Abstract

We present a detailed investigation of different methods of the characterization of atmospheric turbulence with the adaptive optics systems of the W. M. Keck Observatory. The main problems of such a characterization are the separation of instrumental and atmospheric effects and the accurate calibration of the devices involved. Therefore we mostly describe the practical issues of the analysis. We show that two methods, the analysis of differential image motion structure functions and the Zernike decomposition of the wave-front phase, produce values of the atmospheric coherence length r 0 that are in excellent agreement with results from long-exposure images. The main error source is the calibration of the wave-front sensor. Values determined for the outer scale ℒ0 are consistent between the methods and with typical ℒ0 values found at other sites, that is, of the order of tens of meters.

© 2003 Optical Society of America

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    [CrossRef]

2002

A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156–1166 (2002).
[CrossRef]

2000

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

A. Glindemann, S. Hippler, T. Berkefeld, W. Hackenberg, “Adaptive optics on large telescopes,” Exp. Astron. 10, 5–47 (2000).
[CrossRef]

S. Harder, A. Chelli, “Estimating the point spread function of the adaptive optics system ADONIS using the wavefront sensor measurements,” Astron. Astrophys. Suppl. Ser. 142, 119–135 (2000).
[CrossRef]

M. Schöck, E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17, 1650–1658 (2000).
[CrossRef]

R. Conan, J. Borgnino, A. Ziad, F. Martin, “Analytical solution for the covariance and for the decorrelation time of the angle of arrival of a wave front corrugated by atmospheric turbulence,” J. Opt. Soc. Am. A 17, 1807–1818 (2000).
[CrossRef]

A. Ziad, R. Conan, A. Tokovinin, F. Martin, J. Borgnino, “From the grating scale monitor to the generalized seeing monitor,” Appl. Opt. 39, 5415–5425 (2000).
[CrossRef]

1998

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

1996

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

1994

1991

1990

M. Sarazin, F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 270, 294–300 (1990).

1980

1976

Acton, D. S.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
[CrossRef]

An, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

An, J. R.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Arsenault, R.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Avicola, K.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Barchers, J. D.

B. L. Ellerbroek, D. J. Lee, J. D. Barchers, “Analysis of atmospheric turbulence measurements obtained with the Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 212–224 (1999).
[CrossRef]

Bauman, B. J.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Beeman, B. V.

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Berkefeld, T.

A. Glindemann, S. Hippler, T. Berkefeld, W. Hackenberg, “Adaptive optics on large telescopes,” Exp. Astron. 10, 5–47 (2000).
[CrossRef]

Bloemhof, E. E.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
[CrossRef]

Bonaccini, D.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Borgnino, J.

Boyer, C.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Brack, G.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
[CrossRef]

Brandl, B.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
[CrossRef]

Brase, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Brase, J. M.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Brown, C. G.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Chanan, G. A.

M. Schöck, D. Le Mignant, G. A. Chanan, P. L. Wizinowich, “Atmospheric turbulence characterization with the Keck adaptive optics systems,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 813–824 (2002).
[CrossRef]

Chelli, A.

S. Harder, A. Chelli, “Estimating the point spread function of the adaptive optics system ADONIS using the wavefront sensor measurements,” Astron. Astrophys. Suppl. Ser. 142, 119–135 (2000).
[CrossRef]

Christou, J.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Close, L. M.

L. M. Close, “Review of published galactic and solar system science: a bright future for adaptive optics science,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 758–772 (2000).
[CrossRef]

Conan, J. M.

P. Y. Madec, J. M. Conan, G. Rousset, “Temporal characterization of atmospheric wavefront for adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed., Vol. 42 of ESO Proceedings (European Southern Observatory, Garching, Germany, 1992), p. 471.

Conan, R.

Contos, A. R.

P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
[CrossRef]

Corporon, P.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Crampton, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Danforth, P. M.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Dekany, R. G.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
[CrossRef]

Dekens, F. G.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
[CrossRef]

Ellerbroek, B. L.

