Abstract

COupled SLope and scIntillation Detection And Ranging (CO-SLIDAR) is a recent profiling method of the vertical distribution of atmospheric turbulence strength ( Cn2 profile). It takes advantage of correlations of slopes and of scintillation, both measured with a Shack-Hartmann wavefront sensor on a binary star. In this paper, we present the improved CO-SLIDAR reconstruction method of the Cn2 profile and the first on-sky results of the CO-SLIDAR profiler. We examine CO-SLIDAR latest performance in simulation, taking into account the detection noise bias and estimating error bars along with the turbulence profile. The estimated Cn2 profiles demonstrate the accuracy of the CO-SLIDAR method, showing sensitivity to both low and high altitude turbulent layers. CO-SLIDAR is tested on-sky for the first time, on the 1.5 m MeO (Métrologie Optique) telescope at Observatoire de la Côte d’Azur (France). The reconstructed profiles are compared to turbulence profiles estimated from meteorological data and a good agreement is found. We discuss CO-SLIDAR’s contribution in the Cn2 profilers’ landscape and we propose some improvements of the instrument.

© 2014 Optical Society of America

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  1. M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
    [CrossRef]
  2. T. Fusco, J.-M. Conan, G. Rousset, L. Mugnier, V. Michau, “Optimal wave-front reconstruction strategies for multiconjugate adaptive optics,” J. Opt. Soc. Am. A 18, 2527–2538 (2001).
    [CrossRef]
  3. A. Costille, T. Fusco, “Impact of the Cn2 description on Wide Field AO performance,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).
  4. E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
    [CrossRef]
  5. R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103–108 (2002).
    [CrossRef]
  6. T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
    [CrossRef]
  7. A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
    [CrossRef]
  8. A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
    [CrossRef]
  9. R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
    [CrossRef]
  10. A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: Principle of the ”Generalized SCIDAR”,” Publ. Astron. Soc. Pac. 110, 86–91 (1998).
    [CrossRef]
  11. N. Védrenne, V. Michau, C. Robert, J.-M. Conan, “Cn2 profile measurement from Shack-Hartmann data,” Opt. Lett. 32, 2659–2661 (2007).
    [CrossRef]
  12. J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).
  13. J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).
  14. Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
    [CrossRef]
  15. C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
    [CrossRef]
  16. L. M. Mugnier, G. Le Besnerais, S. Meimon, “Inversion in optical imaging through atmospheric turbulence,” in Bayesian Approach to Inverse Problems,J. Idier, ed. (ISTE, 2008), pp. 243–283.
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    [CrossRef]
  18. N. Védrenne, “Propagation optique et correction en forte turbulence,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2008).
  19. J.-L. Prieur, G. Daigne, R. Avila, “SCIDAR measurements at Pic du Midi,” Astron. Astrophys. 371, 366–377 (2001).
    [CrossRef]
  20. J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
    [CrossRef]
  21. R. Conan, “Modélisation des effets de l’ échelle externe de cohérence spatiale du front d’onde pour l’observation à haute résolution angulaire en astronomie: application à l’optique adaptative, à l’interférométrie et aux très grands telescopes,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2000).
  22. A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
    [CrossRef]
  23. J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).
  24. E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).
  25. F. Vidal, E. Gendron, G. Rousset, “Tomography approach for multi-object adaptive optics,” J. Opt. Soc. Am. A 27, 253–264 (2010).
    [CrossRef]
  26. L. Gilles, B. L. Ellerbroek, “Real-time turbulence profiling with a pair of laser guide star shack hartmann wavefront sensors for wide-field adaptive optics systems on large to extremely large telescopes,” J. Opt. Soc. Am. A 27, 76–83 (2010).
    [CrossRef]
  27. A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
    [CrossRef]

2013 (2)

E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
[CrossRef]

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

2012 (3)

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

2010 (2)

2007 (1)

2006 (3)

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
[CrossRef]

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

2003 (1)

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

2002 (2)

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103–108 (2002).
[CrossRef]

E. Thiebaut, “Optimization issues in blind deconvolution algorithms,” Proc. SPIE 4847, 174–183 (2002).
[CrossRef]

2001 (2)

2000 (1)

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

1998 (1)

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

1997 (1)

R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
[CrossRef]

1974 (1)

A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[CrossRef]

Abahamid, A.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Aristidi, E.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Avila, R.

