Abstract

Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42m telescope case.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.
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    [CrossRef]
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  16. T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
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  17. D. T. Gavel, “Tomography for multiconjugate adaptive optics systems using laser guide stars,” Proc. SPIE 5490, 1356-1373 (2004).
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  18. B. L. Ellerbroek, “Adaptive optics without borders: performance evaluation in the infinite aperture limit,” Proc. SPIE 5490, 625-636 (2004).
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  19. B. L. Ellerbroek, “Linear systems modeling of adaptive optics in the spatial-frequency domain,” J. Opt. Soc. Am. A 22, 310-322 (2005).
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    [CrossRef]
  22. F. Rigaut and E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677-684 (1992).
  23. R. Ragazzoni, “Multiple field of view layer oriented,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2001), Vol. 58, pp. 75-82.
  24. C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”
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    [CrossRef]
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  27. F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
    [CrossRef]
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2008

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

A. Tokovinin, “Performance and error budget of a GLAO system,” Proc. SPIE 7015, 701526 (2008).
[CrossRef]

2007

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
[CrossRef]

2006

2005

2004

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233, 27-38 (2004).
[CrossRef]

D. T. Gavel, “Tomography for multiconjugate adaptive optics systems using laser guide stars,” Proc. SPIE 5490, 1356-1373 (2004).
[CrossRef]

B. L. Ellerbroek, “Adaptive optics without borders: performance evaluation in the infinite aperture limit,” Proc. SPIE 5490, 625-636 (2004).
[CrossRef]

2002

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

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

2001

2000

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

F. Rigaut, B. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

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

1999

1998

F. Rigaut, J.-P. Veran, and O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

1994

1992

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

1990

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

1982

A. Tarantola and B. Valette, “Generalized nonlinear inverse problems solved using the least squares criterion,” Rev. Geophys. Space Phys. 20, 219-232 (1982).
[CrossRef]

Assémat, F.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
[CrossRef]

Bello, D.

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

Buat, V.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Burgarella, D.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Cayatte, V.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Conan, J.-M.

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

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

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

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

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Conan, R.

L. Jolissaint, J.-P. Veran, and R. Conan, “Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach,” J. Opt. Soc. Am. A 23, 382-394 (2006).
[CrossRef]

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

Courbin, F.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Ellerbroek, B.

F. Rigaut, B. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

Ellerbroek, B. L.

Flicker, R.

F. Rigaut, B. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

Flores, H.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Foy, R.

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

Fusco, T.

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

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

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

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

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Gavel, D. T.

D. T. Gavel, “Tomography for multiconjugate adaptive optics systems using laser guide stars,” Proc. SPIE 5490, 1356-1373 (2004).
[CrossRef]

Gendron, E.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
[CrossRef]

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

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Guinouard, I.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Hammer, F.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
[CrossRef]

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Hubin, N.

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

Jocou, L.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Johnston, D. C.

Jolissaint, L.

Kulcsár, C.

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”

Lai, O.

F. Rigaut, J.-P. Veran, and O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

Lançon, A.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Le Louarn, M.

Le Roux, B.

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

Michau, V.

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

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

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

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

Monnet, G.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Mouchine, M.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Mugnier, L.

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

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

Mugnier, L. M.

Neichel, B.

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

Petit, C.

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”

Ragazzoni, R.

R. Ragazzoni, “Multiple field of view layer oriented,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2001), Vol. 58, pp. 75-82.

Raynaud, H.-F.

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”

Rigaud, F.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Rigaut, F.

F. Rigaut, B. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

F. Rigaut, J.-P. Veran, and O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

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

F. Rigaut, “Ground conjugate wide field adaptive optics for the ELTs,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 11-16.

Rouan, D.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Rousset, G.

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

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

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

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

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Sarazin, M.

Sayede, F.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Tallon, M.

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

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

Tarantola, A.

A. Tarantola and B. Valette, “Generalized nonlinear inverse problems solved using the least squares criterion,” Rev. Geophys. Space Phys. 20, 219-232 (1982).
[CrossRef]

Tokovinin, A.

A. Tokovinin, “Performance and error budget of a GLAO system,” Proc. SPIE 7015, 701526 (2008).
[CrossRef]

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

A. Tokovinin and E. Viard, “Limiting precision of tomographic phase estimation,” J. Opt. Soc. Am. A 18, 873-882 (2001).
[CrossRef]

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

Valette, B.

A. Tarantola and B. Valette, “Generalized nonlinear inverse problems solved using the least squares criterion,” Rev. Geophys. Space Phys. 20, 219-232 (1982).
[CrossRef]

Veran, J.-P.

