Abstract

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.

© 2010 Optical Society of America

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2010 (1)

2009 (1)

2008 (3)

E. A. Laag, S. M. Ammons, D. T. Gavel, and R. Kupke, “Multiconjugate adaptive optics results from the laboratory for adaptive optics MCAO/MOAO testbed,” J. Opt. Soc. Am. A 25, 2114–2121 (2008).
[CrossRef]

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

2006 (2)

F. Quirós-Pacheco, “Reconstruction and control laws for multi-conjugate adaptive optics in astronomy,” Ph.D. dissertation (Imperial College London, 2006).

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef] [PubMed]

2005 (5)

L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005).
[CrossRef] [PubMed]

C. Paterson, “Constraints of ground-based observations: The atmosphere,” in Optics in Astrophysics, NATO Science Series, R.Foy and F.Foy, eds. (Springer, 2005), pp. 1–10.

S. Esposito, “Introduction to multi-conjugate adaptive optics systems,” C. R. Phys. 6, 1039–1048 (2005).
[CrossRef]

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

2004 (2)

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L.-M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[CrossRef]

2003 (2)

M. Lloyd-Hart and N. M. Milton, “Fundamental limits on isoplanatic correction with multiconjugate adaptive optics,” J. Opt. Soc. Am. A 20, 1949–1957 (2003).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

2002 (1)

2001 (2)

2000 (4)

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
[CrossRef]

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

R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (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 (3)

F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999).
[CrossRef]

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

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

1998 (1)

C. Dessenne, “Commande modale et predictive en optique adaptative,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1998).

1997 (2)

J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

J.-P. Véran, “Estimation de la reponse impulsionnelle et restauration d’image en optique adaptative,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1997).

1996 (1)

1995 (2)

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

E. Gendron, “Optimisation de la commande modale en optique adaptative: applications a l’astronomie,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1995).

1994 (5)

1992 (1)

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

1990 (1)

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

1988 (1)

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt, 1988).

1982 (2)

W. H. Southwell, “What’s wrong with cross coupling in modal wave-front estimation?” Proc. SPIE 365, 97–104 (1982).

D. L. Fried, “Anisoplanatism in adaptive optics,” J. Opt. Soc. Am. 72, 52–61 (1982).
[CrossRef]

1981 (1)

1976 (1)

Ageorges, N.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Ammons, S. M.

Amorim, A.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Arsenault, R.

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Assemat, F.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
[CrossRef]

Bagnara, P.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Baruffolo, A.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Bouy, H.

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

Brast, R.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Charton, J.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Chemla, F.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Conan, J. M.

J. M. Conan, “Etude de la Correction Partielle en Optique Adaptative,” Ph.D. dissertation (Université de Paris XI Orsay, 1994).

Conan, J. -M.

A. Costille, C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[CrossRef]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[CrossRef] [PubMed]

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L.-M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[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 F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
[CrossRef]

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

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

Conzelmann, R.

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

Costille, A.

Dai, G. M.

de Lesegno, P. V.

Delabre, B.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

Dessenne, C.

C. Dessenne, “Commande modale et predictive en optique adaptative,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1998).

Donaldson, R.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
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R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (2000).
[CrossRef]

Feautrier, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Fedrigo, E.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

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

Foy, R.

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Frank, C.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Fried, D. L.

Fusco, T.

A. Costille, C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
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E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
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B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L.-M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
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T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[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).
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T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
[CrossRef]

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

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

Gavel, D. T.

Gendron, E.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

E. Gendron, “Optimisation de la commande modale en optique adaptative: applications a l’astronomie,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1995).

E. Gendron and P. Léna, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

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

Gigan, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Gilles, L.

Gratadour, D.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

Hammer, F.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Herrmann, J.

Hubin, N.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Huelamo, N.

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

Jagourel, P.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Johnston, D. C.

Kern, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Kolb, J.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

Kulcsar, C.

Kulcsár, C.

Kupke, R.

Laag, E. A.

Lacombe, F.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Lagrange, A. M.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Lagrange, A. -M.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Laporte, P.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Le Louarn, M.

Le Roux, B.

Léna, P.

E. Gendron and P. Léna, “Astronomical adaptive optics I. Modal control optimization,” Astron. Astrophys. 291, 337–347 (1994).

Lima, J.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Liotard, A.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Lizon, J. L.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Lloyd-Hart, M.

Madec, P. Y.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

Madec, P. -Y.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

Maitre, H.

