Abstract

We propose an optimal approach for the phase reconstruction in a large field of view (FOV) for multiconjugate adaptive optics. This optimal approach is based on a minimum-mean-square-error estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the Cn2 profile in order to optimally estimate the correction wave front to be applied to each deformable mirror (DM). This optimal approach also accounts for the fact that the number of DMs will always be smaller than the number of turbulent layers, since the Cn2 profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consists of a full tomographic reconstruction of the turbulence volume followed by a projection onto the DMs accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions [model-approximation (MA) approach], which might be a crude approximation, is also considered for comparison. This MA approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and MA approaches is proposed. It is shown that the optimal approach provides very good performance even with a small number of DMs (typically, one or two). For instance, good Strehl ratios (greater than 20%) are obtained for a 4-m telescope on a 150-arc sec×150-arc sec FOV by using only three guide stars and two DMs.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Hardy, J. E. Lefevbre, C. L. Koliopoulos, “Real time atmospheric compensation,” J. Opt. Soc. Am. 67, 360–369 (1977).
    [CrossRef]
  2. G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).
  3. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, UK, 1999).
  4. D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
    [CrossRef]
  5. F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
    [CrossRef]
  6. T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
    [CrossRef]
  7. R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605–615 (1975).
    [CrossRef]
  8. J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.
  9. R. Ragazzoni, “No laser guide stars for adaptive optics in giant telescopes?” Astron. Astrophys. Suppl. Ser. 136, 205–209 (1999).
    [CrossRef]
  10. T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
    [CrossRef]
  11. 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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
    [CrossRef]
  12. T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
    [CrossRef]
  13. A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in multiconjugate adaptive optics system,” J. Opt. Soc. Am. A 17, 1819–1827 (2000).
    [CrossRef]
  14. 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]
  15. 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]
  16. M. Tallon, R. Foy, J. Vernin, “3-D wavefront sensing for multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 517–521.
  17. D. C. Johnston, B. M. Welsh, “Analysis of multiconjugate adaptive optics,” J. Opt. Soc. Am. A 11, 394–408 (1994).
    [CrossRef]
  18. R. Flicker, F. Rigaut, B. Ellerbroek, “Comparison of multiconjugate adaptive optics configurations and control algorithms for the Gemini-South 8-m telescope,” in Adaptive Optical Systems Technology, P. Wizinovich, ed., Proc. SPIE4007, 1032–1043 (2000).
    [CrossRef]
  19. M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).
  20. R. Ragazzoni, E. Marchetti, F. Rigaut, “Modal tomography for adaptive optics,” Astron. Astrophys. 342, L53–L56 (1999).
  21. F. Roddier, “The effects of atmospherical turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. XIX, pp. 281–376.
  22. G. Rousset, “Wavefront sensing,” in Adaptive Optics for Astronomy, D. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Cargèse, France,1993), pp. 115–137.
  23. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).
  24. T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
    [CrossRef]
  25. E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983).
    [CrossRef]
  26. A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
    [CrossRef]
  27. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  28. F. Rigaut, E. Gendron, “Laser guide star in adaptative optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  29. B. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Ulrich, ed., Proc. SPIE74, 225–233 (1976).
    [CrossRef]
  30. G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
    [CrossRef]
  31. J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
    [CrossRef]
  32. L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
    [CrossRef]
  33. W. J. Vetter, “Derivative operations on matrices,” IEEE Trans. Autom. Control AC-15, 241–244 (1970).
    [CrossRef]

2000 (3)

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in 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 (3)

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

R. Ragazzoni, “No laser guide stars for adaptive optics in giant telescopes?” Astron. Astrophys. Suppl. Ser. 136, 205–209 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

1998 (2)

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

1994 (2)

1992 (1)

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

1990 (2)

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

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

1989 (1)

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

1983 (1)

1982 (1)

1977 (1)

1976 (1)

1975 (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605–615 (1975).
[CrossRef]

1970 (1)

W. J. Vetter, “Derivative operations on matrices,” IEEE Trans. Autom. Control AC-15, 241–244 (1970).
[CrossRef]

Assémat, F.

