Abstract

Adaptive optics provides a real-time compensation for atmospheric turbulence that severely limits the resolution of ground-based observation systems. The correction quality relies on a key component, that is, the wavefront sensor (WFS). When observing extended sources, WFS precision is limited by anisoplanatism effects. Anisoplanatism induces a variation of the turbulent phase and of the collected flux in the field of view. We study the effect of this phase and scintillation anisoplanatism on wavefront analysis. An analytical expression of the error induced is given in the Rytov regime. The formalism is applied to a solar and an endoatmospheric observation. Scintillation effects are generally disregarded, especially in astronomical conditions. We shall prove that this approximation is not valid with extended objects.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  19. F. Mahé, V. Michau, G. Rousset, and J.-M. Conan, 'Scintillation effects on wavefront sensing in the Rytov regime,' in Propagation through the Atmosphere IV, M. Roggemann, ed., Proc. SPIE 4125, 77-86 (2000).
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    [CrossRef]
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    [CrossRef]
  26. T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
    [CrossRef]

2004 (6)

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., 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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., 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,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (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)

L. Poyneer, 'Scene-based Shack-Hartmann wave-front sensing: analysis and simulation,' Appl. Opt. 42, 5807-5815 (2003).
[CrossRef] [PubMed]

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

2001 (3)

2000 (2)

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

F. Rigaut, B. L. Ellerbroek, and R. Flicker, 'Principles, limitations and performance of multi-conjugate adaptive optics,' in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

1999 (2)

V. P. Lukin and B. V. Fortes, 'Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations,' in Propagation and Imaging through the Atmosphere III, M. C. Roggemann and L. R. Bissonnette, eds., Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

J. A. Rubio, A. M. Belmonte, and A. Comeron, 'Numerical simulation of long-path spherical wave propagation in three-dimensional random media,' Opt. Eng. (Bellingham) 38, 1462-1469 (1999).
[CrossRef]

1998 (1)

1994 (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]

1988 (1)

1975 (1)

R. H. Dicke, 'Phase-contrast detection of telescope seeing and their correction,' Astron. J. 198, 605-615 (1975).

Barchers, J. D.

Beckers, J. M.

J. M. Beckers, 'Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,' in Very Large Telescopes and Their Instrumentation, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1988), pp. 693-703.

Belmonte, A. M.

J. A. Rubio, A. M. Belmonte, and A. Comeron, 'Numerical simulation of long-path spherical wave propagation in three-dimensional random media,' Opt. Eng. (Bellingham) 38, 1462-1469 (1999).
[CrossRef]

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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 260-267 (2004).
[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]

Comeron, A.

J. A. Rubio, A. M. Belmonte, and A. Comeron, 'Numerical simulation of long-path spherical wave propagation in three-dimensional random media,' Opt. Eng. (Bellingham) 38, 1462-1469 (1999).
[CrossRef]

Conan, J.-M.

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]

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (2004).
[CrossRef]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (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]

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

Denker, C. J.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Dicke, R. H.

R. H. Dicke, 'Phase-contrast detection of telescope seeing and their correction,' Astron. J. 198, 605-615 (1975).

Didkovsky, L. V.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Ellerbroek, B. L.

Flatté, S. M.

Fletcher, S.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Flicker, R.

F. Rigaut, B. L. Ellerbroek, and R. Flicker, 'Principles, limitations and performance of multi-conjugate adaptive optics,' in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE 4007, 1022-1031 (2000).
[CrossRef]

Fortes, B. V.

V. P. Lukin and B. V. Fortes, 'Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations,' in Propagation and Imaging through the Atmosphere III, M. C. Roggemann and L. R. Bissonnette, eds., Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

Foy, R.

M. Tallon, R. Foy, and J. Vernin, '3-d wavefront sensing for multiconjugate adaptive optics,' in Progress in Telescope and Instrumentation Technologies, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1992), pp. 517-521.

Fusco, T.

