Abstract

We present a technique to test the frozen flow hypothesis quantitatively, using data from wave-front sensors such as those found in adaptive optics systems. Detailed treatments of the theoretical background of the method and of the error analysis are presented. Analyzing data from the 1.5-m and 3.5-m telescopes at the Starfire Optical Range, we find that the frozen flow hypothesis is an accurate description of the temporal development of atmospheric turbulence on time scales of the order of 1–10 ms but that significant deviations from the frozen flow behavior are present for longer time scales.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  20. M. C. Roggemann, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).
  21. R. Q. Fugate, “Observations of faint objects with laser beacon adaptive optics,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 10–21 (1994).
    [CrossRef]
  22. J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
    [CrossRef]
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1998 (3)

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

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

M. Schöck, E. J. Spillar, “Measuring wind speeds and turbulence with a wave-front sensor,” Opt. Lett. 23, 150–152 (1998).
[CrossRef]

1997 (1)

1996 (1)

E. Gendron, P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 2, 221–228 (1996).
[CrossRef]

1995 (1)

1994 (3)

1991 (1)

1990 (1)

J. Caccia, J. Vernin, “Wind fluctuation measurements in the buoyancy range by stellar scintillation analysis,” J. Geophys. Res. 95, 12683–13690 (1990).

1987 (1)

1975 (1)

R. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

1973 (1)

Agabi, A.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Aitken, G.

Aitken, G. J. M.

M. B. Jorgensen, G. J. M. Aitken, “Wave front prediction for adaptive optics,” in International Commission for Optics and ESO Meeting on Adaptive Optics, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 143–148.

Allen, J. G.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Ameer, G. A.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Avila, R.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Baum, G.

Borgnino, J.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Brown, J. M.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Caccia, J.

J. Caccia, J. Vernin, “Wind fluctuation measurements in the buoyancy range by stellar scintillation analysis,” J. Geophys. Res. 95, 12683–13690 (1990).

Christou, J. C.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Conan, J.-M.

Conan, R.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Dicke, R.

R. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
[CrossRef]

Duncan, T. S.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Eager, R. J.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Ealey, M. A.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Ellerbroek, B. L.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

Fuchs, A.

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

Fugate, R. Q.

R. Q. Fugate, “Observations of faint objects with laser beacon adaptive optics,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 10–21 (1994).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Gendron, E.

E. Gendron, P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 2, 221–228 (1996).
[CrossRef]

Harrington, P. M.

P. M. Harrington, B. M. Welsh, “Frequency-domain analysis of an adaptive optical system’s temporal response,” Opt. Eng. 33, 2336–2342 (1994).
[CrossRef]

Hege, E.

Jones, G. W.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Jorgensen, M.

Jorgensen, M. B.

M. B. Jorgensen, G. J. M. Aitken, “Wave front prediction for adaptive optics,” in International Commission for Optics and ESO Meeting on Adaptive Optics, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 143–148.

Koeffler, S. C.

Kuhns, R. M.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Lee, D. J.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Léna, P.

E. Gendron, P. Léna, “Single layer atmospheric turbulence demonstrated by adaptive optics observations,” Astrophys. Space Sci. 2, 221–228 (1996).
[CrossRef]

Lloyd-Hart, M.

M. Lloyd-Hart, P. McGuire, “Spatio-temporal predictions for adaptive optics wave-front reconstructors,” in Adaptive Optics, M. Cullum, ed., OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 95–101 .

Lowrey, W. H.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Lukin, V.

Madec, P.-Y.

Martin, F.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

McGaughey, D.

McGuire, P.

M. Lloyd-Hart, P. McGuire, “Spatio-temporal predictions for adaptive optics wave-front reconstructors,” in Adaptive Optics, M. Cullum, ed., OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 95–101 .

Oliker, M.

T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

Oliker, M. D.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Pennington, T. L.

T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

Ribak, E. N.

Roddier, F.

Roggemann, M. C.

M. C. Roggemann, B. Welsh, Imaging through Turbulence (CRC Press, Boca Raton, Fla., 1996).

Rousset, G.

Ruane, R. E.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Sarazin, M.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Schöck, M.

M. Schöck, E. J. Spillar, “Measuring wind speeds and turbulence with a wave-front sensor,” Opt. Lett. 23, 150–152 (1998).
[CrossRef]

M. Schöck, “An analysis of turbulent layers with a wave-front sensor,” Ph.D. dissertation (University of Wyoming, Laramie, Wyoming, 1998).