Marchesi, M.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Marchetti, E.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (2000).
[CrossRef]

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

Marteaud, M.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Martin, E. L.

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

Michau, V.

Milton, N. M.

Mouillet, D.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Mugnier, L. -M.

Navascus, D. B. Y.

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
[CrossRef]

Noll, R. J.

Oberti, S.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Paterson, C.

C. Paterson, “Constraints of ground-based observations: The atmosphere,” in Optics in Astrophysics, NATO Science Series, R.Foy and F.Foy, eds. (Springer, 2005), pp. 1–10.

Petit, C.

Pitsianis, N. P.

Plemmons, R. J.

Puech, M.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Puget, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Quirós-Pacheco, F.

F. Quirós-Pacheco, “Reconstruction and control laws for multi-conjugate adaptive optics in astronomy,” Ph.D. dissertation (Imperial College London, 2006).

Rabaud, D.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Rabou, P.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Ragazzoni, R.

R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (2000).
[CrossRef]

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

Raynaud, H. -F.

Reiss, R.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Rigaut, F.

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

J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

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

Rigaut, F. J.

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

Robert, C.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

Roddier, F.

F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999).
[CrossRef]

Rouan, D.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

Rousset, G.

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G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
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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).
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T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
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T. Fusco, J.-M. Conan, V. Michau, L.-M. Mugnier, and G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
[CrossRef]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

Sarazin, M.

Schreiber, L.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

Soenke, C.

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

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W. H. Southwell, “What’s wrong with cross coupling in modal wave-front estimation?” Proc. SPIE 365, 97–104 (1982).

Stadler, E.

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

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[CrossRef]

Stuik, R.

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
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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).
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E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
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J.-P. Véran, “Estimation de la reponse impulsionnelle et restauration d’image en optique adaptative,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1997).

J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

Viard, E.

Welsh, B. M.

Zamkotsian, F.

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

Zins, G.

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (5)

H. Bouy, J. Kolb, E. Marchetti, E. L. Martin, N. Huelamo, and D. B. Y. Navascus, “Multi-conjugate adaptive optics images of the trapezium cluster,” Astron. Astrophys. 477, 681–690 (2008).
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M. Tallon and R. Foy, “Adaptive telescope with laser probe—Isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

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

C. R. Phys. (3)

S. Esposito, “Introduction to multi-conjugate adaptive optics systems,” C. R. Phys. 6, 1039–1048 (2005).
[CrossRef]

N. Hubin, R. Arsenault, R. Conzelmann, B. Delabre, M. Le Louarn, S. Stroebele, and R. Stuik, “Ground layer adaptive optics,” C. R. Phys. 6, 1099–1109 (2005).
[CrossRef]

E. Gendron, F. Assemat, F. Hammer, P. Jagourel, F. Chemla, P. Laporte, M. Puech, M. Marteaud, F. Zamkotsian, A. Liotard, J.-M. Conan, T. Fusco, and N. Hubin, “FALCON: multi-object AO,” C. R. Phys. 6, 1110–1117 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

T. Fusco, G. Rousset, D. Rabaud, E. Gendron, D. Mouillet, F. Lacombe, G. Zins, P. Y. Madec, A. M. Lagrange, J. Charton, D. Rouan, N. Hubin, and N. Ageorges, “NAOS on-line characterization of turbulence parameters and adaptive optics performance,” J. Opt. A, Pure Appl. Opt. 6, 585–596 (2004).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (15)

B. L. Ellerbroek, C. Vanloan, N. P. Pitsianis, and R. J. Plemmons, “Optimizing closed-loop adaptive-optics performance with use of multiple control bandwidths,” J. Opt. Soc. Am. A 11, 2871–2886 (1994).
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B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L.-M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[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]

G. M. Dai, “Modal wave-front reconstruction with Zernike polynomials and Karhunen–Loeve functions,” J. Opt. Soc. Am. A 13, 1218–1225 (1996).
[CrossRef]

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

M. Lloyd-Hart and N. M. Milton, “Fundamental limits on isoplanatic correction with multiconjugate adaptive optics,” J. Opt. Soc. Am. A 20, 1949–1957 (2003).
[CrossRef]

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

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]

J.-P. Véran, F. Rigaut, H. Maitre, and D. Rouan, “Estimation of the adaptive optics long-exposure point-spread function using control loop data,” J. Opt. Soc. Am. A 14, 3057–3069 (1997).
[CrossRef]

