Abstract

The subaperture images in Shack–Hartmann wavefront sensors are elongated when using sodium laser guide stars, due to the parallax effect and the nonzero thickness of the sodium layer. This elon gation increases the measurement error in each subaperture and introduces a correlation between the measurements in the orthogonal x and y pixel axes. We show, via end-to-end numerical simulations, that including these errors in a matrix-vector-multiply maximum a posteriori reconstructor sig nificantly improves the expected performance of a laser tomography adaptive optics system for the 42m diameter European Extremely Large Telescope. In particular, including this noise-weighted re construction shows the detected photon requirement is similar for both central and side launch of the sodium lasers.

© 2010 Optical Society of America

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  26. J. Kolb, M. Downing, and R. M. Clare, “Detectors for LGS WF sensing on an ELT: characteristics, special features, limitations, technology,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 05014.
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2010

2009

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]

L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
[CrossRef]

2008

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

R. M. Clare, M. Le Louarn, S. Oberti, and A. Garcia-Rissmann, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 7015, 701572(2008).
[CrossRef]

S. Thomas, S. Adkins, D. Gavel, T. Fusco, and V. Michau, “Study of optimal wavefront sensing with elongated laser guide stars,” Mon. Not. R. Astron. Soc. 387, 173–187 (2008).
[CrossRef]

O. Lardière, R. Conan, C. Bradley, K. Jackson, and G. Herriot, “A laser guide star wavefront sensor bench demonstrator for TMT,” Opt. Express 16, 5527–5543 (2008).
[CrossRef] [PubMed]

2007

2006

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]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, and P. L. Wizinowich, “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540(2006).
[CrossRef] [PubMed]

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[CrossRef] [PubMed]

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

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

2005

2004

M. Le Louarn, C. Verinaud, V. Korkiakoski, and E. Fedrigo, “Parallel simulation tools for AO on ELTS,” Proc. SPIE 5490 (2004).
[CrossRef]

M. Le Louarn and N. Hubin, “Wide-field adaptive optics for deep-field spectroscopy in the visible,” Mon. Not. R. Astron. Soc. 349, 1009–1018 (2004).
[CrossRef]

2000

1999

1998

B. L. Ellerbroek and D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North Telescope,” Publ. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

1985

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Adkins, S.

S. Thomas, S. Adkins, D. Gavel, T. Fusco, and V. Michau, “Study of optimal wavefront sensing with elongated laser guide stars,” Mon. Not. R. Astron. Soc. 387, 173–187 (2008).
[CrossRef]

Argall, P. S.

Arsenault, R.

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

Béchet, C.

C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
[CrossRef]

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

C. Béchet, M. Le Louarn, R. M. Clare, M. Tallon, I. Tallon-Bosc, and É. Thiébaut, “Closed-loop ground layer adaptive optics simulations with elongated spots: impact of modeled noise correlations,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03004.

Bouchez, A. H.

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

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

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, and P. L. Wizinowich, “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540(2006).
[CrossRef] [PubMed]

Bradley, C.

Brown, C. G.

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Campbell, R. D.

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

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

Chin, J. C. Y.

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

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Clare, R. M.

C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
[CrossRef]

R. M. Clare, M. Le Louarn, S. Oberti, and A. Garcia-Rissmann, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 7015, 701572(2008).
[CrossRef]

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

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[CrossRef] [PubMed]

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

J. Kolb, M. Downing, and R. M. Clare, “Detectors for LGS WF sensing on an ELT: characteristics, special features, limitations, technology,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 05014.

R. M. Clare and M. Le Louarn, “Simulations of laser guide star adaptive optics systems for the European Extremely Large Telescope,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03005.

C. Béchet, M. Le Louarn, R. M. Clare, M. Tallon, I. Tallon-Bosc, and É. Thiébaut, “Closed-loop ground layer adaptive optics simulations with elongated spots: impact of modeled noise correlations,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03004.

Conan, J.-M.

L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
[CrossRef]

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

Conan, R.

Contos, A. R.

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Danforth, P. M.

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Dekany, R.

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

Diolaiti, E.

L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
[CrossRef]

Downing, M.

J. Kolb, M. Downing, and R. M. Clare, “Detectors for LGS WF sensing on an ELT: characteristics, special features, limitations, technology,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 05014.

Ellerbroek, B.

Ellerbroek, B. L.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[CrossRef] [PubMed]

B. L. Ellerbroek and D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North Telescope,” Publ. Astron. Soc. Pac. 110, 165–185 (1998).
[CrossRef]

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

Fedrigo, E.

M. Le Louarn, C. Verinaud, V. Korkiakoski, and E. Fedrigo, “Parallel simulation tools for AO on ELTS,” Proc. SPIE 5490 (2004).
[CrossRef]

Foppiani, I.

L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
[CrossRef]

Foy, R.