B. L. Ellerbroek, D. J. Lee, J. D. Barchers, “Analysis of atmospheric turbulence measurements obtained with the Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 212–224 (1999).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C. 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Fletcher, J. M.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Friedman, H. W.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

Gates, E. L.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Gathright, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gavel, D.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gavel, D. T.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (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]

Ghez, A.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Gigan, P.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Glindemann, A.

A. Glindemann, S. Hippler, T. Berkefeld, W. Hackenberg, “Adaptive optics on large telescopes,” Exp. Astron. 10, 5–47 (2000).
[CrossRef]

Gredel, R.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Gregory, T.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
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Hackenberg, W.

A. Glindemann, S. Hippler, T. Berkefeld, W. Hackenberg, “Adaptive optics on large telescopes,” Exp. Astron. 10, 5–47 (2000).
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Harder, S.

S. Harder, A. Chelli, “Estimating the point spread function of the adaptive optics system ADONIS using the wavefront sensor measurements,” Astron. Astrophys. Suppl. Ser. 142, 119–135 (2000).
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Hayward, T. L.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
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Hippler, S.

A. Glindemann, S. Hippler, T. Berkefeld, W. Hackenberg, “Adaptive optics on large telescopes,” Exp. Astron. 10, 5–47 (2000).
[CrossRef]

Ho, K.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Hubin, N.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Hurd, R. L.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Jagourel, P.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Johnston, B.

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
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Jones, H. E.

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
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Kuklo, T. C.

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
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P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
[CrossRef]

Larkin, J.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
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Le Mignant, D.

M. Schöck, D. Le Mignant, G. A. Chanan, P. L. Wizinowich, “Atmospheric turbulence characterization with the Keck adaptive optics systems,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 813–824 (2002).
[CrossRef]

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
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Lee, D. J.

B. L. Ellerbroek, D. J. Lee, J. D. Barchers, “Analysis of atmospheric turbulence measurements obtained with the Starfire Optical Range 3.5-m telescope adaptive optical system,” in Adaptive Optics Systems and Technology, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3762, 212–224 (1999).
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Léna, P.

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

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Lupton, W.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Macintosh, B.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
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Macintosh, B. A.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
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Madec, P. Y.

P. Y. Madec, J. M. Conan, G. Rousset, “Temporal characterization of atmospheric wavefront for adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed., Vol. 42 of ESO Proceedings (European Southern Observatory, Garching, Germany, 1992), p. 471.

Martin, F.

Max, C.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
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Max, C. E.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
[CrossRef]

Neyman, C.

P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
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Noll, R. J.

Olivier, S.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
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Olivier, S. S.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

J. M. Brase, J. R. An, K. Avicola, B. V. Beeman, D. T. Gavel, R. L. Hurd, B. Johnston, H. E. Jones, T. C. Kuklo, C. E. Max, S. S. Olivier, K. E. Waltjen, J. A. Watson, “Wavefront control system for the Keck telescope,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 517–521 (1998).
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Oppenheimer, B. R.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
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Patience, J.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
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Pennington, D. M.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
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Prado, P.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C. 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Prieto, E.

D. Bonaccini, E. Prieto, P. Corporon, D. Le Mignant, P. Prado, R. Gredel, N. Hubin, J. Christou, “Performance of the ESO AO system, Adonis, at La Silla 3.6 m telescope,” in Sol-Gel Optics IV, B. S. Dunn, J. D. MacKenzie, E. J. Pope, H. K. Schmidt, M. Yamane, eds., Proc. SPIE3136, 589–594 (1997).

Rigaut, F.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Roddier, F.

M. Sarazin, F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 270, 294–300 (1990).

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 281–376.
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Rouan, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Rousset, G.

P. Y. Madec, J. M. Conan, G. Rousset, “Temporal characterization of atmospheric wavefront for adaptive optics,” in Progress in Telescope and Instrumentation Technologies, M.-H. Ulrich, ed., Vol. 42 of ESO Proceedings (European Southern Observatory, Garching, Germany, 1992), p. 471.

Salmon, D.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Sarazin, M.