J.-M. Conan, G. Rousset, and P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[CrossRef]

E. A. Laag, S. M. Ammons, D. T. Gavel, and R. Kupke, “Multiconjugate adaptive optics results from the laboratory for adaptive optics MCAO/MOAO testbed,” J. Opt. Soc. Am. A 25, 2114–2121 (2008).
[CrossRef]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsar, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (6)

T. Fusco, J.-M. Conan, V. Michau, G. Rousset, and F. Assemat, “Multi-conjugate adaptive optics: Comparison of phase reconstruction approaches for large field of view,” Proc. SPIE 4167, 168–179 (2000).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Kern, A.-M. Lagrange, P.-Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE 4839, 140–149 (2003).
[CrossRef]

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

R. Ragazzoni, J. Farinato, and E. Marchetti, “Adaptive optics for 100m class telescopes: new challenges require new solutions,” Proc. SPIE 4007, 1076–1087 (2000).
[CrossRef]

W. H. Southwell, “What’s wrong with cross coupling in modal wave-front estimation?” Proc. SPIE 365, 97–104 (1982).

E. Marchetti, R. Brast, B. Delabre, R. Donaldson, E. Fedrigo, C. Frank, N. Hubin, J. Kolb, J. L. Lizon, M. Marchesi, S. Oberti, R. Reiss, C. Soenke, S. Tordo, A. Baruffolo, P. Bagnara, A. Amorim, and J. Lima, “MAD on sky results in star oriented mode,” Proc. SPIE 7015, 70150F (2008).
[CrossRef]

Other (10)

C. Dessenne, “Commande modale et predictive en optique adaptative,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1998).

E. Gendron, “Optimisation de la commande modale en optique adaptative: applications a l’astronomie,” Ph.D. dissertation (Université Denis Diderot-Paris VII, 1995).

J.-P. Véran, “Estimation de la reponse impulsionnelle et restauration d’image en optique adaptative,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1997).

C. Paterson, “Constraints of ground-based observations: The atmosphere,” in Optics in Astrophysics, NATO Science Series, R.Foy and F.Foy, eds. (Springer, 2005), pp. 1–10.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, “Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors” (submitted to J. Opt. Soc. Am. A).

We will denote the covariance matrices in the eigenspace with an MP, which stands for modes propres, or eigenmodes in French.

J. M. Conan, “Etude de la Correction Partielle en Optique Adaptative,” Ph.D. dissertation (Université de Paris XI Orsay, 1994).

F. Quirós-Pacheco, “Reconstruction and control laws for multi-conjugate adaptive optics in astronomy,” Ph.D. dissertation (Imperial College London, 2006).

F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999).
[CrossRef]

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt, 1988).

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Figures (12)

Fig. 1
Fig. 1

(a) Normalized eigenvalues of H T H in descending order (from well-seen to unseen modes). (b) Representation of eigenmodes number 50, 200, and 217.

Fig. 2
Fig. 2

Variance distribution in the eigenspace after propagation through (a) the LS reconstructor and (b) the MMSE reconstructor ( D / r 0 = 1 and SNR = 10 ). The plots show the variance of the turbulence (diagonal of C φ M P ), the remaining error (diagonal of C φ M P ), the noise (diagonal of C w M P ), and the error related to R (diagonal of C R M P ) for the MMSE reconstructor.

Fig. 3
Fig. 3

Contributions to the global reconstruction error σ r e c 2 as a function of the FoV. The different contributions are the remaining error σ φ 2 , the measurement noise σ w 2 , and the reconstructor error σ R 2 . (a), (b), and (c) Errors propagated through the LS reconstructor with 2, 10, and 50 truncated eigenmodes, respectively. (d) Errors propagated through the MMSE reconstructor ( D / r 0 = 1 and SNR = 10 in all cases).

Fig. 4
Fig. 4

Contributions to the global reconstruction error σ r e c 2 as a function of the number of GSs. The different contributions are the remaining error σ φ 2 , the measurement noise σ w 2 , and the reconstructor error σ R 2 . (a) Errors propagated through the LS reconstructor with two truncated eigenmodes. (b) Errors propagated through the MMSE reconstructor. D / r 0 = 1 and SNR = 10 in both cases.

Fig. 5
Fig. 5

Discrete-time block diagrams for the i th eigenmode control loop. (a) Closed-loop operation. (b) Open-loop operation considered in the J i D criterion defined in Eq. (70).