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (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]

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]

Goode, P. R.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Gregory, S.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Hegwer, S. L.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Kulcsár, C.

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (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]

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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Le Roux, B.

Lee, D. J.

Leroux, B.

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., 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,' in Propagation and Imaging through the Atmosphere III, M. C. Roggemann and L. R. Bissonnette, eds., 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,' in Propagation through the Atmosphere IV, M. Roggemann, ed., Proc. SPIE 4125, 77-86 (2000).
[CrossRef]

Marino, J.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Marquette, W.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Martin, J. M.

Michau, V.

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (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]

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

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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

Mugnier, L. M.

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]

Petit, C.

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (2004).
[CrossRef]

Poyneer, L.

Quiros-Pacheco, F.

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (2004).
[CrossRef]

Raynaud, H.-F.

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (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]

Ren, D.

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Rigaut, F.

F. Rigaut, B. L. Ellerbroek, and R. Flicker, 'Principles, limitations and performance of multi-conjugate adaptive optics,' in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE 4007, 1022-1031 (2000).
[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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 59-66 (2004).
[CrossRef]

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

Robert, C.

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

Roddier, F.

F. Roddier, Progress in Optics, Vol. XIX, E.Wolf, ed. (North Holland, 1981), pp. 281-376.
[CrossRef]

Roggemann, M. C.

Rousset, G.

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (2004).
[CrossRef]

V. Michau, T. Fusco, J.-M. Conan, C. Robert, B. Leroux, and G. Rousset, 'MCAO for astronomical and near-to-ground applications,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (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]

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

Rubio, J. A.

J. A. Rubio, A. M. Belmonte, and A. Comeron, 'Numerical simulation of long-path spherical wave propagation in three-dimensional random media,' Opt. Eng. (Bellingham) 38, 1462-1469 (1999).
[CrossRef]

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.

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

Sasiela, R. J.

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence Evaluation and Application of Mellin Transforms (Springer-Verlag, 1995).

Smith, F. G.

F. G. Smith, Atmospheric Propagation of Radiation (SPIE, 1993), Chap. 2, pp. 217-224.

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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

Tallon, M.

M. Tallon, R. Foy, and J. Vernin, '3-d wavefront sensing for multiconjugate adaptive optics,' in Progress in Telescope and Instrumentation Technologies, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1992), pp. 517-521.

Vernin, J.

M. Tallon, R. Foy, and J. Vernin, '3-d wavefront sensing for multiconjugate adaptive optics,' in Progress in Telescope and Instrumentation Technologies, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1992), pp. 517-521.

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.

T. Berkefeld, D. Soltau, and O. F. H. von der Luhe, 'Second-generation adaptive optics for the 1.5 m solar telescope GREGOR, Tenerife,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5490, 260-267 (2004).
[CrossRef]

Appl. Opt. (3)

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]

Astron. J. (1)

R. H. Dicke, 'Phase-contrast detection of telescope seeing and their correction,' Astron. J. 198, 605-615 (1975).

J. Opt. (Paris) (1)

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

J. Opt. Soc. Am. A (4)

Opt. Eng. (Bellingham) (1)

J. A. Rubio, A. M. Belmonte, and A. Comeron, 'Numerical simulation of long-path spherical wave propagation in three-dimensional random media,' Opt. Eng. (Bellingham) 38, 1462-1469 (1999).
[CrossRef]

Proc. SPIE (9)

C. Robert, J.-M. Conan, V. Michau, and T. Fusco, 'Anisoplanatism in Shack-Hartmann wavefront sensing,' in Optics in Atmospheric Propagation and Adaptive Systems VII, J. D. Gonglewski and K. Stein, eds., Proc. SPIE 5572, 223-234 (2004).
[CrossRef]

T. R. Rimmele, K. Richards, S. L. Hegwer, D. Ren, S. Fletcher, S. Gregory, L. V. Didkovsky, C. J. Denker, W. Marquette, J. Marino, and P. R. Goode, 'Solar adaptive optics: a progress report,' in Adaptive Optical System Technologies II, P. L. Wizinowich and D. Bonaccini, eds., Proc. SPIE 4839, 635-646 (2003).
[CrossRef]

