Abstract

Anisoplanatism limits the correction field of adaptive optics (AO). In the case of Shack–Hartmann measurement performed on extended sources it may also strongly affect wavefront estimation accuracy. An analytical formalism has been previously proposed to quantify anisoplanatism slope measurement error. It is exploited here to derive the most relevant quantity in AO, the wavefront error. Analytical and end-to-end simulation results are compared in three cases: solar observation, weakly perturbed near-to-ground observation, and strongly perturbed near-to-ground observation. In every case, anisoplanatism wavefront error takes significant values. The accuracy of the analytical model is investigated in detail. Three contributions to the slope error previously identified are considered: phase anisoplanatism, scintillation anisoplanatism, and coupling between scintillation and phase anisoplanatism. The influence of both scintillation and coupling contributions to the wavefront error is confirmed here.

© 2007 Optical Society of America

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    [CrossRef]
  2. T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
    [CrossRef]
  3. M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  6. V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2006 (3)

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, "Scintillation and phase anisoplanatism in shack-hartmann wavefront sensing," J. Opt. Soc. Am. A 23, 613-624 (2006).
[CrossRef]

2004 (6)

T. R. Rimmele, "Recent advances in solar adaptive optics," Proc. SPIE 5490, 34-46 (2004).
[CrossRef]

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29, 2743-2745 (2004).
[CrossRef] [PubMed]

2003 (1)

2001 (1)

V. V. Voitsekhovich, V. G. Orlov, and L. J. Sanchez, "Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors," Astron. Astrophys. 368, 1133-1136 (2001).
[CrossRef]

2000 (1)

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

1999 (1)

V. P. Lukin and B. V. Fortes, "Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations," Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

1998 (1)

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

1991 (1)

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]

1979 (2)

R. Cubalchini, "Modal wave-front estimation from phase derivative measurements," J. Opt. Soc. Am. A 69, 972-977 (1979).
[CrossRef]

D. L. Fried, "Angular dependence of the atmospheric turbulence effect in speckle interferometry," Opt. Acta 26, 597-613 (1979).
[CrossRef]

1977 (1)

1976 (1)

1966 (1)

Berkefeld, T.

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

Bouchez, A. H.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Campbell, R. D.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

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]

Chin, J. C. Y.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Conan, J.

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

Conan, J.-M.

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, "Scintillation and phase anisoplanatism in shack-hartmann wavefront sensing," J. Opt. Soc. Am. A 23, 613-624 (2006).
[CrossRef]

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

C. Robert, J.-M. Conan, L. M. Mugnier, V. Michau, and G. Rousset, "A comparative study of modal wavefront reconstructions for the Shack-Hartmann," in International Workshop on Wavefront Sensing and its Applications (Canterbury, England, July 19-24, 1999).

J.-M. Conan, "Étude de la correction partielle en optique adaptative," Ph.D. thesis (Université Paris XI Orsay, 1994).

Cubalchini, R.

R. Cubalchini, "Modal wave-front estimation from phase derivative measurements," J. Opt. Soc. Am. A 69, 972-977 (1979).
[CrossRef]

Fortes, B. V.

V. P. Lukin and B. V. Fortes, "Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations," Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

Fried, D. L.

Fusco, T.

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, "Scintillation and phase anisoplanatism in shack-hartmann wavefront sensing," J. Opt. Soc. Am. A 23, 613-624 (2006).
[CrossRef]

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29, 2743-2745 (2004).
[CrossRef] [PubMed]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

Hartman, S. K.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Hegwer, S.

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Johansson, E. M.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Lafon, R. E.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Lai, O.

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

Langlois, M.

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Le Mignant, D.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Leroux, B.

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

Lukin, V. P.

V. P. Lukin and B. V. Fortes, "Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations," Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

Mahé, F.

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

Michau, V.

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, "Scintillation and phase anisoplanatism in shack-hartmann wavefront sensing," J. Opt. Soc. Am. A 23, 613-624 (2006).
[CrossRef]

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29, 2743-2745 (2004).
[CrossRef] [PubMed]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

C. Robert, J.-M. Conan, L. M. Mugnier, V. Michau, and G. Rousset, "A comparative study of modal wavefront reconstructions for the Shack-Hartmann," in International Workshop on Wavefront Sensing and its Applications (Canterbury, England, July 19-24, 1999).