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

Beckers, J. M.

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.

Boyer, C.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Chassat, F.

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

Conan, J.-M.

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

Dicke, R. H.

R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605–615 (1975).
[CrossRef]

Ellerbroek, B.

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

Ellerbroek, B. L.

Fletcher, M.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Flicker, R.

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

Fontanella, J.-C.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Foy, R.

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 for multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 517–521.

Fried, D. L.

Fuchs, A.

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
[CrossRef]

Fusco, T.

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

Gaffard, J.-P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Gendron, E.

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

Gigan, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Hardy, J. W.

Herriot, G.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (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]

Jagourel, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Johnston, D. C.

Kern, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Koliopoulos, C. L.

Le Louarn, M.

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in 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]

Lefevbre, J. E.

Léna, P.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Marchetti, E.

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

McGlamery, B.

B. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Ulrich, ed., Proc. SPIE74, 225–233 (1976).
[CrossRef]

Merkle, F.

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Michau, V.

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

Morris, S.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Mugnier, L.

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, L. Mugnier, G. Rous-set, “Efficient phase estimation for large field of view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

Mugnier, L. M.

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

Noll, R. J.

Ragazzoni, R.

R. Ragazzoni, “No laser guide stars for adaptive optics in giant telescopes?” Astron. Astrophys. Suppl. Ser. 136, 205–209 (1999).
[CrossRef]

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

Richardson, E.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Rigaut, F.

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

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

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

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

Robert, C.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

Roberts, S.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Roddier, F.

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

Rousset, G.

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

J.-M. Conan, L. M. Mugnier, T. Fusco, V. Michau, G. Rousset, “Myopic deconvolution of adaptive optics images using object and point spread function power spectra,” Appl. Opt. 37, 4614–4622 (1998).
[CrossRef]

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

G. Rousset, “Wavefront sensing,” in Adaptive Optics for Astronomy, D. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Cargèse, France,1993), pp. 115–137.

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

Rous-set, G.

Saddlemyer, L.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Salem, S.

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[CrossRef]

Sarazin, M.

A. Tokovinin, M. Le Louarn, M. Sarazin, “Isoplanatism in 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]

Singh, J.-P.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Tallon, M.

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
[CrossRef]

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 for multiconjugate adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1992), pp. 517–521.

Tokovinin, A.

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]

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

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

Véran, G.

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

Vernin, J.

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
[CrossRef]

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

Vetter, W. J.

W. J. Vetter, “Derivative operations on matrices,” IEEE Trans. Autom. Control AC-15, 241–244 (1970).
[CrossRef]

Wallner, E. P.

Welsh, B. M.

Appl. Opt. (1)

Astron. Astrophys. (4)

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

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).

G. Rousset, J.-C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J.-P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, 29–32 (1990).

Astron. Astrophys. Suppl. Ser. (2)

R. Ragazzoni, “No laser guide stars for adaptive optics in giant telescopes?” Astron. Astrophys. Suppl. Ser. 136, 205–209 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, L. Mugnier, V. Michau, G. Rousset, “Characterisation of adaptive optics point spread function for anisoplanatic imaging. Application to stellar field deconvolution,” Astron. Astrophys. Suppl. Ser. 142, 149–156 (2000).
[CrossRef]

Astron. J. (1)

R. H. Dicke, “Phase-contrast detection of telescope seeing and their correction,” Astron. J. 198, 605–615 (1975).
[CrossRef]

IEEE Trans. Autom. Control (1)

W. J. Vetter, “Derivative operations on matrices,” IEEE Trans. Autom. Control AC-15, 241–244 (1970).
[CrossRef]

J. Opt. (Paris) (1)

F. Chassat, “Calcul du domaine d’isoplanétisme d’un système d’optique adaptative fonctionnant à travers la turbulence atmosphérique,” J. Opt. (Paris) 20, 13–23 (1989).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

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

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]

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (1)

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR’,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
[CrossRef]

Other (13)

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

G. Rousset, “Wavefront sensing,” in Adaptive Optics for Astronomy, D. Alloin, J.-M. Mariotti, eds. (Kluwer Academic, Cargèse, France,1993), pp. 115–137.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968).