V. P. Lukin and B. V. Fortes, 'Phase correction of an image turbulence broadening under conditions of strong intensity fluctuations,' in Propagation and Imaging through the Atmosphere III, M. C. Roggemann and L. R. Bissonnette, eds., Proc. SPIE 3763, 61-72 (1999).
[CrossRef]

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

C. Petit, F. Quiros-Pacheco, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, and G. Rousset, 'Kalman filter-based control for adaptive optics,' in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE 5490, 1414-1425 (2004).
[CrossRef]

F. Rigaut, B. L. Ellerbroek, and R. Flicker, 'Principles, limitations and performance of multi-conjugate adaptive optics,' in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE 4007, 1022-1031 (2000).
[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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., 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,' in ALT'03 International Conference on Advanced Laser Technologies: Biomedical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., 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,' in Advanced Wavefront Control: Methods, Devices and Applications II, J. D. Gonglewski, M. T. Gruneisen, and M. K. Giles, eds., Proc. SPIE 5553, 170-181 (2004).
[CrossRef]

Other (6)

R. J. Sasiela, Electromagnetic Wave Propagation in Turbulence Evaluation and Application of Mellin Transforms (Springer-Verlag, 1995).

F. G. Smith, Atmospheric Propagation of Radiation (SPIE, 1993), Chap. 2, pp. 217-224.

F. Roddier, Progress in Optics, Vol. XIX, E.Wolf, ed. (North Holland, 1981), pp. 281-376.
[CrossRef]

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

J. M. Beckers, 'Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,' in Very Large Telescopes and Their Instrumentation, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1988), pp. 693-703.

M. Tallon, R. Foy, and J. Vernin, '3-d wavefront sensing for multiconjugate adaptive optics,' in Progress in Telescope and Instrumentation Technologies, M.-H.Ulrich, ed., ESO Conference and Workshop Proceedings (European Southern Observatory, 1992), pp. 517-521.

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Figures (10)

Fig. 1
Fig. 1

Phase and scintillation anisoplanatism: the double-star case.

Fig. 2
Fig. 2

Images of a double star at the subaperture focal plane. (a) χ = 0 , φ = 0 nonturbulent case. (b) φ = 0 scintillation effects only. The intensities of the star images are different. (c) χ = 0 phase effects only. One star is displaced in relation to the other. (d) χ , φ , scintillation and phase effects.

Fig. 3
Fig. 3

Hufnagel C n 2 profile sampled with 20 layers compared with the equivalent two-layer C n 2 profile: one in the pupil plane and the other at an altitude of 10 km. The equivalence is checked looking at the similitude between the phase correlation curves (on the right) calculated with the Hufnagel profile (upper right) and the two-layer profile (lower right). We calculate the normalized coefficient of correlation of the phase decomposed on the Zernike polynomials Z = 2 ( tilt ) , Z = 15 , and Z = 36 .

Fig. 4
Fig. 4

Measurement error variance as a function of the separation of the two-point source: contribution of the different terms. The reference is the direction α 0 = α . We use the equivalent two-layer C n 2 profile. The error variances obtained numerically with phase effects only (scintillation effects only) are denoted by triangles (diamonds). The numerical error variances with both scintillation and phase effects is denoted by squares. The error variances obtained analytically with phase effects only (scintillation effects only) are shown by a dashed curve (solid curve). The sum of both contributions (dashed curve and solid curve) is shown for comparison (dashed–dotted curve).

Fig. 5
Fig. 5

Measurement error variance as a function of the separation of the two-point source: contribution of the different terms. The reference is the middle direction α 0 = 0 . We use the equivalent two-layer C n 2 profile. The error variances obtained numerically with phase effects only (scintillation effects only) are denoted by triangles (diamonds). The numerical error variances with both scintillation and phase effects is denoted by squares. The error variances obtained analytically with phase effects only (scintillation effects only) are shown with a dashed curve (solid curve). The total error variance of both contributions (dashed curve and solid curve) plus the coupling effect (dotted curve) is shown for comparison (dashed–dotted curve).