Moretto, G.

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Mugnier, L. M.

C. Robert, J.-M. Conan, L. M. Mugnier, V. Michau, and G. Rousset, "A comparative study of modal wavefront reconstructions for the Shack-Hartmann," in International Workshop on Wavefront Sensing and its Applications (Canterbury, England, July 19-24, 1999).

Nicolle, M.

Noll, R. J.

Orlov, V. G.

V. V. Voitsekhovich, V. G. Orlov, and L. J. Sanchez, "Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors," Astron. Astrophys. 368, 1133-1136 (2001).
[CrossRef]

Poyneer, L. A.

Richards, K.

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Rigaut, F.

F. Rigaut, "Ground-conjugate wide field adaptive optics for the ELTs," in Proceedings of the Conference on Beyond Conventional Adaptive Optics, E.Vernet, R.Ragazzoni, S.Esposito, and N.Hubin, eds. (Padova, Italy, May 7-10, 2001).

Rigaut, F. J.

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

Rimmele, T. R.

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

T. R. Rimmele, "Recent advances in solar adaptive optics," Proc. SPIE 5490, 34-46 (2004).
[CrossRef]

Robert, C.

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, "Scintillation and phase anisoplanatism in shack-hartmann wavefront sensing," J. Opt. Soc. Am. A 23, 613-624 (2006).
[CrossRef]

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

C. Robert, J.-M. Conan, L. M. Mugnier, V. Michau, and G. Rousset, "A comparative study of modal wavefront reconstructions for the Shack-Hartmann," in International Workshop on Wavefront Sensing and its Applications (Canterbury, England, July 19-24, 1999).

Roddier, C.

Roddier, F.

F. Roddier and C. Roddier, "Wavefront reconstruction using iterative Fourier transforms," Appl. Opt. 30, 1325-1327 (1991).
[CrossRef] [PubMed]

F. Roddier, The Effects of Atmospherical Turbulence in Optical Astronomy, E.Wolf, ed. (North Holland,1981).

Rousset, G.

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, "MCAO for astronomical and near-to-ground applications," Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

M. Nicolle, T. Fusco, G. Rousset, and V. Michau, "Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics," Opt. Lett. 29, 2743-2745 (2004).
[CrossRef] [PubMed]

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

C. Robert, J.-M. Conan, L. M. Mugnier, V. Michau, and G. Rousset, "A comparative study of modal wavefront reconstructions for the Shack-Hartmann," in International Workshop on Wavefront Sensing and its Applications (Canterbury, England, July 19-24, 1999).

Sanchez, L. J.

V. V. Voitsekhovich, V. G. Orlov, and L. J. Sanchez, "Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors," Astron. Astrophys. 368, 1133-1136 (2001).
[CrossRef]

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence (Springer-Verlag, 1994).
[CrossRef]

Soltau, D.

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

Stomski, P. J.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Summers, D. M.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation In a Turbulent Medium (Dover, 1961).

van Dam, M. A.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Vedrenne, N.

Védrenne, N.

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

Veran, J.

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

Voitsekhovich, V. V.

V. V. Voitsekhovich, V. G. Orlov, and L. J. Sanchez, "Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors," Astron. Astrophys. 368, 1133-1136 (2001).
[CrossRef]

von der Luhe, O. F. H.

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

Wizinowich, P. L.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
[CrossRef]

Appl. Opt. (2)

Astron. Astrophys. (1)

V. V. Voitsekhovich, V. G. Orlov, and L. J. Sanchez, "Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors," Astron. Astrophys. 368, 1133-1136 (2001).
[CrossRef]

J. Opt. (Paris) (1)

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[CrossRef]

Opt. Lett. (1)

Proc. SPIE (9)

F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, "Scintillation effects on wavefront sensing in the Rytov regime," Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

N. Védrenne, V. Michau, C. Robert, and J.-M. Conan, "Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor," Proc. SPIE 6303 (2006).