Fig. 6
Fig. 6

Variance distribution in the eigenspace for the system configuration described in Subsection 3C1 ( D / r 0 = 38 at 700 nm, SNR = 10 or 100). Eigenmodes are ordered in descending order of eigenvalues.

Fig. 7
Fig. 7

Examples of analytical PSDs that are required to evaluate the criterion J i . ( D / r 0 = 38 at 700 nm and SNR = 10 or 100). (a) PSDs associated with eigenmode number 50. (b) PSDs associated with eigenmode number 200.

Fig. 8
Fig. 8

Residual variance J i = var { φ r e s , i M P } as a function of the gain g i ( D / r 0 = 38 at 700 nm and SNR = 10 ). (a) Eigenmode number 50. (b) Eigenmode number 200. The individual contributions to J i are all shown. Also, the residual variance J i neglecting the remaining error term ( turb + noise ) is also shown.

Fig. 9
Fig. 9

Optimized modal gains minimizing the criterion J i for (a) SNR = 10 , (b) SNR = 100 . (Plus signs) Gains computed by taking into account all the three terms in Eq. (69). (Squares) Gains computed by neglecting the remaining error term.

Fig. 10
Fig. 10

SR at 2.2 μ m across the center of the 2 arc min FoV obtained with the MOMGI control law. (a) SNR = 10 , (b) SNR = 100 . The optimized modal gains used in these simulations are shown in Fig. 9.

Fig. 11
Fig. 11

PSD of φ m e s , i M P , O L obtained from simulations for (a) eigenmode number 50, (b) eigenmode number 200. The theoretical PSDs of the turbulence, the remaining error, and the propagated measurement noise are also shown ( D / r 0 = 38 at 700 nm and SNR = 10 ).

Fig. 12
Fig. 12

Modal gains minimizing the criteria J i D (diamonds) and J i (plus signs).

Equations (77)