R. Foy and A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Fusco, T.

S. Thomas, S. Adkins, D. Gavel, T. Fusco, and V. Michau, “Study of optimal wavefront sensing with elongated laser guide stars,” Mon. Not. R. Astron. Soc. 387, 173–187 (2008).
[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]

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

Garcia-Rissmann, A.

R. M. Clare, M. Le Louarn, S. Oberti, and A. Garcia-Rissmann, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 7015, 701572(2008).
[CrossRef]

Gavel, D.

S. Thomas, S. Adkins, D. Gavel, T. Fusco, and V. Michau, “Study of optimal wavefront sensing with elongated laser guide stars,” Mon. Not. R. Astron. Soc. 387, 173–187 (2008).
[CrossRef]

Gendron, E.

D. Gratadour, E. Gendron, G. Rousset, and F. Rigaut, “Fratricide effect on ELTs,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 04005.

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]

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P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
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Le Louarn, M.

C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
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M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” Publ. Astron. Soc. Pac. 118, 310–318 (2006).
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P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
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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).
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Mwangi, M. M.

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).
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Oberti, S.

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Pennington, D. M.

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
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L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
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Rousset, G.

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).
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T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, “Efficient phase estimation for large-field-of-view adaptive optics,” Opt. Lett. 24, 1472–1474 (1999).
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D. Gratadour, E. Gendron, G. Rousset, and F. Rigaut, “Fratricide effect on ELTs,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 04005.

Schreiber, L.

L. Schreiber, I. Foppiani, C. Robert, E. Diolaiti, J.-M. Conan, and M. Lombini, “Laser guide stars for extremely large telescopes: efficient Shack-Hartmann wavefront sensor design using the weighted centre-of-gravity algorithm,” Mon. Not. R. Astron. Soc. 396, 1513–1521 (2009).
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Sica, R. J.

Stoesz, J.

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Stomski, P. J.

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

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
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M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” Publ. Astron. Soc. Pac. 118, 310–318 (2006).
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Tallon, M.

É. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010).
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C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
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M. Tallon, I. Tallon-Bosc, É. Thiébaut, and C. Béchet, “Shack-Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
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C. Béchet, M. Le Louarn, R. M. Clare, M. Tallon, I. Tallon-Bosc, and É. Thiébaut, “Closed-loop ground layer adaptive optics simulations with elongated spots: impact of modeled noise correlations,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03004.

Tallon-Bosc, I.

C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
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M. Tallon, I. Tallon-Bosc, É. Thiébaut, and C. Béchet, “Shack-Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
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C. Béchet, M. Le Louarn, R. M. Clare, M. Tallon, I. Tallon-Bosc, and É. Thiébaut, “Closed-loop ground layer adaptive optics simulations with elongated spots: impact of modeled noise correlations,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03004.

Thiébaut, É.

C. Béchet, M. Tallon, I. Tallon-Bosc, É. Thiébaut, M. Le Louarn, and R. M. Clare, “Optimal reconstruction for closed-loop ground layer adaptive optics with elongated spots,” J. Opt. Soc. Am. A 27, A1–A8 (2010).
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É. Thiébaut and M. Tallon, “Fast minimum variance wavefront reconstruction for extremely large telescopes,” J. Opt. Soc. Am. A 27, 1046–1059 (2010).
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M. Tallon, I. Tallon-Bosc, É. Thiébaut, and C. Béchet, “Shack-Hartmann wavefront reconstruction with elongated sodium laser guide stars: improvements with priors and noise correlations,” Proc. SPIE 7015, 70151N (2008).
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C. Béchet, M. Le Louarn, R. M. Clare, M. Tallon, I. Tallon-Bosc, and É. Thiébaut, “Closed-loop ground layer adaptive optics simulations with elongated spots: impact of modeled noise correlations,” in Proceedings of the First International Conference on Adaptive Optics for Extremely Large Telescopes, Y.Clénet, J.-M.Conan, T.Fusco, and G.Rousset, eds. (EDP Sciences, 2009), p. 03004.

Thomas, S.

S. Thomas, S. Adkins, D. Gavel, T. Fusco, and V. Michau, “Study of optimal wavefront sensing with elongated laser guide stars,” Mon. Not. R. Astron. Soc. 387, 173–187 (2008).
[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).
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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).
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B. L. Ellerbroek and D. W. Tyler, “Adaptive optics sky coverage calculations for the Gemini-North Telescope,” Publ. Astron. Soc. Pac. 110, 165–185 (1998).
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van Dam, M. A.

R. M. Clare, M. A. van Dam, and A. H. Bouchez, “Modeling low order aberrations in laser guide star adaptive optics systems,” Opt. Express 15, 4711–4725 (2007).
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M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” Publ. Astron. Soc. Pac. 118, 310–318 (2006).
[CrossRef]

M. A. van Dam, A. H. Bouchez, D. Le Mignant, and P. L. Wizinowich, “Quasi-static aberrations induced by laser guide stars in adaptive optics,” Opt. Express 14, 7535–7540(2006).
[CrossRef] [PubMed]

P. L. Wizinowich, D. Le Mignant, A. H. Bouchez, R. D. Campbell, J. C. Y. Chin, A. R. Contos, M. A. van Dam, S. K. Hartman, E. M. Johansson, R. E. Lafon, H. Lewis, P. J. Stomski, D. M. Summers, C. G. Brown, P. M. Danforth, and D. M. Pennington, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
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Vassiliev, O. N.