Fig. 6
Fig. 6

Phase term C 2 as a function of the size of the uniform square with reference α 0 at the center. Comparison between a continuous square (solid curve) and a discrete one (analytical, dotted curve; numerical simulation, diamonds). (a) 3 × 3 discrete square. (b) 15 × 15 discrete square.

Fig. 7
Fig. 7

Measurement error variance as a function of the size of the uniform square: contribution of the different terms. The reference is square center α 0 = 0 . We use the equivalent two-layer C n 2 profile. The error variances obtained numerically with phase effects only (scintillation effects only) are denoted by triangles (diamonds). The numerical error variances with both scintillation and phase effects is denoted by squares. The error variances obtained analytically with phase effects only (scintillation effects only) are shown with a dashed curve (solid curve). The total error variance of both contributions (dashed curve and solid curve) plus the coupling effect (dotted curve) is drawn for comparison (dashed–dotted curve).

Fig. 8
Fig. 8

Measurement error variance obtained analytically and numerically as a function of the size of the uniform square with a reference α 0 = 0 at the center. We use the daytime Hufnagel C n 2 profile sampled with 20 layers. The error variances obtained numerically with phase effects only (scintillation effects only) are denoted by triangles (diamonds). The numerical error variances with both scintillation and phase effects is denoted by squares. We give the total WFS error (dashed–dotted curve), which is the sum of the scintillation term A 2 (solid curve), of the phase term C 2 (dashed curve), and of the coupling term 2 A C (dotted curve).

Fig. 9
Fig. 9

Measurement error variance as a function of the size of the uniform square source: contribution of the different terms. The reference α 0 is at the square center. We use a high-altitude single-layer C n 2 profile. The log amplitude of a point source σ χ 2 = 0.04 (Rytov). Error variances obtained numerically with phase effects only (scintillation effects only) are denoted by triangles (diamonds). Numerical error variances with both scintillation and phase effects are denoted by squares. Error variances obtained analytically with phase effects only (scintillation effects only) are shown with a dashed curve) (solid curve). The resulting error variances of both contributions (dashed curve and solid curve) plus the coupling effect (dotted curve) as shown for comparison (dashed–dotted curve).

Fig. 10
Fig. 10

Measurement error variance as a function of the size of the uniform square source: contribution of the different terms. The reference α 0 is at the square center. We use a high-altitude single-layer C n 2 profile. The log amplitude of a point source σ χ 2 = 0.39 . Error variances obtained numerically with phase effects only (scientillation effects only) are denoted by triangles (diamonds). Numerical error variances with both scintillation and phase effects are denoted by squares. Error variances obtained analytically with phase effects only (scintillation effects only) are shown with a dashed curve (solid curve). The resulting error variances of both contributions (dashed curve and solid curve) plus the coupling effect (dotted curve) are shown for comparison (dashed–dotted curve).

Equations (52)