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[CrossRef]

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[CrossRef]

C. Robert, J. Conan, V. Michau, and T. Fusco, "Anisoplanatism in Shack-Hartmann wavefront sensing," Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

T. R. Rimmele, "Recent advances in solar adaptive optics," Proc. SPIE 5490, 34-46 (2004).
[CrossRef]

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, "Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife," Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

M. Langlois, G. Moretto, K. Richards, S. Hegwer, and T. R. Rimmele, "Solar multiconjugate adaptive optics at the Dunn solar telescope: preliminary results," Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

M. A. van Dam, A. H. Bouchez, D. Le Mignant, E. M. Johansson, P. L. Wizinowich, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, R. E. Lafon, P. J. Stomski, Jr., and D. M. Summers, "The W. M. Keck observatory laser guide star adaptive optics system: performance characterization," Publ. Astron. Soc. Pac. 118, 310-318 (2006).
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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Zernike decomposition of wavefront error: Zernike coefficients variance for solar observation. Total wavefront error: open square, simulated; solid curve, analytical. Scintillation anisoplanatism wavefront error: open triangle, simulated; dotted curve, analytical. Phase anisoplanatism wavefront error: crosses, simulated; dashed curve, analytical. Coupling between phase and scintillation anisoplanatism: dashed–dotted curve, analytical. The wavefront variances measured in the reference direction α 0 are also plotted for comparison: diamonds, simulated; dashed–triple-dotted curve, analytical. (a) Total wavefront error for 2 , 6 , and 10 , square. (b) Contributions to the wavefront error for a 6 square.

Fig. 2
Fig. 2

Influence of flux fluctuations inside subaperture: slope error variances as a function of square size in the Rytov case [curves (a)] and limit-Rytov case [curves (b)]. With flux fluctuations inside subaperture, open square; without flux fluctuations inside subaperture, crosses; flux fluctuations inside subaperture error, plus signs.

Fig. 3
Fig. 3

Phase anisoplanatism slope error variance as a function of object size in the Rytov case [curves (a)] and in the limit-Rytov case [curves (b)]. Analytical slope error variance ( C x 2 ) , open squares; end-to-end simulation slope error variance with normalized intensity fluctuation ( ϵ δ i = 0 x 2 ) , crosses.

Fig. 4
Fig. 4

Scintillation anisoplanatism slope error variance as a function of object size in the Rytov case [curves (a)] and in the limit-Rytov case [curves (b)]. Analytical slope error variance ( A x 2 ) , open squares; end-to-end simulation slope error variance with normalized phase fluctuation ( ϵ δ φ = 0 x 2 ) , open triangles; end-to-end simulation slope error variance obtained with the first-order expansion ( ϵ δ φ = 0 , L D x 2 ) ; plus signs.

Fig. 5
Fig. 5

Zernike decomposition of wavefront error: Zernike coefficient variances (a) total error for 0.4 m , 1.2 m , and 2.7 m objects, Rytov case. (b) Phase, scintillation anisoplanatism, and their coupling contributions to wavefront error for a 1.2 m object, Rytov case. (c) Total error for 0.4 m , 1.2 m , and 2.7 m objects, limit-Rytov case. (d) Phase, scintillation anisoplanatism, and their coupling contributions to wavefront error for a 1.2 m object, limit-Rytov case. The different contributions are plotted with the same symbols and conventions as in Fig. 1.

Fig. 6
Fig. 6

Power spectral components of the scintillation contribution to wavefront error. Object contribution, dotted curve [see Eq. (2)]; Von Karman PSD of the phase fluctuations, dashed curve [see Eq. (4)]; Fresnel propagation kernel, dotted–dashed curve; subaperture averaging function, dashed–triple-dotted curve; Fourier reconstruction operator, long-dashed curve; PSD of the scintillation anisoplanatism contribution, solid curve.

Fig. 7
Fig. 7

Contributions to anisoplanatism wavefront error projected on the Fourier basis. Scintillation anisoplanatism contribution, dashed–double-dotted curve; phase anisoplanatism contribution, lower dashed curve; coupling, dotted–dashed curve; total wavefront error, solid curve; wavefront spectrum, upper dashed curve.

Fig. 8
Fig. 8

Contributions to anisoplanatism wavefront error projected on the Zernike modes. Scintillation anisoplanatism contribution, dotted curve; phase anisoplanatism contribution, dashed curve; coupling, dotted–dashed curve; total wavefront error, solid curve; wavefront spectrum, dashed–triple–dotted curve.

