid black squares correspond to odd and even pistons.

Fig. 6
Fig. 6

Last singular modes when piston and tilt cannot be measured from the LGS (top line, lowest DM; bottom line, highest DM). The numbers are the EVs associated with each mode. The solid black squares correspond to odd and even pistons.

Fig. 7
Fig. 7

EV spectra scaled to the highest singular value when increasing the FOV (solid curve) and with zero FOV (dashed curve) in the PTR case. The FOV is widened by adding actuators to the DM conjugated to the upper height, so the number of modes is increased from 50 to 74. The number of even modes is unchanged, while 21 odd modes and three singular modes are added.

Fig. 8
Fig. 8

Odd waffle modes when FOV is increased in the PTR case. The solid black squares correspond to even pistons.

Fig. 9
Fig. 9

Geometry in two dimensions of a multiple LGS system. There are two LGSs and one NGS. Two turbulent layers are represented, each having a defocus, in opposite direction with respect to each other. We can see that even if the defocus does compensate over the field, each object in this field goes through a different part of these aberrations. They must therefore be measured and corrected if the FOV is to be increased.

Fig. 10
Fig. 10

Spectrum of EVs for four LGSs (dashed curve, PTR case) and four LGSs and one NGS (solid curve) that measures five modes (tilts, defocus, astigmatisms). The number of zero EVs drops from 12 to 7 thanks to the NGS.

Fig. 11
Fig. 11

Error maps for an NGS reconstruction of turbulence in the PR case (left) and the four-LGS PTR case (right), reconstructing a zero FOV (correction of the cone effect only). The structure observed reveals the 13×13 actuators. Note the edge effects on both error maps, seen as a crown around the reconstructed area. For the LGS case, the map is computed from the sum of the reconstructed phases. The stretch is logarithmic, and lighter shades indicate a smaller error. The contours of the IF of the lower-left-corner actuator are plotted on the NGS map. It can be seen that the shape of the corners of the error map is due to the form of the IF.

Fig. 12
Fig. 12

Error coefficient due to fitting and aliasing errors in an NGS system as a function of the linear number of subapertures. The solid and dashed curves correspond to the PR and PTR cases, respectively.

Fig. 13
Fig. 13

Increase of the error due to the cone effect on an 8-m telescope as the height of the second turbulent layer increases. The simulation results are given by the solid curve, and the theoretical predictions are given by the dashed curve.

Fig. 14
Fig. 14

Error maps for the lower height (left) and the upper height (right) for the four-LGS PTR case when no FOV is reconstructed. The errors seen in these figures cancel out when the total wave front, madeup of the sum of these two contributions, is computed (see Fig. 11). The stretch is logarithmic, and lighter shades indicate a smaller error. The color bar indicates the negative log10 base of the error variance.

Fig. 15
Fig. 15

Ratio of the error coefficient to the coefficient for an on-axis NGS at the center of the field for different reconstructed FOVs. NGS modes are removed. At the edge of the field, the error coefficient is at most ∼5% higher.

Fig. 16
Fig. 16

Strehl ratio, on axis, for four-LGS 3D mapping system. One on-axis NGS would provide a Strehl ratio of 85%. One LGS would provide a Strehl ratio of 10% on an 8-m telescope.

Fig. 17
Fig. 17

Error coefficient due to the mismeasurement of the height of the highest layer as a function of the real location of this layer. The errors are computed for a correction of the cone effect only. The solid and dotted–dashed curves represent the error made on the reconstruction of the lower and higher layers, respectively. The total error (dashed curve) is not very sensitive to this mismeasurement.

Fig. 18
Fig. 18

Effect of a third layer when only two are reconstructed. This layer is located at 10 km plus the height indicated on the x axis of the plot. The solid and dotted–dashed curves represent the error made on the reconstruction of the lower and higher layers, respectively. The dashed curve is the total error (including the third layer).

Fig. 19
Fig. 19

Isoplanatic angle θ2 for two DMs with use of the three-layer atmospheric model, with one layer variable in height. Note that when the third layer is superimposed onto one of the others (i.e., when the height error is 0 or 10 km), the isoplanatic angle becomes infinite, since when only two layers are present, full correction is assumed.

Equations (13)

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

x=1-hHxpupil-hθxl,
y=1-hHypupil-hθyl,
b=AX,
f(x, y)=p(x/ds)p(y/ds),
p(x)=1-|x|if|x|10otherwise.
bil=bil-αlxi-βlyi,
αl=ixibilixi2,βl=iyibiliyi2.
bil=jδij-xixjkxk2-yiyjkyk2bjl,
bil=jδij-1Nsub2bjl.
NlasersNDM+i=1NDM 2hiθ-DhiHNaD2.
θmax=1-hmaxHD2hmax.
σf&a2=αdsr05/3.
β2=1n1n1λ2,

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