L. Jolissaint, J.-P. Veran, and R. Conan, “Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach,” J. Opt. Soc. Am. A 23, 382-394 (2006).
[CrossRef]

F. Rigaut, J.-P. Veran, and O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

Vérinaud, C.

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233, 27-38 (2004).
[CrossRef]

Viard, E.

A. Tokovinin and E. Viard, “Limiting precision of tomographic phase estimation,” J. Opt. Soc. Am. A 18, 873-882 (2001).
[CrossRef]

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

Welsh, B. M.

Zamkotsian, F.

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

Astron. Astrophys.

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

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

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

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

F. Assémat, E. Gendron, and F. Hammer, “The FALCON concept: multi-object adaptive optics and atmospheric tomography for integral field spectroscopy--principles and performance on an 8-m telescope,” Mon. Not. R. Astron. Soc. 376, 287-312 (2007).
[CrossRef]

Opt. Commun.

C. Vérinaud, “On the nature of the measurements provided by a pyramid wave-front sensor,” Opt. Commun. 233, 27-38 (2004).
[CrossRef]

Opt. Lett.

Proc. SPIE

F. Rigaut, B. Ellerbroek, and R. Flicker, “Principles, limitations, and performance of multiconjugate adaptive optics,” Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, and G. Rousset, “Noise propagation for multiconjugate adaptive optics system,” Proc. SPIE 4538, 144-155 (2002).
[CrossRef]

D. T. Gavel, “Tomography for multiconjugate adaptive optics systems using laser guide stars,” Proc. SPIE 5490, 1356-1373 (2004).
[CrossRef]

B. L. Ellerbroek, “Adaptive optics without borders: performance evaluation in the infinite aperture limit,” Proc. SPIE 5490, 625-636 (2004).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and L. Mugnier, “Isoplanatic angle and optimal guide star separation for multiconjugate adaptive optics,” Proc. SPIE 4007, 1044-1055 (2000).
[CrossRef]

B. Neichel, T. Fusco, J.-M. Conan, C. Petit, and G. Rousset, “PSD based simulation algorithm for Wide FoV AO design. Application to ELT studies,” Proc. SPIE 7015, 701573 (2008).
[CrossRef]

F. Rigaut, J.-P. Veran, and O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” Proc. SPIE 3353, 1038-1048 (1998).
[CrossRef]

A. Tokovinin, “Performance and error budget of a GLAO system,” Proc. SPIE 7015, 701526 (2008).
[CrossRef]

Rev. Geophys. Space Phys.

A. Tarantola and B. Valette, “Generalized nonlinear inverse problems solved using the least squares criterion,” Rev. Geophys. Space Phys. 20, 219-232 (1982).
[CrossRef]

Other

F. Hammer, F. Sayede, E. Gendron, T. Fusco, D. Burgarella, V. Cayatte, J.-M. Conan, F. Courbin, H. Flores, I. Guinouard, L. Jocou, A. Lançon, G. Monnet, M. Mouchine, F. Rigaud, D. Rouan, G. Rousset, V. Buat, and F. Zamkotsian, “The FALCON concept: multi-object spectroscopy combined with MCAO in near-IR,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 139-148.

R. Ragazzoni, “Multiple field of view layer oriented,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2001), Vol. 58, pp. 75-82.

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, ONERA, BP72, Chatillon FR-92322, are preparing a manuscript to be called, “LQG control for AO and MCAO: experimental and numerical analysis.”

F. Rigaut, “Ground conjugate wide field adaptive optics for the ELTs,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 11-16.

J.-M. Conan, B. Le Roux, D. Bello, T. Fusco, and G. Rousset, “Optimal reconstruction in multiconjugate adaptive optics,” in Beyond Conventional Adaptive Optics: ESO Conference and Workshop (European Southern Observatory, 2002), Vol. 58, pp. 209-215.

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Figures (20)

Fig. 1
Fig. 1

Illustration of the system geometry. In this example, the atmosphere is simulated with three layers at altitudes h n = 1 , 2 , 3 , weighted by a λ n = 1 , 2 , 3 factor ( n = 1 N L λ n = 1 ) . Two guide stars are considered in directions α i = 1 , 2 , the optimization is done in three directions β j = 1 , 2 , 3 , the correction is perfomed with two DMs at altitudes h n = 1 , 2 D M , and the final performance is evaluated in one direction θ.