M. Sarazin, F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 270, 294–300 (1990).

Schöck, M.

M. Schöck, E. J. Spillar, “Method for a quantitative investigation of the frozen flow hypothesis,” J. Opt. Soc. Am. A 17, 1650–1658 (2000).
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M. Schöck, D. Le Mignant, G. A. Chanan, P. L. Wizinowich, “Atmospheric turbulence characterization with the Keck adaptive optics systems,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 813–824 (2002).
[CrossRef]

Severson, S. A.

D. T. Gavel, C. E. Max, S. S. Olivier, B. J. Bauman, D. M. Pennington, B. A. Macintosh, J. Patience, C. G. Brown, P. M. Danforth, R. L. Hurd, E. L. Gates, S. A. Severson, J. P. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optic system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, ed., Proc. SPIE4839, 354–359 (2002).
[CrossRef]

Shelton, C.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
[CrossRef]

Shi, F.

M. Troy, R. G. Dekany, G. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. Brandl, “Palomar adaptive optics project: status and performance,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 31–40 (2000).
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Southwell, W. H.

Spillar, E. J.

Stilburn, J.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Stomski, P.

P. Wizinowich, D. S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, J. Brase, J. An, K. Avicola, S. Olivier, D. Gavel, B. Macintosh, A. Ghez, J. Larkin, “First light adaptive optics images from the Keck II Telescope: a new era of high angular resolution imagery,” Publ. Astron. Soc. Pac. 112, 315–319 (2000).
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Stomski, P. J.

P. L. Wizinowich, D. S. Acton, T. Gregory, P. J. Stomski, J. R. An, K. Avicola, J. M. Brase, H. W. Friedman, D. T. Gavel, C. E. Max, “Status of the W. M. Keck adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 568–578 (1998).
[CrossRef]

P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C. 2nd ed. (Cambridge U. Press, Cambridge, England, 1992).

Thomas, J.

F. Rigaut, D. Salmon, R. Arsenault, J. Thomas, O. Lai, D. Rouan, J. P. Véran, P. Gigan, D. Crampton, J. M. Fletcher, J. Stilburn, C. Boyer, P. Jagourel, “Performance of the Canada-France-Hawaii Telescope adaptive optics bonnette,” Publ. Astron. Soc. Pac. 110, 152–164 (1998).
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Trinh, T.

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[CrossRef]

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[CrossRef]

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[CrossRef]

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P. L. Wizinowich, D. Le Mignant, P. J. Stomski, D. S. Acton, A. R. Contos, C. Neyman, “Adaptive optics developments at Keck Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 9–20 (2002).
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[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Representation of the fiber spot moving across the pixels of Keck WFS subapertures. Shown in white are the pixels of four adjacent quadrant cells. The pixels of the guard rail in between the quadrant cells are shown in gray. The range of motion shown is approximately the maximum range over which the spot can be moved without vignetting. The parameter w of Eq. (1), corresponding to the linear pixel size, is also indicated.

Fig. 2
Fig. 2

Calibration of the spot size on the WFS. The asterisks and diamonds show the experimentally determined intensity on a pixel (averaged over all like pixels). The solid curves are the best-fit theoretical curves corresponding to these data.

Fig. 3
Fig. 3

Plot of centroids as measured by the Keck II WFS. Asterisks are the experimental data; the solid curve is the theoretical shape obtained by use of the values for spot size and pixel width that were determined by the fit shown in Fig. 2. The dotted curve is the theoretical curve for a spot size 0.25 arcsec larger than the best-fit value, and the dashed curve is for a spot size 0.25 arcsec smaller than the best-fit value.

Fig. 4
Fig. 4

Example of the frequency of occurrence of AA values for a set of 1000 frames of open-loop diagnostics data. In all cases, the solid curves are histograms of the observed quantities and the dotted curves are the best-fit Gaussians to these observations. The x components are shown on the left and the y components are shown on the right, offset by 2 units or 2 arcsec for clarity. (a) Measured centroids. Note that the static aberrations were not removed for this example. (b) AA reconstructed with the constant conversion factor method. (c) AA reconstructed with the inversion of Eq. (8). (d) Same as (c) but after removal of static aberrations.

