Abstract

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack–Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars’ flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.

© 2010 Optical Society of America

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References

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  1. R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astrophys. J. 152, 29–31 (1985).
  2. M. A. van Dam, A. H. Bouchez, D. L. Mignant, and P. L. Wizinowich, “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540 (2006).
    [CrossRef] [PubMed]
  3. M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
    [CrossRef]
  4. R. Conan, O. Lardière, G. Herriot, C. Bradley, and K. Jackson, “Experimental assessment of the matched filter for laser guide star wavefront sensing,” Appl. Opt. 48, 1198–1211 (2009).
    [CrossRef]
  5. L. Gilles and B. Ellerbroek, “Shack–Hartmann wavefront sensing with elongated sodium laser beacons:centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
    [CrossRef] [PubMed]
  6. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
    [CrossRef]
  7. R. Clare, M. van Dam, and A. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
    [CrossRef] [PubMed]
  8. R. Clare and M. Le Louarn, “Simulations of laser guide star adaptive optics systems for the European Extremely Large Telescope,” in Proceedings of Adaptive Optics for Extremely Large Telescopes Conference (Paris) (EDP Sciences, 2009), p. 03005.
  9. M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
    [CrossRef]
  10. A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2005).
    [CrossRef]
  11. A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
    [CrossRef]
  12. M. Tallon and R. Foy, “Adaptive telescope with laser probe—Isoplanatism and cone effect,” Astrophys. J. 235, 549–557 (1990).
  13. A. Ziad, R. Conan, A. Tokovinin, F. Martin, and J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5424 (2000).
    [CrossRef]
  14. C. Béchet, M. Tallon, and Éric Thiébaut, “Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems,” J. Opt. Soc. Am. A 26, 497–508 (2009).
    [CrossRef]
  15. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  16. G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge Univ. Press, 1999), Chap. 5, pp. 91–130.
    [CrossRef]
  17. M. Nicolle, T. Fusco, V. Michau, G. Rousset, and J.-L. Beuzit, “Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics,” J. Opt. Soc. Am. A 23, 2233–2245 (2006).
    [CrossRef]
  18. L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993–1002 (2005).
    [CrossRef] [PubMed]
  19. E. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010).
    [CrossRef]
  20. M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.
  21. O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
    [CrossRef]

2010 (1)

2009 (3)

2008 (1)

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

2007 (2)

M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.

R. Clare, M. van Dam, and A. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
[CrossRef] [PubMed]

2006 (4)

2005 (2)

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

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2005).
[CrossRef]

2004 (1)

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

2003 (1)

A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
[CrossRef]

2000 (1)

1999 (1)

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge Univ. Press, 1999), Chap. 5, pp. 91–130.
[CrossRef]

1990 (1)

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

1985 (1)

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astrophys. J. 152, 29–31 (1985).

1965 (1)

Baumont, S.

A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
[CrossRef]

Béchet, C.

C. Béchet, M. Tallon, and Éric Thiébaut, “Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems,” J. Opt. Soc. Am. A 26, 497–508 (2009).
[CrossRef]

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.

Beuzit, J.-L.

Borgnino, J.

Bouchez, A.

Bouchez, A. H.

Bradley, C.

R. Conan, O. Lardière, G. Herriot, C. Bradley, and K. Jackson, “Experimental assessment of the matched filter for laser guide star wavefront sensing,” Appl. Opt. 48, 1198–1211 (2009).
[CrossRef]

O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
[CrossRef]

Clare, R.

R. Clare, M. van Dam, and A. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
[CrossRef] [PubMed]

R. Clare and M. Le Louarn, “Simulations of laser guide star adaptive optics systems for the European Extremely Large Telescope,” in Proceedings of Adaptive Optics for Extremely Large Telescopes Conference (Paris) (EDP Sciences, 2009), p. 03005.

Conan, R.

Ellerbroek, B.

Fedrigo, E.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Foy, R.

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

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astrophys. J. 152, 29–31 (1985).

Fried, D. L.

Fusco, T.

M. Nicolle, T. Fusco, V. Michau, G. Rousset, and J.-L. Beuzit, “Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics,” J. Opt. Soc. Am. A 23, 2233–2245 (2006).
[CrossRef]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

Gilles, L.