Fig. 2
Fig. 2

System geometry for the 2GS two-layer simple case. The altitude of layers is h 1 = 0 and h 2 = h . Two GSs are considered in directions α 1 and α 2 , and the separation α 12 between the GSs is 2 arcmin. Performance is evaluated at the center of the FoV: θ = 0 .

Fig. 3
Fig. 3

Comparison of residual PSDs for the MMSE reconstruction (solid curve) and untruncated LSE reconstruction (dashed curve). Uncorrected Von-Kármán (dotted curve) and on-axis reconstruction (dashed–dotted curve) PSDs are also plotted for comparison. In this example, the two layers have the same turbulent strength and the WFS cut-off frequency is f c = 0.9 m 1 . Two unseen frequencies appear for f 1 = 0.215 m 1 and f 2 = 0.645 m 1 , and two neutral frequencies appear for f 1 = 0.43 m 1 and f 2 = 0.86 m 1 .

Fig. 4
Fig. 4

Same as Fig. 3 with the TLSE reconstructor. The threshold was optimized to minimize the residual variance.

Fig. 5
Fig. 5

Influence of turbulence strength distribution on MMSE reconstruction error.

Fig. 6
Fig. 6

Two-dimensional residual PSDs for the 2GS constellation with the two-layer profile (left) and the ten-layer profile (right). Log scale and inverted colors are used. The GS orientation is the same as in Table 2.

Fig. 7
Fig. 7

Two-dimensional residual PSDs for the 4GS (top) and 8GS (bottom) cases. From left to right: MMSE, TLSE, and nontruncated LSE. Log scale and inverted colors are used. All PSDs are displayed with same scale. The GSs’ orientation are the same orientation as in Table 2.

Fig. 8
Fig. 8

Residual PSD for an error in the altitude of the reconstructed layer. Top, upper altitude is overestimated ( 8.5 km instead of 8 km ). Bottom, upper altitude is underestimated ( 7.5 km instead of 8 km ).

Fig. 9
Fig. 9

Ten-layer profile. Effect of an error on the reconstructed altitudes of each layer. “% of error” means that each reconstructed layer is at an altitude of H ± H X % .

Fig. 10
Fig. 10

Residual PSD for a model error in the number of layers. The real profile is made of two layers, whereas the reconstruction model uses only one layer either in the telescope pupil (solid curve) or at an altitude of 4 km (dashed–dotted curve). The MMSE and TLSE cases are superimposed.

Fig. 11
Fig. 11

Influence of the number of layers used in the reconstruction process. The real profile is the ten layers.

Fig. 12
Fig. 12

Residual phase PSD for an error in noise priors. Top, overestimation of noise by a factor of 10: C b = 10 C b , t . Bottom, underestimation of noise by a factor of 10: C b = C b , t 10 .

Fig. 13
Fig. 13

Residual variance of the MMSE (solid curves) and TLSE (dashed curve) reconstructors with wrong noise model. Error in noise are given in percent of real noise. Dotted lines symbolize the minimal variance level when no errors on noise priors are committed.

Fig. 14
Fig. 14

Robustness of the MMSE/TLSE reconstructor to changes of “real” conditions. The “real” noise level (defined by C b , t ) ranges from 90 % to + 90 % around a reference level ( 0.5 rd 2 when “% of deviation of the real noise variance” = 0 ). The solid and dashed curves show the residual variance for perfectly tuned MMSE and TLSE reconstructors: noise priors follow the real noise variations. Dotted and dotted–dashed curves show the residual variance when noise priors are set to the reference noise level.

Fig. 15
Fig. 15

Error on turbulence strength priors with real turbulence distribution defined by [ λ 1 , t = 0.9 , λ 2 , t = 0.1 ]. Top, turbulence strength distribution used by the model is [ λ 1 = 0.1 , λ 2 = 0.9 ] (solid curve). For comparison, we plot the residual PSD if the model were correct (dashed curve). Bottom, turbulence strength distribution used by the model is [ λ 1 = 0.5 , λ 2 = 0.5 ].

Fig. 16
Fig. 16

Geometry used in the simulations. Top, one direction of optimization is considered at the center of the field. Bottom, optimization is performed over the entire field.

Fig. 17
Fig. 17

SR maps for MOAO (top) and GLAO (bottom). GS are 45° rotated compared with Table 2. The SR have been linearly interpolated on a 26 × 26 grid. For MOAO, the SR is 50 % at the center of the field. For GLAO, the SR is 10 % at the center of the field.

Fig. 18
Fig. 18

Mean SR over the field in function of the number of DMs. Error bars represent the standard deviation of the SR.

