Abstract

Sodium laser guide stars (LGSs) increase the sky coverage of adaptive optics systems but have their own limitations. For Shack–Hartmann wavefront sensors (WFSs), the slow variations of the sodium layer altitude and atom density profile induce changing errors on centroid measurements, especially for extremely large telescopes (ELTs), as the spot elongation increases with the telescope diameter. These LGS-induced aberrations are propagated on the science path and must be filtered out by (i) optimizing the LGS WFS and the centroiding algorithm and (ii) adding a high-pass filter on the LGS path and a low- bandwidth natural-guide-star (NGS) WFS. Within the context of the European Southern Observatory European-ELT project, five different centroiding algorithms, namely, the center-of-gravity (CoG), weighted CoG, matched filter, quad cell, and correlation, have been evaluated in a closed loop on the University of Victoria LGS wavefront sensing test bed. This optical bench reproduces, in the laboratory, both NGS spots and LGS elongated spots with changing sodium profiles and turbulence. Each centroiding algorithm performance is compared and discussed for a central- versus side-launch laser: different fields of view, pixel sampling, and signal-to-noise ratios.

© 2010 Optical Society of America

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References

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  1. G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
    [CrossRef]
  2. 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]
  3. 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]
  4. 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]
  5. 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]
  6. 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]
  7. P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
    [CrossRef]
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    [CrossRef]
  9. M. Nicolle, T. Fusco, G. Rousset, and V. Michau, “Improvement of Shack-Hartmann wave-front sensor measurement for extreme adaptive optics,” Opt. Lett. 29, 2743–2745 (2004).
    [CrossRef] [PubMed]
  10. L. Gilles and B. Ellerbroek, “Constrained matched filtering for extended dynamic range and improved noise rejection for Shack-Hartmann wavefront sensing,” Opt. Lett. 33, 1159–1161 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. K. Ogata, Discrete-Time Control Systems (Prentice-Hall, 1994).
  13. D. S. Davis, P. Hickson, G. Herriot, and C.-Y. She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
    [CrossRef] [PubMed]
  14. T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
    [CrossRef]
  18. M. Kissler-Patig, “Overall science goals and top level AO requirements for E-ELT,” presented at the Conference on Adaptive Optics for Extremely Large Telescopes, Paris, France, June 2009.
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    [CrossRef]
  20. F. Assémat, R. Wilson, and E. Gendron, “Method for simulating infinitely long and non stationary phase screens with optimized memory storage,” Opt. Express 14, 988–999(2006).
    [CrossRef] [PubMed]

2009 (3)

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]

T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
[CrossRef]

2008 (5)

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

L. Gilles and B. Ellerbroek, “Constrained matched filtering for extended dynamic range and improved noise rejection for Shack-Hartmann wavefront sensing,” Opt. Lett. 33, 1159–1161 (2008).
[CrossRef] [PubMed]

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 (1)

2006 (6)

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(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. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (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]

F. Assémat, R. Wilson, and E. Gendron, “Method for simulating infinitely long and non stationary phase screens with optimized memory storage,” Opt. Express 14, 988–999(2006).
[CrossRef] [PubMed]

D. S. Davis, P. Hickson, G. Herriot, and C.-Y. She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

1976 (1)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
[CrossRef]

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]

Assémat, F.

Bouchez, A.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Bouchez, A. H.

Bradley, C.

Campbell, R. D.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Chin, J. C. Y.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Clare, R.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

Clare, R. M.

Conan, R.

Contos, A. R.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Davis, D. S.

Ellerbroek, B.

L. Gilles and B. Ellerbroek, “Constrained matched filtering for extended dynamic range and improved noise rejection for Shack-Hartmann wavefront sensing,” Opt. Lett. 33, 1159–1161 (2008).
[CrossRef] [PubMed]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

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]

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

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.

Gilles, L.

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

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]

Hartman, S. K.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Herriot, G.

Hickson, P.

T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
[CrossRef]

D. S. Davis, P. Hickson, G. Herriot, and C.-Y. She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[CrossRef] [PubMed]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

Jackson, K.

Johansson, E. M.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Kissler-Patig, M.

M. Kissler-Patig, “Overall science goals and top level AO requirements for E-ELT,” presented at the Conference on Adaptive Optics for Extremely Large Telescopes, Paris, France, June 2009.

Lafon, R. E.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Lardière, O.

Le Mignant, D.

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. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Lewis, H.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Looze, D.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

Michau, V.

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]

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

Nelson, J.

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

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

Noll, R. J.

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
[CrossRef]

Ogata, K.

K. Ogata, Discrete-Time Control Systems (Prentice-Hall, 1994).

Pfrommer, T.

T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
[CrossRef]

Poyneer, L.

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).
[CrossRef]

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

Sanders, G. H.