L. Gilles and B. Ellerbroek, “Shack–Hartmann wavefront sensing with elongated sodium laser beacons:centroiding versus matched filtering,” Appl. Opt. 45, 6568–6576 (2006).
[CrossRef] [PubMed]

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

Hampton, P.

O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
[CrossRef]

Herriot, G.

Hubin, N. N.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Jackson, K.

R. Conan, O. Lardière, G. Herriot, C. Bradley, and K. Jackson, “Experimental assessment of the matched filter for laser guide star wavefront sensing,” Appl. Opt. 48, 1198–1211 (2009).
[CrossRef]

O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
[CrossRef]

Korkiakoski, V.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Labeyrie, A.

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astrophys. J. 152, 29–31 (1985).

Lardière, O.

O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
[CrossRef]

R. Conan, O. Lardière, G. Herriot, C. Bradley, and K. Jackson, “Experimental assessment of the matched filter for laser guide star wavefront sensing,” Appl. Opt. 48, 1198–1211 (2009).
[CrossRef]

Le Louarn, M.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

R. Clare and M. Le Louarn, “Simulations of laser guide star adaptive optics systems for the European Extremely Large Telescope,” in Proceedings of Adaptive Optics for Extremely Large Telescopes Conference (Paris) (EDP Sciences, 2009), p. 03005.

Martin, F.

Michau, V.

M. Nicolle, T. Fusco, V. Michau, G. Rousset, and J.-L. Beuzit, “Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics,” J. Opt. Soc. Am. A 23, 2233–2245 (2006).
[CrossRef]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

Mignant, D. L.

Nicolle, M.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

M. Nicolle, T. Fusco, V. Michau, G. Rousset, and J.-L. Beuzit, “Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics,” J. Opt. Soc. Am. A 23, 2233–2245 (2006).
[CrossRef]

Rousset, G.

M. Nicolle, T. Fusco, V. Michau, G. Rousset, and J.-L. Beuzit, “Optimization of star-oriented and layer-oriented wavefront sensing concepts for ground layer adaptive optics,” J. Opt. Soc. Am. A 23, 2233–2245 (2006).
[CrossRef]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge Univ. Press, 1999), Chap. 5, pp. 91–130.
[CrossRef]

Tallon, M.

E. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010).
[CrossRef]

C. Béchet, M. Tallon, and Éric Thiébaut, “Comparison of minimum-norm maximum likelihood and maximum a posteriori wavefront reconstructions for large adaptive optics systems,” J. Opt. Soc. Am. A 26, 497–508 (2009).
[CrossRef]

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.

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

Tallon-Bosc, I.

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

Tarantola, A.

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2005).
[CrossRef]

Thiébaut, E.

E. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010).
[CrossRef]

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.

Thiébaut, Éric

Thomas, S.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

Tokovinin, A.

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
[CrossRef]

A. Ziad, R. Conan, A. Tokovinin, F. Martin, and J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5424 (2000).
[CrossRef]

van Dam, M.

van Dam, M. A.

Vasquez, J.

A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
[CrossRef]

Verinaud, C.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Wizinowich, P. L.

Yaitskova, N.

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Ziad, A.

Appl. Opt. (4)

Astrophys. J. (2)

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

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astrophys. J. 152, 29–31 (1985).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Mon. Not. R. Astron. Soc. (3)

A. Tokovinin, S. Baumont, and J. Vasquez, “Statistics of turbulence profile at Cerro Tololo,” Mon. Not. R. Astron. Soc. 340, 52–58 (2003).
[CrossRef]

O. Lardière, R. Conan, C. Bradley, K. Jackson, and P. Hampton, “Radial thresholding to mitigate laser guide star aberrations on centre-of-gravity-based Shack–Hartmann wavefront sensors,” Mon. Not. R. Astron. Soc. 398, 1461–1467 (2009).
[CrossRef]

S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack–Hartmann sensor,” Mon. Not. R. Astron. Soc. 371, 323–336 (2006).
[CrossRef]

Opt. Express (2)

Proc. SPIE (2)

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, “Shack–Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
[CrossRef]

M. Le Louarn, C. Verinaud, N. Yaitskova, V. Korkiakoski, E. Fedrigo, and N. N. Hubin, “Simulations of (MC)AO for a 100-m telescope,” Proc. SPIE 5490, 649–660 (2004).
[CrossRef]

Other (4)

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation (SIAM, 2005).
[CrossRef]

R. Clare and M. Le Louarn, “Simulations of laser guide star adaptive optics systems for the European Extremely Large Telescope,” in Proceedings of Adaptive Optics for Extremely Large Telescopes Conference (Paris) (EDP Sciences, 2009), p. 03005.