M. Schöck, E. J. Spillar, “Analyzing atmospheric turbulence with a Shack–Hartmann wavefront sensor,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1092–1099 (1998).
[CrossRef]

M. Schöck, E. J. Spillar, “Turbulence analysis with the Starfire Optical Range 3.5-m telescope,” in Catching the Perfect Wave: Adaptive Optics and Interferometry in the 21st Century, S. R. Restaino, W. Junor, N. Duric, eds., ASP Conf. Ser. 174 (Astronomical Society of the Pacific, San Francisco, Calif., 1999), pp. 119–123.

Schwartz, C.

Spillar, E. J.

M. Schöck, E. J. Spillar, “Measuring wind speeds and turbulence with a wave-front sensor,” Opt. Lett. 23, 150–152 (1998).
[CrossRef]

M. Schöck, E. J. Spillar, “Turbulence analysis with the Starfire Optical Range 3.5-m telescope,” in Catching the Perfect Wave: Adaptive Optics and Interferometry in the 21st Century, S. R. Restaino, W. Junor, N. Duric, eds., ASP Conf. Ser. 174 (Astronomical Society of the Pacific, San Francisco, Calif., 1999), pp. 119–123.

M. Schöck, E. J. Spillar, “Analyzing atmospheric turbulence with a Shack–Hartmann wavefront sensor,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1092–1099 (1998).
[CrossRef]

Spinhirne, J. M.

T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Swindle, D.

T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

Swindle, D. W.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
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A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR,’ ” Proc. Astron. Soc. Pac. 110, 86–91 (1998).
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Tokovinin, A.

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Vernin, J.

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR,’ ” Proc. Astron. Soc. Pac. 110, 86–91 (1998).
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J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
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J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Wilson, K. B.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Wynia, J. L.

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

Ziad, A.

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Zuev, V.

Appl. Opt. (2)

Astron. Astrophys. (1)

F. Martin, A. Tokovinin, A. Ziad, R. Conan, J. Borgnino, R. Avila, A. Agabi, M. Sarazin, “First statistical data on wavefront outer scale at La Silla observatory from the GSM instrument,” Astron. Astrophys. 336, L49–L52 (1998).

Astrophys. J. (1)

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Astrophys. Space Sci. (1)

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J. Geophys. Res. (1)

J. Caccia, J. Vernin, “Wind fluctuation measurements in the buoyancy range by stellar scintillation analysis,” J. Geophys. Res. 95, 12683–13690 (1990).

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

P. M. Harrington, B. M. Welsh, “Frequency-domain analysis of an adaptive optical system’s temporal response,” Opt. Eng. 33, 2336–2342 (1994).
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Opt. Lett. (2)

Proc. Astron. Soc. Pac. (1)

A. Fuchs, M. Tallon, J. Vernin, “Focusing on a turbulent layer: principle of the ‘generalized SCIDAR,’ ” Proc. Astron. Soc. Pac. 110, 86–91 (1998).
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Other (10)

M. B. Jorgensen, G. J. M. Aitken, “Wave front prediction for adaptive optics,” in International Commission for Optics and ESO Meeting on Adaptive Optics, F. Merkle, ed. (European Southern Observatory, Garching, Germany, 1993), pp. 143–148.

M. Lloyd-Hart, P. McGuire, “Spatio-temporal predictions for adaptive optics wave-front reconstructors,” in Adaptive Optics, M. Cullum, ed., OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 95–101 .

M. Schöck, E. J. Spillar, “Analyzing atmospheric turbulence with a Shack–Hartmann wavefront sensor,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1092–1099 (1998).
[CrossRef]

M. Schöck, E. J. Spillar, “Turbulence analysis with the Starfire Optical Range 3.5-m telescope,” in Catching the Perfect Wave: Adaptive Optics and Interferometry in the 21st Century, S. R. Restaino, W. Junor, N. Duric, eds., ASP Conf. Ser. 174 (Astronomical Society of the Pacific, San Francisco, Calif., 1999), pp. 119–123.

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T. L. Pennington, D. Swindle, M. Oliker, B. L. Ellerbroek, J. M. Spinhirne, “Performance measurements of generation III wavefront sensors at the Starfire Optical Range,” in Adaptive Optical Systems and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE2534, 327–337 (1995).
[CrossRef]

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R. Q. Fugate, “Observations of faint objects with laser beacon adaptive optics,” in Adaptive Optics in Astronomy, M. A. Ealey, F. Merkle, eds., Proc. SPIE2201, 10–21 (1994).
[CrossRef]

J. M. Spinhirne, J. G. Allen, G. A. Ameer, J. M. Brown, J. C. Christou, T. S. Duncan, R. J. Eager, M. A. Ealey, B. L. Ellerbroek, R. Q. Fugate, G. W. Jones, R. M. Kuhns, D. J. Lee, W. H. Lowrey, M. D. Oliker, R. E. Ruane, D. W. Swindle, J. K. Voas, W. J. Wild, K. B. Wilson, J. L. Wynia, “The Starfire Optical Range 3.5-m telescope adaptive optics system,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 22–33 (1998).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Time series of the cumulative autocorrelation obtained from different SOR data sets. Dashed curves, iCi2(Δt) found for 1.5-m data; solid curves, iCi2(Δt) found for 3.5-m data. The numbers next to each curve refer to the order in which the data sets are listed in Table 1. The error limits calculated from Eq. (33) are shown at the bottom of the graph.