Véran, J.-P.

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, “Adaptive optics sky coverage modeling for extremely large telescopes,” Appl. Opt. 45, 8964–8978 (2006).
[CrossRef] [PubMed]

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

Verinaud, C.

M. Le Louarn, C. Verinaud, V. Korkiakoski, and E. Fedrigo, “Parallel simulation tools for AO on ELTS,” Proc. SPIE 5490 (2004).
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Vérinaud, C.

N. Hubin, B. L. Ellerbroek, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J.-P. Véran, and C. Vérinaud, “Adaptive optics for Extremely Large Telescopes,” in Proceedings of the International Astronomical Union: Scientific Requirements for Extremely Large Telescopes P.Whitelock, M.Dennefeld, and B.Leibundgut, eds. (Cambridge U. Press2005), pp. 60–85.

Wizinowich, P. L.

M. A. van Dam, A. H. Bouchez, D. Le Mignant, R. D. Campbell, J. C. Y. Chin, S. K. Hartman, E. M. Johansson, R. Lafon, P. J. Stomski Jr., D. M. Summers, and P. L. Wizinowich, “The W. M. Keck Observatory laser guide star adaptive optics system: performance characterization,” Publ. Astron. Soc. Pac. 118, 310–318 (2006).
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Figures (8)

Fig. 1
Fig. 1

Example spot elongation patterns for the 42 m EELT for (a) central launch and (b) side launch. There are only 11 × 11 subapertures here for illustration, and the FWHM of the sodium layer is 10.0 km . The crosses denote the laser launch locations.

Fig. 2
Fig. 2

Example metapupils at an altitude of 12 km for an LTAO system for the 42 m EELT with four LGS in a circle of radius 45 arc sec for (a) central launch and (b) side launch. Again, there are only 11 × 11 subapertures here for illustration, and the FWHM of the sodium layer is 10.0 km . The crosses denote the laser launch locations.

Fig. 3
Fig. 3

Normalized sodium profiles: (a) Gaussian of FWHM 11.4 km and (b) lidar mean profile.

Fig. 4
Fig. 4

Strehl in K band versus the detected photon flux per subaperture without noise-optimal weighting ( α = 0 ) for central (solid curve) and side (dashed curve) launch for (a) the Gaussian sodium profile and (b) the lidar mean profile.

Fig. 5
Fig. 5

Strehl in K band versus the noise weighting parameter α with a signal level of 100 photons/subaperture/frame for central (solid curve) and side (dashed curve) launch for (a) the Gaussian profile and (b) the lidar mean profile.

Fig. 6
Fig. 6

Strehl in K band versus the detected photon flux per subaperture for central launch with ( α = 0.6 , solid curve) and without ( α = 0 , dashed curve) noise-optimal weighting for (a) the Gaussian profile and (b) the lidar mean profile.

Fig. 7
Fig. 7

Strehl in K band versus the detected photon flux per subaperture for side launch with ( α = 0.3 , solid curve) and without ( α = 0 , dashed curve) noise-optimal weighting for (a) the Gaussian profile and (b) the lidar mean profile.

Fig. 8
Fig. 8

Strehl in K band versus the number of detected photons/subaperture/frame with noise-optimal weighting for central (solid curve) and side (dashed curve) launch for (a) the Gaussian profile and (b) the lidar mean profile.

Tables (2)

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Table 1 Atmospheric Model Used for Simulations

Tables Icon

Table 2 LTAO System Parameters

Equations (14)

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β = cos ( ζ ) b t h 2 ,
σ θ = θ S N R ,
d k ; m = S k ; m w m + n k ; m ,
d k = S k w + n k ,
( S T C 1 S + W 1 ) w ^ = S T C 1 d ,
C = ( C 1 0 C k 0 C N ) ,
W = ( W 1 ( L 0 , r 0 ; m = 1 ) 0 0 W 2 ( L 0 , r 0 ; m = 2 ) ) ,
d = ( d 1 d k d N ) .
S = ( S 1 S k S N ) .
w ^ = ( S T C 1 S + W 1 ) 1 S T C 1 d ,
w ^ = G d .
G = ( S T C 1 S + W 1 ) 1 S T C 1 .
[ C k ] 1 = 1 σ n 2 θ 2 θ 2 + α 2 ( β x 2 + β y 2 ) ( 1 + α 2 β y 2 / θ 2 α 2 β x β y / θ 2 α 2 β x β y / θ 2 1 + α 2 β x 2 / θ 2 ) ,
σ n 2 = π 2 2 ln ( 2 ) 1 N p ( θ θ d ) 2 ,

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