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, F. Assémat, “Multiconjugate adaptive optics:  comparison of phase reconstruction approaches for large field of view”, in Atmospheric Propagation, Adaptive Systems, and Laser Radar Technology for Remote Sensing, J. D. Gonglewski, G. W. Kadmerman, A. Kohnle, eds., Proc. SPIE4167, 168–179 (2000).
[CrossRef]

B. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” in Image Processing, J. C. Ulrich, ed., Proc. SPIE74, 225–233 (1976).
[CrossRef]

G. Herriot, S. Morris, S. Roberts, M. Fletcher, L. Saddlemyer, J.-P. Singh, G. Véran, E. Richardson, “Innovations in the Gemini adaptive optics system design,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 488–499 (1998).
[CrossRef]

L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, S. Salem, “Regularized multiframe myopic deconvolution from wavefront sensing,” in Propagation through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 134–144 (1999).
[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 through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 125–133 (1999).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” in Adaptive Optical Systems Technology, P. Wizinowich, ed., Proc. SPIE4007, 1044–1055 (2000).
[CrossRef]

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

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Very Large Telescopes and Their Instrumentation, M. H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Concept of a MCAO system. Several DMs are conjugated to different heights in the atmosphere. The wave-front analysis is made on several GSs located in the FOV.

Fig. 2
Fig. 2

Decentered part of the metapupil associated with the altitude hj. The variable vector r is defined on the telescope pupil. The zone of interest is centered on hjαi.

Fig. 3
Fig. 3

(a) Turbulence (four layers) and DM (one, two, and four) repartition for the four systems presented in Subsection 4B. (b) Geometrical repartition of the GS pupil projection and FOV on the highest layer (h=7.5 km). The physical size of the DM is equal to the physical size of the layers.

Fig. 4
Fig. 4

Singular value of the systems versus mode number. The different considered thresholds are plotted. The optimal threshold (optimal result) is chosen as the one that gives the minimal residual variance in the whole FOV of interest (150 arc sec×150 arc sec), as shown in Fig. 5.

Fig. 5
Fig. 5

Comparison between the Kolmogorov regularization (solid curve) and a SVD using different thresholds. The SR versus the FOV position is plotted for the x axis defined in Fig. 3(b).

Fig. 6
Fig. 6

Comparison of the optimal phase estimation and MA approaches in the case of a one-GS (on the optical axis) and one-DM (conjugated at 3.75 km) system. In each case, an X cut of the FOV is presented. These simulation are made for a four-layer Cn2 profile and a 4-m telescope. We plot the tomographic reconstruction (four DMs located on each turbulent layer) for comparison.

Fig. 7
Fig. 7

Comparison of the optimal phase estimation and MA approaches in the case of a one-GS (on the optical axis) and one-DM (conjugated at 6.5 km) system. Note that the DM is misplaced with regard to the Cn2 profile. In each case, an X cut of the FOV is presented. These simulations are made for a four-layer Cn2 profile and a 4-m telescope. We plot the tomographic reconstruction (four DMs located on each turbulent layer) for comparison.

Fig. 8
Fig. 8

Upper plots: comparison of iso-SR maps between the MA approach (two DMs) and the tomographic case (four DMs). Lower plots: iso-SR maps computed by using the optimal approach in the case of a two-DM and 3-GS system (case c). Three optimized FOVs are considered: 20, 60, and 120 arc sec. Note that, in all maps, only SR10% are plotted. Black corresponds to 10%, and the succeeding levels (dark to light) are 20%, 30%… .

Fig. 9
Fig. 9

Comparison of the optimal and MA approaches is for two DMs and a four-layer atmospheric profile. The FOVs of interest are, for the optimal approach, 20, 60, and 120 arc sec. The MA approach (in which the results are independent of a given FOV) is plotted as a dotted curve. The tomographic phase estimation (four DMs in the four turbulent layers) is plotted (solid curve) for comparison. All these curves are, in fact, an X cut (at Y=0) of each corresponding iso-SR map presented in Fig. 8.