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φ t u r = ( φ t u r L 1 φ t u r L j φ t u r L N L ) .
ϕ t u r ( r , α k ) = j = 1 N L ψ t u r L j ( r + h j α k ) ,
ϕ t u r α k = M α k L φ t u r ,
M α k L = [ M α k L 1 M α k L j M α k L N L ] ,
M α L = [ ( M α 1 L ) T ( M α k L ) T ( M α N G S L ) T ] T .
ϕ t u r α = ( ϕ t u r α 1 ϕ t u r α k ϕ t u r α N G S ) ,
ϕ t u r α = M α L φ t u r .
ϕ c o r α = M α D M φ c o r .
ϕ r e s β = M β L φ t u r M β D M φ c o r .
s = D ϕ t u r α + w = D M α L φ t u r + w .
φ t u r = ( φ t u r L 1 φ t u r L j φ t u r L N L ) ,     φ t u r = ( φ t u r L 1 φ t u r L j φ t u r L N L ) .
ϕ t u r α k = M α k L j φ t u r L j ,
ϕ t u r α k = M α k L j φ t u r L j ,
M α k L = [ M α k L 1 M α k L j M α k L N L ] ,
M α k L = [ M α k L 1 M α k L j M α k L N L ] .
p α k = max j { n m o d L j } ,
n m o d = j ( n m o d L j 1 ) .
M α L = [ ( M α 1 L ) T ( M α k L ) T ( M α N G S L ) T ] T ,
M α L = [ ( M α 1 L ) T ( M α k L ) T ( M α N G S L ) T ] T .
s = D M α L φ t u r + D M α L φ t u r + w .
H D M α L .
H D M α L .
s = H φ t u r + H φ t u r + w .
φ ̂ t u r = R s ,
J L S s H φ ̂ t u r 2 .
H = U Σ V T ,
R L S = V Σ n U T ,
Σ n = diag ( x i ) ,     where   x i = { σ i 1 if   λ i λ m a x > Λ 0 if   λ i λ m a x < Λ , }
σ r e c 2 φ ̂ t u r φ t u r 2 ,
R M M S E = φ t u r s T s s T 1 ,
s H φ t u r + w .
R M M S E = [ H T C w 1 H + C φ 1 ] 1 H T C w 1 = C φ H T [ H C φ H T + C w ] 1 ,
φ ̂ t u r = R M M S E s ,
φ c o r = P D M L φ ̂ t u r .
σ r e c 2 = ϵ 2 = trace { ϵ ϵ T } = trace { C ϵ } .
ϵ = [ R H I ] φ t u r + R H φ t u r + R w ,
C ϵ R C w R T + [ R H I ] C φ [ R H I ] T + [ R H ] C φ [ R H ] T ,
C φ M P V T C φ V .
C ϵ M P V T C ϵ V = C w M P + C R M P + C φ M P ,
C w M P V T R C w R T V ,
C R M P V T [ R H I ] C φ [ R H I ] T V ,
C φ M P V T R [ H ] C φ [ H ] T R T V .
σ r e c 2 = trace { C ϵ M P } = trace { C w M P } + trace { C R M P } + trace { C φ M P } ,
σ w 2 trace { C w M P } ,
σ R 2 trace { C R M P } ,
σ φ 2 trace { C φ M P } .
n L j D j D 1 ( n L 1 + 1 ) 1 ,
σ n 2 = 0.162 ( 2 π ) 2 SNR ( D r 0 ) 5 / 3 ( 1 n s ) 5 / 3 .
C w M P = [ Σ n U T ] C w [ Σ n U T ] T ,
C R M P = [ Σ Σ n I ] V T C φ V [ Σ Σ n I ] ,
C φ M P = [ Σ n U T ] [ H ] C φ [ H ] T [ Σ n U T ] T .
s ( l ) = D ϕ r e s α ( l d s ) + w ( l ) ,
φ c o r ( l + 1 ) = N u ( l ) ,
φ m e s M P ( l ) = Σ n U T s ( l ) ,
φ c o r M P ( l ) = φ c o r M P ( l 1 ) + C M P φ m e s M P ( l ) ,
u ( l ) = V φ c o r M P ( l ) ,
φ c o r ( l + 1 ) = φ c o r ( l ) + N V C M P Σ n U T [ D ϕ r e s α ( l 1 ) + w ( l ) ] .
M α M α L = M α D M .
ϕ r e s α = M α ( φ t u r φ c o r ) + M α φ t u r .
φ t u r M P Σ n U T D M α φ t u r ,
φ t u r M P Σ n U T D M α φ t u r ,
φ c o r M P Σ n U T D M α φ c o r ,
φ m e s M P = Σ n U T s ,
w M P Σ n U T w ,
φ c o r M P ( l + 1 ) = φ c o r M P ( l ) + C M P [ φ t u r ( l 1 ) φ c o r M P ( l 1 ) + φ t u r M P ( l 1 ) + w M P ( l ) ] .
φ ̃ c o r , i M P ( z ) = H i ( z ) [ φ ̃ t u r , i M P ( z ) + φ ̃ t u r , i M P ( z ) ] + H n , i ( z ) w ̃ i M P ( z ) ,
φ r e s , i M P = φ t u r , i M P φ c o r , i M P .
φ ̃ r e s , i M P ( z ) = E i ( z ) φ ̃ t u r , i M P ( z ) H i ( z ) φ ̃ t u r , i M P ( z ) H n , i ( z ) w ̃ i M P ( z ) ,
J i PSD { φ r e s , i M P } d ω = | E i ( e j ω ) | 2 PSD { φ t u r , i M P } d ω + | H i ( e j ω ) | 2 PSD { φ t u r , i M P } d ω + | H n , i ( e j ω ) | 2 PSD { w i M P } d ω ,
J i D PSD { φ m e s , i M P } d ω = | E i ( e j ω ) | 2 PSD { φ m e s , i M P , O L } d ω ,
φ ̃ m e s , i M P ( z ) = z 2 φ ̃ r e s , i M P ( z ) + z 2 φ ̃ t u r , i M P ( z ) + z 1 w ̃ i M P ( z ) .
var { φ m e s , i M P } = var { φ r e s , i M P } + var { w i M P } + var { φ t u r , i M P } + 2   covar { φ r e s , i M P , φ t u r , i M P } + 2   covar { φ r e s , i M P , w i M P } .
covar { φ r e s , i M P , φ t u r , i M P } = var { φ t u r , i M P } + E i ( e j ω ) PSD { φ t u r , i M P } d ω .
f c ( n i ) 0.3 ( n i + 1 ) V D ,
PSD { φ t u r , i M P } j ( Σ n U T D M α ) i , j 2 PSD { φ t u r , j } ,
PSD { φ t u r , i M P } j ( Σ n U T D M α ) i , j 2 PSD { φ t u r , j } ,
PSD { w i M P } = T [ C w M P ] i , i .

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