J.-L. Prieur, G. Daigne, R. Avila, “SCIDAR measurements at Pic du Midi,” Astron. Astrophys. 371, 366–377 (2001).
[CrossRef]

R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
[CrossRef]

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Basden, A.

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Benkhaldoun, Z.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Blary, F.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Bondoux, E.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Bonifacio, P.

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Borgnino, J.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Bounhir, A.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Butterley, T.

T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
[CrossRef]

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Conan, J.-M.

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

N. Védrenne, V. Michau, C. Robert, J.-M. Conan, “Cn2 profile measurement from Shack-Hartmann data,” Opt. Lett. 32, 2659–2661 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

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

Conan, R.

R. Conan, “Modélisation des effets de l’ échelle externe de cohérence spatiale du front d’onde pour l’observation à haute résolution angulaire en astronomie: application à l’optique adaptative, à l’interférométrie et aux très grands telescopes,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2000).

Cortés, A.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

Costille, A.

A. Costille, T. Fusco, “Impact of the Cn2 description on Wide Field AO performance,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

Daigne, G.

J.-L. Prieur, G. Daigne, R. Avila, “SCIDAR measurements at Pic du Midi,” Astron. Astrophys. 371, 366–377 (2001).
[CrossRef]

Dhillon, V. S.

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Douet, R.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Ellerbroek, B. L.

Fanteï-Caujolle, Y.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Fini, L.

E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
[CrossRef]

Fleury, B.

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

Fuchs, A.

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

Fuensalida, J.

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Fusco, T.

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

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

A. Costille, T. Fusco, “Impact of the Cn2 description on Wide Field AO performance,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Gendron, E.

F. Vidal, E. Gendron, G. Rousset, “Tomography approach for multi-object adaptive optics,” J. Opt. Soc. Am. A 27, 253–264 (2010).
[CrossRef]

Gilles, L.

Guesalaga, A.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

Guzman, D.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

Hach, Y.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Hubin, N.

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Jabiri, A.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Kornilov, V.

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

Lantéri, H.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Lascaux, F.

E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
[CrossRef]

Le Besnerais, G.

L. M. Mugnier, G. Le Besnerais, S. Meimon, “Inversion in optical imaging through atmospheric turbulence,” in Bayesian Approach to Inverse Problems,J. Idier, ed. (ISTE, 2008), pp. 243–283.

Le Louarn, M.

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Martin, F.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Masciadri, E.

E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
[CrossRef]

R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
[CrossRef]

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Meimon, S.

L. M. Mugnier, G. Le Besnerais, S. Meimon, “Inversion in optical imaging through atmospheric turbulence,” in Bayesian Approach to Inverse Problems,J. Idier, ed. (ISTE, 2008), pp. 243–283.

Mékarnia, D.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Michau, V.

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

N. Védrenne, V. Michau, C. Robert, J.-M. Conan, “Cn2 profile measurement from Shack-Hartmann data,” Opt. Lett. 32, 2659–2661 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

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

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

Morris, T. J.

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Mugnier, L.

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

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

Mugnier, L. M.

L. M. Mugnier, G. Le Besnerais, S. Meimon, “Inversion in optical imaging through atmospheric turbulence,” in Bayesian Approach to Inverse Problems,J. Idier, ed. (ISTE, 2008), pp. 243–283.

Neichel, B.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

Osborn, J.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Prieur, J.-L.

J.-L. Prieur, G. Daigne, R. Avila, “SCIDAR measurements at Pic du Midi,” Astron. Astrophys. 371, 366–377 (2001).
[CrossRef]

Rigaut, F.

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

Robert, C.

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

N. Védrenne, V. Michau, C. Robert, J.-M. Conan, “Cn2 profile measurement from Shack-Hartmann data,” Opt. Lett. 32, 2659–2661 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Rocca, A.

A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[CrossRef]

Roddier, F.

A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[CrossRef]

Rousset, G.

F. Vidal, E. Gendron, G. Rousset, “Tomography approach for multi-object adaptive optics,” J. Opt. Soc. Am. A 27, 253–264 (2010).
[CrossRef]

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

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

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Sabil, M.

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Sarazin, M.