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

She, C.-Y.

T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
[CrossRef]

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

D. S. Davis, P. Hickson, G. Herriot, and C.-Y. She, “Temporal variability of the telluric sodium layer,” Opt. Lett. 31, 3369–3371 (2006).
[CrossRef] [PubMed]

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Stomski, P. J.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

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).
[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]

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).
[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]

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Véran, J.-P.

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

Wilson, R.

Wizinowich, P.

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Wizinowich, P. L.

Appl. Opt. (2)

Geophys. Res. Lett. (1)

T. Pfrommer, P. Hickson, and C.-Y. She, “A large-aperture sodium fluorescence lidar with very high resolution for mesopause dynamics and adaptive optics studies,” Geophys. Res. Lett. 36, L15831 (2009).
[CrossRef]

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

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. A 66, 207–211 (1976).
[CrossRef]

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

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]

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, 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]

Opt. Express (4)

Opt. Lett. (3)

Proc. SPIE (3)

G. Herriot, P. Hickson, B. Ellerbroek, J.-P. Véran, C.-Y. She, R. Clare, and D. Looze, “Focus errors from tracking sodium layer altitude variations with laser guide star adaptive optics for the Thirty Meter Telescope,” Proc. SPIE 6272, 62721I(2006).
[CrossRef]

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

P. Wizinowich, D. Le Mignant, A. 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, and D. M. Summers, “The W. M. Keck Observatory laser guide star adaptive optics system: overview,” Publ. Astron. Soc. Pac. 118, 297–309 (2006).
[CrossRef]

Other (2)

K. Ogata, Discrete-Time Control Systems (Prentice-Hall, 1994).

M. Kissler-Patig, “Overall science goals and top level AO requirements for E-ELT,” presented at the Conference on Adaptive Optics for Extremely Large Telescopes, Paris, France, June 2009.

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Figures (11)

Fig. 1
Fig. 1

Principle of the LGS aberration filtering with a LB NGS-WFS. (a) AO system subjected to LGS aberrations. R ( z ) is the atmospheric turbulence. The LGS aberrations D ( z ) are internal feedback disturbances fully propagated on the science path C ( z ) . (b) LGS aberration filtering: an HPF must be implemented after the LGS WFS. The LPF is the lower frame rate of the NGS WFS. HPF ( z ) + LPF ( z ) must be 1 to act as a pure integrator for turbulence. The RTFs are plotted for both inputs R ( z ) and D ( z ) for a closed-loop system running at 800 Hz , and g = 0.2 .

Fig. 2
Fig. 2

Theoretical response of the WCoG for symmetric and asymmetric spots (left-hand side column). The weighting function is an unshifted copy of the spot itself (ideal case—the snapshot spot matches the reference image).

Fig. 3
Fig. 3

Quad-cell sampling of an elongated spot. Dithering for real-time gain measurements.

Fig. 4
Fig. 4

Sodium profile time series used on the UVic LGS bench. (a) Initial data from the UBC LIDAR, night 20080804 [14], with a 24 m vertical resolution and a 1 s time resolution. The solid curve represents the mean altitude of each sodium profile, while the dotted curve shows the skewness (the third central moment) of each profile (arbitrary unit). (b) Same profile time series used on the test bed with no altitude variations and after applying a 20 s width median filter to smooth the lidar photon noise.

Fig. 5
Fig. 5

Implementation on the bench of the LBWFS and the HPF. The LBWFS is emulated by averaging the images of the TWFS during one update period (LPF). Similarly, the LGS offsets are the average slopes (or voltages here) of the last update period (HPF). For the MF and Cor, the HPF is not needed because the update of the reference image I o acts already as an HPF. The LBWFS frames, LGS offsets, I o , and gains are updated by the same reset signal. The TWFS is used only during the first two updates to start the closed loop, pending valid gains and reference images, and to measure the performance of the algorithm closing the loop. For the tests without turbulence, the gains and I o are computed from high flux images to keep a good SNR when the sodium profile time series is played in fast motion.

Fig. 6
Fig. 6

(a) Modeling of the LGS aberrations induced by a uniform pixel thresholding of the spots (Ref. [5]). (b) LGS aberrations measured on the test bed for a central- and a side-launch laser with the CoG and a uniform pixel threshold. The mean altitude changes of the sodium profiles are removed to mimic the zoom optics planned to be used with LGS. The SNR is about 120 for the unelongated spots.

Fig. 7
Fig. 7

(a) Tip–tilt, (b) focus, and (c) higher-order modes induced by the sodium layer structure variations with a side-launch laser for the five centroiding algorithms. There is no variation of the mean altitude of the sodium profiles, no turbulence, and no LBWFS. The tip–tilt and focus errors match quite well the sodium layer skewness, plotted in (d). For information, the maximum intensity and the FWHM of the sodium profiles are plotted, too. Gains and reference images are updated every 20 s . 300 photons/subaperture/frame, pixel size is 0.96 arc sec, FoV = 12 × 12 pixels.