G. Rousset, “Wave-front sensors,” in Adaptive Optics in Astronomy, F.Roddier, ed. (Cambridge Univ. Press, 1999), Chap. 5, pp. 91–130.
[CrossRef]

M. Tallon, E. Thiébaut, and C. Béchet, “A fractal iterative method for fast wavefront reconstruction for extremely large telescopes,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM (Optical Society of America, 2007), p. PMA2.

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Figures (7)

Fig. 1
Fig. 1

Elongated spots geometries on a Shack–Hartmann WFS illustrated with only 11 × 11 subapertures. The cross indicates the LLT positions. Top, central launching; bottom; side launching.

Fig. 2
Fig. 2

Linear size of the square box of 50% EE versus α, the fraction of elongation in the improved noise model. Dashed curve, central launching; solid curve, side launching.

Fig. 3
Fig. 3

Linear size of the square box of 50% EE versus average number of photons per frame and per sub-aperture, for central launching. Dashed, curve, uniform and uncorrelated noise model; solid curve, improved noise model.

Fig. 4
Fig. 4

Same axes as in Fig. 3, for side launching. Dashed curve, uniform and uncorrelated noise model; solid curve, improved noise model.

Fig. 5
Fig. 5

Same axes as in Fig. 3. Improved noise modeled in the reconstructor. Squares, central launching; triangles, side launching.

Fig. 6
Fig. 6

Same axes as in Fig. 3. All curves are obtained with uniform and uncorrelated noise modeled in the reconstructor. Two different atmospheric profiles are simulated. Dashed (and upper), bad profile; dotted (and lower), good profile. Circles, central launching; triangles, side launching. Horizontal lines illustrate the seeing level.

Fig. 7
Fig. 7

Same as Fig. 6 but with improved noise modeled in the reconstructor. Squares, central launching; triangles, side launching.

Tables (1)

Tables Icon

Table 1 C n 2 Distribution in the Layers and Seeing Values for the Median, Good, and Bad Profiles

Equations (20)

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

β FWHM Na ( r sa r llt ) h 0 2 ,
d k = S w k G a + n k ,
w k = w GL + w k HL ,
d k = S w GL G a + e k ,
e k = d k HL + n k
C GL = w GL w GL T = K K T
C err = e e T = n n T + d HL d HL T = C noise + C HL ,
C noise σ noise 2 I ,
[ C HL ] k , l = d k HL d l HL T = S w k HL w l HL T S T .
C HL σ HL 2 I ,
C err unif = σ err 2 I ,
[ C err ] 2 × 2 = σ err 2 ( 1 + ϵ x x ϵ x y ϵ x y 1 + ϵ y y ) ,
ϵ x x = α 2 β x 2 ω PSF 2 ,
ϵ x y = α 2 β x β y ω PSF 2 ,
ϵ y y = α 2 β y 2 ω PSF 2 ,
( S T ( k = 1 n s C err , k 1 ) S + C GL 1 ) w ̂ GL = S T ( k = 1 n s C err , k 1 ( d k + G a ) ) ,
( n s S T S + σ err 2 C GL 1 ) w ̂ GL = S T ( k = 1 n s ( d k + G a ) ) .
[ C err 1 ] 2 × 2 = ω PSF 2 σ err 2 ( ω PSF 2 + α 2 β 2 ) ( 1 + ϵ y y ϵ x y ϵ x y 1 + ϵ x x ) ,
b ( n ) = b ( n 1 ) + γ ( w ̂ GL ( n ) b ( n 2 ) )
a ( n ) = P b ( n ) ,

Metrics