T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
[CrossRef]

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Sauvage, J.-F.

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

Shatsky, N.

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

Shepherd, H. W.

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Tallon, M.

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

Thiebaut, E.

E. Thiebaut, “Optimization issues in blind deconvolution algorithms,” Proc. SPIE 4847, 174–183 (2002).
[CrossRef]

Tokovinin, A.

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

Védrenne, N.

N. Védrenne, V. Michau, C. Robert, J.-M. Conan, “Cn2 profile measurement from Shack-Hartmann data,” Opt. Lett. 32, 2659–2661 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

N. Védrenne, “Propagation optique et correction en forte turbulence,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2008).

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

Vernin, J.

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

R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
[CrossRef]

A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[CrossRef]

Vidal, F.

F. Vidal, E. Gendron, G. Rousset, “Tomography approach for multi-object adaptive optics,” J. Opt. Soc. Am. A 27, 253–264 (2010).
[CrossRef]

Voyez, J.

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

Voziakova, O.

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

Wilson, R.

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Wilson, R. W.

T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
[CrossRef]

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103–108 (2002).
[CrossRef]

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Ziad, A.

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

Appl. Opt. (1)

R. Avila, J. Vernin, E. Masciadri, “Whole atmospheric-turbulence profiling with generalized scidar,” Appl. Opt. 36, 7898–7905 (1997).
[CrossRef]

Astron. Astrophys. (2)

J.-L. Prieur, G. Daigne, R. Avila, “SCIDAR measurements at Pic du Midi,” Astron. Astrophys. 371, 366–377 (2001).
[CrossRef]

A. Ziad, F. Blary, J. Borgnino, Y. Fanteï-Caujolle, E. Aristidi, F. Martin, H. Lantéri, R. Douet, E. Bondoux, D. Mékarnia, “First results of the PML monitor of atmospheric turbulence profile with high vertical resolution,” Astron. Astrophys. 559, L6 (2013).
[CrossRef]

J. Opt. Soc. Am. A (1)

C. Robert, J.-M. Conan, V. Michau, T. Fusco, N. Védrenne, “Scintillation and phase anisoplanatism in Shack-Hartmann wavefront sensing,” J. Opt. Soc. Am. A 23, 613–624 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Rocca, F. Roddier, J. Vernin, “Detection of atmospheric turbulent layers by spatiotemporal and spatioan-gular correlation measurements of stellar-light scintillation,” J. Opt. Soc. Am. 64, 1000–1004 (1974).
[CrossRef]

J. Opt. Soc. Am. A (1)

F. Vidal, E. Gendron, G. Rousset, “Tomography approach for multi-object adaptive optics,” J. Opt. Soc. Am. A 27, 253–264 (2010).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

A. Cortés, B. Neichel, A. Guesalaga, J. Osborn, F. Rigaut, D. Guzman, “Atmospheric turbulence profiling using multiple laser star wavefront sensors,” Mon. Not. R. Astron. Soc. 427, 2089–2099 (2012).
[CrossRef]

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

M. Le Louarn, N. Hubin, M. Sarazin, A. Tokovinin, “New challenges for adaptive optics: extremely large telescopes,” Mon. Not. R. Astron. Soc. 317, 535–544 (2000).
[CrossRef]

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

A. Tokovinin, V. Kornilov, N. Shatsky, O. Voziakova, “Restoration of turbulence profile from scintillation indices,” Mon. Not. R. Astron. Soc. 343, 891–899 (2003).
[CrossRef]

Mon. Not. R. Astron. Soc. (4)

E. Masciadri, F. Lascaux, L. Fini, “MOSE: operational forecast of the optical turbulence and atmospheric parameters at European Southern Observatory ground-based sites–I. Overview and vertical stratification of atmospheric parameters at 0–20 km,” Mon. Not. R. Astron. Soc. 436, 1968–1985 (2013).
[CrossRef]

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337, 103–108 (2002).
[CrossRef]

T. Butterley, R. W. Wilson, M. Sarazin, “Determination of the profile of atmospheric optical turbulence strength from SLODAR data,” Mon. Not. R. Astron. Soc. 369, 835–845 (2006).
[CrossRef]

Y. Hach, A. Jabiri, A. Ziad, A. Bounhir, M. Sabil, A. Abahamid, Z. Benkhaldoun, “Meteorological profiles and optical turbulence in the free atmosphere with NCEP/NCAR data at Oukaïmeden - I. Meteorological parameters analysis and tropospheric wind regimes,” Mon. Not. R. Astron. Soc. 420, 637–650 (2012).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

J. Voyez, C. Robert, V. Michau, J.-M. Conan, T. Fusco, “Accurate measurement of Cn2 profile with Shack-Hartmann data,” Proc. SPIE 8447, 8447 (2012).