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S = s ( α ) I ( α ) d α I ( α ) d α .
ϵ = S S ( s 0 s 0 ) = δ S δ s 0 .
σ x 2 = ( δ S x δ s 0 x ) 2 A 2 + C 2 + 2 A C .
A 2 = 1 Σ 2 d f α D ̃ ( f α ) 2 F ̃ ( f α ) ,
C 2 = 1 Σ 2 d f α { O ̃ ( f α ) 2 2 Σ R [ exp ( 2 i π f α α 0 ) ] O ̃ ( f α ) + Σ 2 } G ̃ ( f α ) ,
A C = 1 Σ 2 d f α D ̃ ( f α ) * [ O ̃ ( f α ) Σ exp ( 2 i π f α α 0 ) ] H ̃ ( f α ) ,
δ i r ( α ) = 2 φ ( r ) 1 λ z cos ( π r 2 λ z ) δ ( r z α ) P ( r ) ,
F ( α ) = 4 d z PSD z ( f ) P ̃ ( f ) 2 sin 2 ( π z λ f 2 ) exp ( 2 i π z f α ) d f ,
F ̃ ( f α ) = 4 z 2 d z PSD z ( f α z ) P ̃ ( f α z ) 2 sin 2 [ π z λ ( f α z ) 2 ] .
A 2 = 4 Σ 2 0 L d z z 2 D ̃ ( f α ) 2 PSD z ( f α z ) P ̃ ( f α z ) 2 sin 2 [ π z λ ( f α z ) 2 ] d f α .
δ s x , r ( α ) = φ ( r ) x 1 λ z sin ( π r 2 λ z ) δ ( r z α ) P ( r ) .
G ( α ) = ( 2 π ) 2 f x  2 d z PSD z ( f ) P ̃ ( f ) 2 cos 2 ( π z λ f 2 ) exp ( 2 i π z f α ) d f ,
C 2 = ( 2 π ) 2 Σ 2 0 L d z z 4 f α x 2 { O ̃ ( f α ) 2 2 Σ R [ exp ( 2 i π f α α 0 ) ] O ̃ ( f α ) + Σ 2 } × PSD z ( f α z ) P ̃ ( f α z ) 2 cos 2 [ π z λ ( f α z ) 2 ] d f α ,
H ( α ) = i 2 π f x d z PSD z ( f ) P ̃ ( f ) 2 sin ( 2 π z λ f 2 ) exp ( 2 i π z f α ) d f .
A C = 2 i π Σ 2 0 L d z z 3 f α x [ D ̃ ( f α ) ] * [ O ̃ ( f α ) Σ exp ( 2 i π f α α 0 ) ] × PSD z ( f α z ) P ̃ ( f α z ) 2 sin [ 2 π z λ ( f α z ) 2 ] d f α .
d z PSD z ( f ) = 9 . 7 × 10 3 ( 2 π λ ) 2 C n 2 ( z ) d z [ f  2 + ( 1 L 0 ) 2 ] 11 6 .
A 2 = ( 2 α ) 2 + d f α z 2 sin 2 ( 2 π α f α x ) × PSD z ( f α z ) d z ( P ̃ ( f α z ) ) 2 sin 2 [ π z λ ( f α z ) 2 ] ,
C 2 = ( 2 π ) 2 + d f α z 4 f α x 2 sin 2 ( 2 π α f α x ) × PSD z ( f α z ) d z ( P ̃ ( f α z ) ) 2 cos 2 [ π z λ ( f α z ) 2 ] .
A 2 = ( 2 α ) 2 + d f α z 2 sin 2 ( 2 π α f α x ) × PSD z ( f α z ) d z [ P ̃ ( f α z ) ] 2 sin 2 [ π z λ ( f α z ) 2 ] ,
C 2 = ( 2 π ) 2 + d f α z 4 f α x 2 ( cos ( 2 π α f α x ) 1 ) 2 × PSD z ( f α z ) d z [ P ̃ ( f α z ) ] 2 cos 2 [ π z λ ( f α z ) 2 ] ,
A C = 2 π + d f α z 3 f α x sin ( 2 π α f α x ) [ cos ( 2 π α f α x ) 1 ] × PSD z ( f α z ) d z [ P ̃ ( f α z ) ] 2 sin [ 2 π z λ ( f α z ) 2 ] .
ϵ = S S ( s 0 s 0 ) = δ S δ s 0 .