Tables (3)

Tables Icon

Table 1 Characteristic Parameters for the Two Cases

Tables Icon

Table 2 Total Wavefront Error Variances for Three Object Sizes in the Two Cases

Tables Icon

Table 3 Contributions to Wavefront Error for a 1.2 m Object Numerically Estimated in the Two Cases

Equations (30)

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S m = s m ( α ) I m ( α ) d α I m ( α ) d α .
I m ( α ) = O ( α ) [ 1 + δ i m ( α ) ] ,
ϵ m = δ S m δ s m ( α 0 ) .
1 I m ( α ) d α = 1 Σ [ 1 δ Σ m Σ + o ( δ Σ m Σ ) ] ,
A m = O ( α ) ( s m ( α ) S O ) δ i m ( α ) d α Σ .
ϵ m A m + C m ,
A m k A n l = FT [ PSD A A k l ( f ) ] 1 ( d m n ) ,
C m k C n l = FT [ PSD C C k l ( f ) ] 1 ( d m n ) ,
A m k C n l + C m k A n l = FT [ PSD A C + C A k l ( f ) ] 1 ( d m n ) ,
δ s 0 = M δ Φ 0 .
δ S = M δ Φ 0 + ϵ ,
δ Φ ̂ = R δ S = R M δ Φ 0 + R ϵ ,
C a w f e = δ Φ a w f e δ Φ a w f e T = R ϵ ϵ T R T = R C ϵ R T ,
S m = j s m ( α j ) I m ( α j ) j I m ( α j ) .
σ δ φ δ i w f e 2 = σ n a w f e 2 σ δ i = 0 w f e 2 σ δ φ = 0 w f e 2 ,
S = j s ( α j ) I ( α j ) j O ( α j ) ( 1 j δ i ( α j ) O ( α j ) j O ( α j ) ) .
PSD A A k l ( f ) = 1 Σ 2 0 L d z [ D ̃ k ( z e f ) ] * [ D ̃ l ( z e f ) ] F ̃ ( f ) .
D ̃ k ( z e f ) = FT [ α k O ( α ) S k O ( α ) ] ( z e f ) ,
F ̃ ( f ) = 4 PSD z e ( f ) P ̃ ( f ) 2 sin 2 ( π z e λ f 2 ) .
PSD z e ( f ) = k 0 2 ( z e z ) 5 3 0.033 C n 2 ( z ) ( 2 π ) 2 3 exp ( 2 π f 2 ( l 0 z e z ) 2 5.9 2 ) [ f 2 + ( L 0 z e z ) 2 ] 11 6 ,
PSD C C k l ( f ) = 1 Σ 2 0 L d z E ̃ ( z e f ) 2 f k f l G ̃ ( f ) .
E ̃ ( z e f ) = O ̃ ( z e f ) Σ exp ( 2 i π α 0 z e f ) ,
G ̃ ( f ) = ( 2 π d ) 2 PSD z e ( f ) P ̃ ( f ) 2 cos 2 ( π z e λ f 2 ) .
PSD A C + C A k l ( f ) = 1 Σ 2 0 L d z [ f l E ̃ ( z e f ) D ̃ k * ( z e f ) + f k E ̃ * ( z e f ) D ̃ l ( z e f ) ] H ̃ ( f ) ,
H ̃ ( f ) = i 2 π k 0 d 2 PSD z e ( f ) P ̃ ( f ) 2 sin ( 2 π z e λ f 2 ) .
S ̃ x ( f ) M ̃ x ( f ) φ ̃ ( f ) .
M ̃ x ( f ) = 2 i π f x sinc ( π f x d ) sinc ( π f y d ) .
φ ̂ ̃ ( f ) = M ̃ x * ( f ) S ̃ x ( f ) + M ̃ y * ( f ) S ̃ y ( f ) M ̃ x ( f ) 2 + M ̃ y ( f ) 2 ,
PSD a w f e ( f ) = M ̃ x ( f ) 2 PSD ε x x ( f ) + M ̃ y ( f ) 2 PSD ε y y ( f ) M ̃ x ( f ) 4 + M ̃ y ( f ) 4 + 2 R ( M ̃ x * ( f ) M ̃ y ( f ) PSD ε x y ( f ) ) M ̃ x ( f ) 4 + M ̃ y ( f ) 4 ,
PSD ε k l ( f ) = PSD A A k l ( f ) + PSD C C k l ( f ) + PSD A C + C A k l ( f ) ,

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