E. Thiebaut, “Optimization issues in blind deconvolution algorithms,” Proc. SPIE 4847, 174–183 (2002).
[CrossRef]

Proc. SPIE (1)

J.-F. Sauvage, L. Mugnier, T. Fusco, G. Rousset, “Post processing of differential images for direct extrasolar planet detection from the ground,” Proc. SPIE 6272, 62722B (2006).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

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

Other (7)

A. Costille, T. Fusco, “Impact of the Cn2 description on Wide Field AO performance,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

N. Védrenne, “Propagation optique et correction en forte turbulence,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2008).

L. M. Mugnier, G. Le Besnerais, S. Meimon, “Inversion in optical imaging through atmospheric turbulence,” in Bayesian Approach to Inverse Problems,J. Idier, ed. (ISTE, 2008), pp. 243–283.

J. Voyez, C. Robert, N. Védrenne, B. Fleury, V. Michau, T. Fusco, “Cn2 profilometry from Shack-Hartmann data: model and experiment,” in Second International Conference on Adaptive Optics for Extremely Large Telescopes(2011).

R. Conan, “Modélisation des effets de l’ échelle externe de cohérence spatiale du front d’onde pour l’observation à haute résolution angulaire en astronomie: application à l’optique adaptative, à l’interférométrie et aux très grands telescopes,” Ph.D. thesis, Université de Nice-Sophia Antipolis (2000).

J. Osborn, R. W. Wilson, T. Butterley, R. Avila, V. S. Dhillon, T. J. Morris, H. W. Shepherd, “Stereo SCIDAR: Profiling atmospheric optical turbulence with improved altitude resolution,” inThird International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

E. Masciadri, G. Rousset, T. Fusco, A. Basden, P. Bonifacio, J. Fuensalida, C. Robert, M. Sarazin, R. Wilson, A. Ziad, “A roadmap for a new era turbulence studies program applied to the ground-based astronomy supported by AO,” in Third International Conference on Adaptive Optics for Extremely Large Telescopes(2013).

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Figures (13)

Fig. 1
Fig. 1

Example of simulated Shack-Hartmann turbulent and noisy images. (a) Full Shack-Hartmann long-exposure image. (b) Subaperture short-exposure image.

Fig. 2
Fig. 2

Correlation maps from simulated slope and scintillation data. One pixel of these maps shows the correlation averaged over all pairs of subapertures with given separation. (a), (b), (c) Auto-correlation maps. (d), (e), (f) Cross-correlation maps. (a), (d) Correlations of x-slopes. (b), (e) Correlations of y-slopes. (c), (f) Correlations of scintillation.

Fig. 3
Fig. 3

(a) ML reconstruction of the C n 2 profile from correlations of slopes only, of scintillation only and with the CO-SLIDAR method, in simulation. In all cases, the detection noise bias has been estimated jointly with the C n 2 profile. (b) Absolute error on the reconstruction.

Fig. 4
Fig. 4

ML CO-SLIDAR reconstruction of the C n 2 profile, with joint estimation of the detection noise bias and with exclusion of the variances from the direct problem, in simulation.

Fig. 5
Fig. 5

ML CO-SLIDAR reconstruction of the C n 2 profile, with joint estimation of the detection noise bias, and with the estimated 3σ error bars, in simulation.

Fig. 6
Fig. 6

(a) ML and MAP CO-SLIDAR reconstructions of the C n 2 profile and comparison with the reconstruction from correlations of scintillation only, in simulation. (b) Absolute error on the reconstruction.

Fig. 7
Fig. 7

Experimental Shack-Hartmann turbulent images, for a 3 ms exposure time. (a) Full Shack-Hartmann long-exposure image. (b) Subaperture short-exposure image.