Fig. 10
Fig. 10

Comparison of the optimal (dashed curve) and the MA (dotted curve) approach for two DMs and a four-layer atmospheric profile. The FOV of interest is, for the optimal approach, two areas of 5-arc sec diameter located at -60 and 60 arc sec. The tomographic phase estimation (four DMs in the four turbulent layers) is plotted (solid curve) for comparison.

Equations (36)

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

Φ(r, α)=j=1Ntϕj(r+hjα),
={α}FOVΦˆ(r, α)-Φ(r, α)2 dαΦ,noise,
Φm(r, αi)=Φ(r, αi)+ni(r),
Φm(r, αi)=j=1Ntϕj(r+hjαi)+ni(r).
Φˆ(r, α)=k=1NDMϕˆk(r+hkα).
={α}FOVk=1NDMϕˆk(r+hkα)-j=1Ntϕj(r+hjα)2 dαϕ,noise.
Φ(r, α)=MαNtϕ,
Φm(r, αi)=MαiNtϕ+ni,
Φˆ(r, α)=MαNDMϕˆ,
ϕ=ϕ1ϕjϕNt,ϕˆ=ϕˆ1ϕˆkϕˆNDM.
={α}FOVMαNDMϕˆ-MαNtϕ2 dαϕ,noise.
ϕˆ=WΦm with Φm=MNGSNtϕ+n,
MNGSNt=(Mα1Nt ,, MαiNt ,, MαNGSNt),
Φm=Φm(r, α1)Φm(r, αi)Φm(r, αNGS,n=n1(r)ni(r)nNGS(r).
W=W1WjWNDM,
ϕˆj=WjΦm.
={α}FOVMαNDM(WMNGSNtϕ+Wn)-MαNtϕ2ϕ,noise dα.
W={α}FOV(MαNDM)TMαNDM dα+×{α}FOV(MαNDM)TMαNt dα×Cϕ(MNGSNt)T[MNGSNtCϕ(MNGSNt)T+Cn]-1,
WNDM=Nt=Cϕ(MNGSNt)T[MNGSNtCϕ(MNGSNt)T+Cn]-1.
={α}FOVMαNt(ϕˆ-ϕ)2 dαϕ,noise.
=ϕˆ-ϕ2ϕ,noise,
PNDM,Nt={α}FOV(MαNDM)TMαNDM dα+×{α}FOV(MαNDM)TMαNt dα.
Φα(r)j=1NELϕj(r+hjα),
Φαim(r)j=1NELϕj(r+hjαi)+ni(r).
WMA=Cϕ(MNGSNEL)T[MNGSNELCϕ(MNGSNEL)T+CN]-1.
ϕj(ρj)=l=2al, jZl, j(ρj),
Dj=D+2hjαmax.
σres2(α)=Φ(r, α)-Φˆ(r, α)2,
ϕˆ=[(MNGSNEL)TMNGSNEL]+(MNGSNEL)TΦm,
AB=AB11AB1nABm1ABmn.
={α}FOVtrace[(MαNELWMNGSNt-MαNt)×ϕϕT(MαNELWMNGSNt-MαNt)T+MαNELWnnT(MαNtW)T]dα.
Cϕ=ϕ1ϕ1T0000000000ϕjϕjT0000000000ϕNtϕNtT,
Cn=n1n1T0000000000niniT0000000000nNGSnNGST,
={α}FOVtrace[MαNtCϕ(MαNt)T+MαNELWMNGSNtCϕ(MNGSNt)TW T(MαNEL)T-2MαNtCϕ(MNGSNt)TW T(MαNEL)T+MαNELWCnW T(MαNEL)T]dα.
W={α}FOV[(MαNEL)TMαNELWMNGSNtCϕ(MNGSNt)T-(MαNEL)TMαNtCϕ(MNGSNt)T+(MαNEL)TMαNtWCn]dα=0,
W={α}FOV(MαNEL)TMαNEL dα+{α}FOV(MαNEL)TMαNt dα×Cϕ(MNGSNt)T[MNGSNtCϕ(MNGSNt)T+Cn]-1,

Metrics