Abstract

We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wave-front sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star.

© 2004 Optical Society of America

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References

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  1. J. Brenner, L. Cummings, “The Hadamard maximum determinant problem,” Am. Math. Monthly 79, 626–630 (1972).
    [CrossRef]
  2. J. H. van Lint, R. M. Wilson, A Course in Combinatorics (Cambridge U. Press, New York, 1993).
  3. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
    [CrossRef] [PubMed]
  4. J. Y. Wang, J. K. Markey, “Modal compensation of atmospheric turbulence phase distortion,” J. Opt. Soc. Am. 68, 78–87 (1978).
    [CrossRef]
  5. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  6. M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
    [CrossRef]
  7. R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

2003 (1)

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

2000 (1)

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

1988 (1)

1978 (1)

1976 (1)

1972 (1)

J. Brenner, L. Cummings, “The Hadamard maximum determinant problem,” Am. Math. Monthly 79, 626–630 (1972).
[CrossRef]

Alonso, J.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Arsenault, R.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Bonnet, H.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Brenner, J.

J. Brenner, L. Cummings, “The Hadamard maximum determinant problem,” Am. Math. Monthly 79, 626–630 (1972).
[CrossRef]

Brynnel, J.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Cummings, L.

J. Brenner, L. Cummings, “The Hadamard maximum determinant problem,” Am. Math. Monthly 79, 626–630 (1972).
[CrossRef]

Delabre, B.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Delplancke, F.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Donaldson, R.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Dupuy, C.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Erm, T.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Farinato, J.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Fedrigo, E.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Gigan, P.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Glindemann, A.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Herbst, T.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Hippler, S.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Hubin, N.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Ivanescu, L.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Kasper, M.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Lizon, J.-L.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Looze, D. P.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Markey, J. K.

Noll, R. J.

Oberti, S.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Ott, T.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Paufique, J.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Pouplard, F.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Quattri, M.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Reiss, R.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Roddier, F.

Rossi, S.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Silber, A.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Spyromilio, J.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Stroebele, S.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Tordo, S.

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

van Lint, J. H.

J. H. van Lint, R. M. Wilson, A Course in Combinatorics (Cambridge U. Press, New York, 1993).

Wang, J. Y.

Wilson, R. M.

J. H. van Lint, R. M. Wilson, A Course in Combinatorics (Cambridge U. Press, New York, 1993).

Wirth, A.

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

Am. Math. Monthly (1)

J. Brenner, L. Cummings, “The Hadamard maximum determinant problem,” Am. Math. Monthly 79, 626–630 (1972).
[CrossRef]

Appl. Opt. (1)

ESO Messenger (1)

R. Arsenault, J. Alonso, H. Bonnet, J. Brynnel, B. Delabre, R. Donaldson, C. Dupuy, E. Fedrigo, J. Spyromilio, T. Erm, J. Farinato, N. Hubin, L. Ivanescu, M. Kasper, S. Oberti, J. Paufique, S. Rossi, S. Tordo, S. Stroebele, J.-L. Lizon, P. Gigan, F. Pouplard, F. Delplancke, A. Silber, M. Quattri, R. Reiss, “MACAO-VLTI first light: adaptive optics at the service of interferometry,” ESO Messenger 112, 7–12 (2003).

Exp. Astron. (1)

M. Kasper, D. P. Looze, S. Hippler, T. Herbst, A. Glindemann, T. Ott, A. Wirth, “ALFA: adaptive optics for the Calar Alto Observatory,” Exp. Astron. 10, 49–73 (2000).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (1)

J. H. van Lint, R. M. Wilson, A Course in Combinatorics (Cambridge U. Press, New York, 1993).

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Figures (3)

Fig. 1
Fig. 1

Hadamard matrix of dimension 60. When viewed as pavements, cells with 1 s are colored black and those with -1 s are colored white.

Fig. 2
Fig. 2

MACAO interaction matrix taken with use of Hadamard modes.

Fig. 3
Fig. 3

MACAO interaction matrix taken with use of the DM influence functions. DM actuator stroke and calibration time is identical to those in Fig. 2.

Tables (1)

Tables Icon

Table 1 Interaction Matrix Noise and Conditioning after Calibration

Equations (15)

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

C=DV+N,
Dˆ=CV-1
E=D-Dˆ=-NV-1.
D^+=(CV-1)+=VC+,
EEt=NV-1V-1tNt.
EEtIF=νm-2NNt.
J(V)=(detEEt)1/2n.
J(V)=(detNNt)1/2n(det V)-1/n.
J˜(V)=det V.
|νij| νm
V=νmHn,
HnHnt=n×I.
D¯=[D0],C¯=[CC2],N¯=[NN2],
V¯=νmHn¯.
EEtHad=n-1νm-2NNt,

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