1 I ( α ) d α = 1 O ( α ) d α 1 1 + δ i ( α ) O ( α ) d α O ( α ) d α = 1 O ( α ) d α [ 1 δ i ( α ) O ( α ) d α O ( α ) d α ] + o ( δ i 2 ) .
S s ( α ) O ( α ) d α O ( α ) d α .
A = s ( α ) O ( α ) ( 1 + δ i ( α ) ) d α O ( α ) d α [ 1 δ i ( α ) O ( α ) d α O ( α ) d α ] s ( α ) O ( α ) d α O ( α ) d α ,
A = O ( α ) ( s ( α ) S ) δ i ( α ) O ( α ) d α .
B = δ s ( α ) O ( α ) ( 1 + δ i ( α ) ) d α O ( α ) d α [ 1 δ i ( α ) O ( α ) d α O ( α ) d α ] δ s ( α ) O ( α ) d α O ( α ) d α ,
B = δ s ( α ) O ( α ) d α O ( α ) d α [ δ i ( α ) δ i ( α ) O ( α ) d α O ( α ) d α ] .
C = δ s ( α ) O ( α ) d α O ( α ) d α δ s 0 ,
C = ( δ s ( α ) δ s 0 ) O ( α ) d α O ( α ) d α .
A = 0 ,
B = 0 ,
C = 0 ,
ε = 0 .
σ x 2 = ( δ S x δ s 0 x ) 2 , = ( A + B + C ) 2 = A 2 + B 2 + C 2 + 2 A B + 2 B C + 2 A C .
σ x 2 = A 2 + C 2 + 2 A C + B 2 .
Σ = O ( α ) d α .
A 2 = 1 Σ 2 d α d α O ( α ) O ( α ) α x α x δ i ( α ) δ i ( α ) ,
C 2 = 1 Σ 2 d α d α O ( α ) O ( α ) ( δ s x ( α ) δ s x ( α 0 ) ) ( δ s x ( α ) δ s x ( α 0 ) ) ,
A C = 1 Σ 2 d α d α O ( α ) O ( α ) α x δ i ( α ) ( δ s x ( α ) δ s x ( α 0 ) ) ,
B 2 = 1 Σ 2 d α d α O ( α ) O ( α ) δ s x ( α ) δ s x ( α ) { δ i ( α ) [ δ i ( α ) O ( α ) d ( α ) ] } { δ i ( α ) [ δ i ( α ) O ( α ) d α ] } .
σ x 2 A 2 + C 2 + 2 A C .
ε ε T = [ σ x 2 σ y x 2 σ x y 2 σ y 2 ] .
ε m = S m S m ( s 0 s 0 ) = δ S m δ s 0 .
ε m ε n T = A m A n T + C m C n T + A m C n T + C m A n T .
A m A n T k l = 1 Σ 2 [ D ̃ k ( f α ) S k O ̃ ( f α ) ] * [ D ̃ l ( f α ) S l O ̃ ( f α ) ] F ̃ m n ( f α ) d f α ,
F ̃ m n ( f α ) = 4 z 2 d z PSD z ( f α z ) P ̃ ( f α z ) 2 sin 2 [ π z λ ( f α z ) 2 ] exp ( 2 i π d m n f α z ) ,
C m C n T k l = 1 Σ 2 O ̃ ( f α ) Σ exp ( 2 i π α 0 f α ) 2 G ̃ m n , k l * ( f α ) d f α ,
G ̃ m n , k l ( f α ) = ( 2 π ) 2 z 4 f α k f α l d z PSD z ( f α z ) P ̃ ( f α z ) 2 cos 2 [ π z λ ( f α z ) 2 ] exp ( 2 i π d m n f α z ) .
A m C n T k l + C m A n T k l
= 1 Σ 2 d f α [ O ̃ ( f α ) Σ exp ( 2 i π α 0 f α ) ] [ [ D ̃ k ( f α ) S k O ̃ ( f α ) ] * H ̃ m n , l ( f α ) [ D ̃ l ( f α ) S l O ̃ ( f α ) ] * H ̃ m n , k * ( f α ) ] ,
H ̃ m n , l ( f α ) = i 2 π z 3 f α l d z PSD z ( f α z ) P ̃ ( f α z ) 2 sin [ 2 π z λ ( f α z ) 2 ] exp ( 2 i π d m n f α z ) .

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