Fig. 8
Fig. 8

Residual focus error versus time obtained without and with the LGS aberration filter (i.e., without and with a LBWFS and HPF) for the CoG algorithm. The TWFS is used to close the loop during the first 40 s , and then the LGS-WFS and LBWFS took over. The frame rates of the LGS WFS and LBWFS are 1 Hz and 1 / 20 Hz , respectively. Central-launch laser, FoV = 11.52 arc sec, pixel size is 0.96 arc sec, 300 photons/subaperture/frame, no turbulence.

Fig. 9
Fig. 9

Closed-loop rms WFE obtained with a LGS-WFS and a LBWFS, for different LGS centroiding algorithms with a central-launch laser and a calm sodium layer, for 300 (left) and 1100 (right) photons/subaperture/frame. The top graphs plot the WFE versus time, and the bottom graphs plot the statistical distribution of the WFE (the box has lines at the lower-quartile, median, and upper-quartile values). Only modes beyond focus up to Z 28 are considered. Sample time is 1 / 700 s ; the update period of the LGS-WFS offsets (and gains) and LBWFS frames is 0. 5 s (i.e., one update every 350 iterations). Na profile time series from UBC 20080804 (profiles 3 to 5), pixel size is 0.48 arc sec, FoV is 11.52 arc sec.

Fig. 10
Fig. 10

Root mean square WFE versus centroiding algorithms with turbulence, side-launch laser, calm sodium layer, for 300 (left) and 1100 (right) photons/subaperture/frame. Na profile time series from UBC 20080804 (profiles 3 to 5), pixel size is 0.96 arc sec, FoV is 23.04 arc sec. More details are in Fig. 9 caption.

Fig. 11
Fig. 11

Root mean square WFE versus centroiding algorithms with turbulence, side-launch laser, and stormy sodium layer for 300 (left) and 1100 (right) photons/subaperture/frame. Na profile time series from UBC 20080804 (profiles 780 to 790), pixel size is 0.96 arc sec, FoV is 23.04 arc sec. More details are in Fig. 9 caption.

Tables (5)

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Table 1 Median rms Phase Error from Mode Z 5 to Z 28 , in Nanometers, Obtained in Closed Loop with Matched Filter for Different FoVs, with LBWFS Running at 0.05 Hz and No Turbulence a

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Table 2 Median rms Phase Error from Mode Z 5 to Z 28 , in Nanometers, Obtained in Closed Loop with Matched Filter for Different Pixel Scales, with LBWFS Running at 0.05 Hz and No Turbulence a

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Table 3 Median rms Phase Error from Mode Z 5 to Z 28 , in Nanometers, for Five Centroiding Algorithms in Different Scenarios a

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Table 4 Median rms Phase Error from Mode Z 5 to Z 28 , in Nanometers, for Different Fields of View in Arcseconds (and in Pixels for Center of Gravity and Matched Filter) per Subaperture a

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Table 5 Median rms Phase Error from Mode Z 5 to Z 28 , in Nanometers, for Different Pixel Sizes in Arcseconds

Equations (19)

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CoG ( I ) = ( x , y x I ( x , y ) x , y I ( x , y ) , x , y y I ( x , y ) x , y I ( x , y ) ) .
θ ^ CoG = CoG ( I ) .
WCoG ( I , I o ) = CoG ( I I o ) ,
WCoG ( I , I o ) = θ + θ o 2 .
WCoG ( I , I o ) = k θ + k o θ o .
θ ^ WCoG = 2 ( WCoG ( I , I o ) 1 2 WCoG ( I o , I o ) ) ,
θ ^ WCoG = 1 k ( WCoG ( I , I o ) k o WCoG ( I o , I o ) ) .
Q x = I 1 + I 2 I 3 I 4 I 1 + I 2 + I 3 + I 4 , Q y = I 1 + I 3 I 2 I 4 I 1 + I 2 + I 3 + I 4 .
θ ^ x = Q x G x , θ ^ y = Q y G y ,
G x = Q x + Q x 2 A ,
I = I o + ( θ x θ o x ) I θ x + ( θ y θ o y ) I θ y .
I I o = G ( θ θ o ) ,
G = I + I 2 A ,
θ ^ MF = R ( I I o ) + θ o ,
θ ^ MF = R ( I I o ) + CoG ( I o ) .
θ ^ Cor = θ peak + θ o ,
A PTV = λ 4 E N ,
E = r t Na h Na 2 σ ,
volt n = volt n 1 + g ( HPF ( volt LGS ) + g NGS volt NGS ) ,

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