Fig. 8
Fig. 8

Correlation maps from experimental slope and scintillation data. (a), (b), (c) Autocorrelation maps. (d), (e), (f) Cross-correlation maps. (a), (d) Correlations of x-slopes. (b), (e) Correlations of y-slopes. (c), (f) Correlations of scintillation.

Fig. 9
Fig. 9

ML reconstruction of the C n 2 profile from correlations of slopes only, of scintillation only and with the CO-SLIDAR method. 1 min dataset acquired around 01:00 UT, on May 15 th , 2012, with a 3 ms exposure time. In all cases, the detection noise bias has been estimated jointly with the C n 2 profile.

Fig. 10
Fig. 10

ML CO-SLIDAR reconstruction of the C n 2 profile, with joint estimation of the detection noise bias and with exclusion of the variances from the direct problem. 1 min dataset from May 15 th , 2012, around 01:00 UT.

Fig. 11
Fig. 11

ML and MAP CO-SLIDAR reconstructions of the C n 2 profile. 1 min dataset from May 15 th , 2012, around 01:00 UT.

Fig. 12
Fig. 12

(a), (b), (c) MAP CO-SLIDAR reconstructions of the C n 2 profile with the estimated 3σ error bars, for three consecutive minutes of observation. Each profile corresponds to one minute of observation. Data from May 15 th , 2012, around 01:00 UT.

Fig. 13
Fig. 13

MAP CO-SLIDAR reconstruction of the C n 2 profile. 1 min dataset from May 15 th , 2012, around 01:00 UT. Comparison with the free atmosphere profile at 00:00 UT and with the mean profile of May 2012, deduced from NCEP/NCAR Reanalysis.

Tables (2)

Tables Icon

Table 1 RMSE in function of the altitude slice for the ML reconstruction of the C n 2 profile, from correlations of slopes only, of scintillation only, and with the CO-SLIDAR method.

Tables Icon

Table 2 RMSE in function of the altitude slice, for the reconstruction of the C n 2 profile from correlations of scintillation only and for the ML and MAP CO-SLIDAR reconstructions.

Equations (16)

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

s u , v k ( α ) s u + δ u , v + δ v l ( α + θ ) = 0 + C n 2 ( h ) W s s k l ( h , ρ , θ ) d h ,
δ i u , v ( α ) δ i u + δ u , v + δ v ( α + θ ) = 0 + C n 2 ( h ) W i i ( h , ρ , θ ) d h ,
C s s k k ( δ u , δ v , θ ) = u , v s u , v k s u + δ u , v + δ v k ( θ ) N ( δ u , δ v ) , k { x , y } ,
C i i ( δ u , δ v , θ ) = u , v δ i u , v δ i u , v + δ v ( θ ) N ( δ u , δ v ) .
C mes = M C n 2 + C d + u .
J ML ( C n 2 ) = ( C mes C d M C n 2 ) T C conv 1 ( C mes C d M C n 2 ) .
J MAP ( C n 2 ) = ( C mes C d M C n 2 ) T C conv 1 ( C mes C d M C n 2 ) + J p ( C n 2 ) .
J p ( C n 2 ) = β C n 2 2 ,
δ h d sub θ ,
δ h 0.78 ( λ | h h gs | ) 1 2 θ ,
H max D θ .
RMSE = ( 1 N l i = 1 N l ( C n est 2 ( h i ) C n th 2 ( h i ) ) 2 ) 1 2 ,
V = 1 N r i = 1 N r x i 2 ,
Y = V σ X 2 = 1 N r i = 1 N r x i 2 σ X 2 .
Y = 1 N r i = 1 N r x i 2 σ X 2 = 0 .
σ Y 2 = Y 2 Y 2 = ( 1 N r i = 1 N r x i 2 σ X 2 ) 2 = ( 1 N r i = 1 N r x i 2 ) 2 + σ X 4 2 σ X 2 × 1 N r i = 1 N r x i 2 = 1 N r 2 i , j x i 2 x j 2 σ X 4 = 1 N r 2 i = 1 N r x i 4 + 1 N r 2 i j x i 2 x j 2 σ X 4 = 1 N r 2 i = 1 N r x i 4 + N r ( N r 1 ) N r 2 σ X 4 σ X 4 = 3 N r σ X 4 1 N r σ X 4 = 2 N r σ X 4 .

Metrics