Fig. 19
Fig. 19

SR maps for an MCAO working with 3 DMs at [ 0 , 3.5 , 9.3 ] km . Comparison between TLSE (top) and MMSE (bottom) reconstructors. SR[min,max,mean,standard devation] = [ 10 % , 42 % , 25 % , 6 % ] for the TLSE and [30%, 57%, 47%, 6%] for MMSE.

Fig. 20
Fig. 20

SR MMSE in the EL approach: turbulence volume is reconstructed only at DMs’ altitudes. Top, TLSE reconstructor SR[min,max,mean,standard deviation] = [ 7 % , 47 % , 21 % , 7 % ] . Bottom, MMSE reconstructor. SR[min,max,mean,standard deviation] = [ 24 % , 58 % , 42 % , 6 % ] .

Tables (2)

Tables Icon

Table 1 Ten-Layer Turbulence Profile Altitudes and Relative Layer Strength

Tables Icon

Table 2 Simulation Configurations

Equations (30)

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σ res , θ 2 = 0 PSD θ res ( f ) F p ( f ) d f
F p ( f ) = 1 [ 2 J 1 ( π D f ) π D f ] 2 ,
C φ n = λ n C ϕ ,
C ϕ ( f ) = 0.023 ( 1 r 0 ) 5 3 ( f 2 + 1 L 0 ) 11 6 ,
λ n = C n 2 ( h n ) δ h n n = 1 N L C n 2 ( h n ) δ h n ,
ϕ ̃ θ res ( f ) = ϕ ̃ θ ( f ) ϕ ̃ θ corr ( f ) ,
ϕ ̃ θ ( f ) = n = 1 L φ ̃ n ( f ) e 2 j π f h n θ ,
ϕ ̃ θ corr ( f ) = n = 1 N D M φ ̃ n D M ( f ) e 2 j π f h n D M θ ,
f c D M = N act 2 D ,
ϕ ̃ θ = P θ L φ turb , ϕ ̃ θ corr = P θ D M φ ̃ D M ,
ϕ ̃ meas = M P α L φ ̃ turb + b ,
φ D M = W ϕ ̃ meas ,
W = P opt W tomo .
φ ̃ ̂ turb = W tomo ϕ ̃ meas ,
σ res 2 = φ ̃ turb W tomo ( M P α L φ ̃ turb + b ) 2 .
W M M S E = [ ( M P α L ) T ( C b ) 1 M P α L + C φ n 1 ] 1 ( M P α L ) T ( C b ) 1 ,
W M M S E = C φ n ( M P α L ) T [ M P α L C φ n ( M P α L ) T + C b ] 1 .
W M M S E = [ ( M P α L ) T M P α L + σ 2 C φ n 1 ] 1 ( M P α L ) T .
σ res 2 = ϕ mes M P α L W tomo ϕ mes 2 .
W L S E = [ ( M P α L ) T M P α L ] 1 ( M P α L ) T .
φ D M = P opt φ ̃ ̂ turb .
P opt = [ ( P β j D M N ) T P β j D M N β ] 1 ( P β j D M N ) T P β j L β ,
ϕ ̃ θ res = P θ L φ ̃ turb P θ D M W ( M P α L φ ̃ turb + b ) .
PSD θ res = ( P θ L P θ D M W M P α L ) C φ n , t ( P θ L P θ D M W M P α L ) T + ( P θ D M W ) C b , t ( P θ D M W ) T .
PSD θ = 0 res = { σ 2 [ 2 cos ( 2 π f ( α 1 θ ) h ) cos ( 2 π f ( α 2 θ ) h ) ] 2 sin 2 ( π f α 12 h ) M 2 for f < f c and for nontruncated frequencies C ϕ for f f c or for truncated frequencies } ,
PSD θ = 0 res = { C ϕ { 2 M C ϕ λ 1 λ 2 σ 2 [ 2 cos ( 2 π f ( α 1 θ ) h ) cos ( 2 π f ( α 2 θ ) h ) ] + σ 4 4 sin 2 ( π f α 12 h ) M 4 C ϕ 2 λ 1 λ 2 + 2 M 2 σ 2 C ϕ + σ 4 } for f < f c C ϕ for f f c } .
PSD θ = 0 res = ( σ 2 2 M 2 ) ,
PSD θ = 0 res = C ϕ ( 8 M 2 C ϕ λ 1 λ 2 + σ 2 2 M 2 C ϕ + σ 2 ) .
P opt = P β L .
P opt = P β j L β ,

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