Fig. 2
Fig. 2

Frequency of the occurrence of values of t90 binned in 5-ms intervals. t90 is the time during which the cumulative autocorrelation remains above 90%, that is, the time for which the normalized correlation between the wave front at times t and t+t90 equals 90%.  

Tables (1)

Tables Icon

Table 1 Details of the Data Used for Fig. 1 a

Equations (35)

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Φ(x, t+Δt)iϕi(x-viΔt, t),
Φ(x, t+Δt)=iϕi(x-viΔt, t)+(x, t, Δt),
f*(x, t)f(x, t)σf (t),
Φ*(x, t)=iσϕi(t)σΦ(t) ϕi*(x, t),
Φ*(x, t+Δt)=iσϕi(t)σΦ(t+Δt) ϕi*(x-viΔt, t)+(x, t, Δt)σΦ(t+Δt).
ΓΦ*(Δx, Δt)=Φ*(x, t)Φ*(x+Δx, t+Δt)x, t,
ΓΦ*(Δx, Δt)
=iCi2(Δt)ϕi*(x, t)ϕi*(x+Δx-viΔt, t)x, t,
ΓΦ*(Δx, Δt)=iCi2(Δt)γϕ*(Δx-vi Δt).
ΓΦ*(Δx, 0)=γϕ*(Δx).
C12(Δt)=σϕi2(t)σΦ(t)σΦ(t+Δt)t=ϕi2(x, t)x{iϕi2(x, t)x×[iϕi2(x-viΔt, t)x+2(x, t, Δt)x]}1/2t,
iCi2(Δt)
=iϕi2(x, t)xiϕi2(x, t)x+[iϕi2(x, t)x2(x, t, Δt)x]1/2t=11+[2(x, t, Δt)x/iϕi2(x, t)x]1/2t11+e2(Δt).
ΓΦ*deconvolved(Δx, Δt)=iCi2(Δt)δ(Δx-viΔt),
α(x, y)=-λ2πx ϕ(x, y),
ΓαSE(Δx, Δy)=σΦ2(0)γα*SE(Δx, Δy)=λ28π2×6.88r0-5/353 (Δx2+Δy2)-1/6-59 Δx2(Δx2+Δy2)-7/6-2D-1/3.
β(x, y)=-λ2πy ϕ(x, y),
Aα(Δx, Δt)=ijkαxi,yj, tkαxi+Δx,yj+Δy, tk+Δtijk1Γα(Δx, Δt),
α1=α2=0,
α1α2=α1α2=0.
σcorr2=(α1α2-α1α2)2=(α1α2)2=α12α22=α12α22.
α12=α22α2
σcorr2=α22.
σstat2(Δx, Δt)=σcorr2Np(Δx, Δt)=α22Np(Δx, Δt)=Aα2(0, 0, 0)Np(Δx, Δt),
S/Nstat(Δx, Δt)=Aα(Δx, Δt)σstat(Δx, Δt)=Aα(Δx, Δt)Aα(0, 0,0)Np(Δx, Δt).
Np,s-l,s-f (Δx, Δt)=o(Δx, 0) Npixbxby,
Np,s-l(Δx, Δt)=oeff(Δx, Δt) Npixeffbx by,
Np,s-l(Δx, Δt)=o(Δx, Δt) NpixbxbyNtNcorr,
S/Nstat(Δx, Δt)=Aα(Δx, Δt)Aα(0, 0, 0)o(Δx, Δt) NpixbxbyNtNcorr1/2.
σstat2(Δx, Δt)=(σcorrintra)2Npintra(Δx, Δt)+(σcorrinter)2Npinter(Δx, Δt),
σstat2(Δx, Δt)(σcorrintra)2Npintra(Δx, Δt)=iαi22Npintra(Δx, Δt)=iAα,i2(0, 0, 0)Npintra(Δx, Δt),
σstat2(Δx, Δt)=[iC14(0)]Aα2(0, 0, 0)Npintra(Δx, Δt).
Np,m-lintra(Δx, Δt)=σeff(Δx, Δt) Npixeffbx by
Np,m-lintra(Δx, Δt)=o(Δx, Δt) NpixbxbyNtNcorr
S/Nstat(Δx, Δt)=Aα(Δx, Δt)Aα(0, 0, 0)1iCi4(0)×o(Δx, Δt) NpixbxbyNtNcorr1/2.

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