Fig. 5
Fig. 5

Histograms of the AA values for a set of 900 frames of TT-loop-closed telemetry data. The data are represented in the same way as in Fig. 4. Static aberrations were not removed. (a) AA calculated with the linear conversion approximation, (b) AA calculated through the inversion of Eq. (8).

Fig. 6
Fig. 6

Longitudinal (top set) and transverse (bottom set) DIM structure functions (G tilt) for a number of different cases. Dotted curves, approximate result from Sarazin and Roddier;16 solid curves, analytical result of Conan et al.19 for circular apertures; crosses, numerical simulation of the analytical results; squares, numerical simulation for square apertures with areas equal to those of the circular apertures; diamonds (only transverse DIM shown), numerical simulation for square apertures with a side length equal to the diameter of the circular aperture. All results are calculated with d = 56.25 cm, λ = 0.5 μm, r 0 = 0.2 m, and an infinite outer scale.

Fig. 7
Fig. 7

Relative difference between the DIM structure functions of square and circular apertures of equal area. The results are calculated for square apertures of d = 56.25-cm side length, λ = 0.5 μm, and r 0 = 0.2 m.

Fig. 8
Fig. 8

Example of DIM structure functions calculated from a set of 600 frames of telemetry data. Symbols represent the data and the curves represent the best-fit theoretical curves. (a) x centroids, (b) y centroids. The fits were performed simultaneously for the entire two-dimensional structure function. The fit parameters are r 0 = 16.5 cm, ℒ0 = 39 m, and σ N = 0.067 arcsec for the x centroids and r 0 = 15.9 cm, ℒ0 = 37 m, and σ N = 0.064 arcsec for the y centroids.

Fig. 9
Fig. 9

Subaperture configurations of the Keck AO systems. The grids represent the 20 × 20 subapertures of the WFSs. The black and white dots indicate the positions of the 349 actuators of the DM, located at the corners of the subapertures. Marked as white squares are, on the left, all 308 subapertures that are surrounded by four actuators; in the center are the 241 fully illuminated apertures for a particular orientation of the Keck pupil; on the right is a subset of 208 subapertures that are always fully illuminated. The configuration on the right, forming an approximately 9-m subpupil, is used for the reconstruction of the phase in our analysis.

Fig. 10
Fig. 10

Examples of the calculation of variances of Zernike modes from the eigenmodes of the phase reconstruction matrix by use of different numbers of Zernike modes. Left, with 6 radial orders (21 modes); right, with 10 radial orders (55 modes), offset by 15 modes to the right for clarity. The asterisks are results from telemetry data and the solid curves indicate theoretical values for Kolmogorov turbulence. The two highest radial orders of each plot are corrupted by correlations with modes not included in the calculation. This is true independent of the number of modes used.

Fig. 11
Fig. 11

Comparison of values of r 0 found using the DIM method (ordinate) and the ZD method (abscissa). The full lengths of the vertical bars indicate the differences between the r 0 values determined from x and y centroids by the DIM method. (a) Results obtained from telemetry data during the nights of 25 June, 28 June, 21 October, and 26 October 2002 with the Keck II AO system and on 21 October 2002 with the Keck I AO system. The data sets are between 56 and 294 s in length and are taken at frame rates between 4 and 6 Hz. (b) Results obtained with the Keck II AO system on 23 September 2002 with diagnostics data and telemetry data taken at frames rates between 2 and 2.5 Hz.

Fig. 12
Fig. 12

Comparison of values of ℒ0 found with the DIM method (ordinate) and the ZD method (abscissa). The full lengths of the vertical bars indicate the differences between the ℒ0 values determined from x and y centroids with the DIM method. Results were obtained from telemetry data during the nights of 25 June, 28 June, 21 October, and 26 October 2002 with the Keck II AO system and on 21 October 2002 with the Keck I AO system. A total of six data points with ℒ0 values greater than 150 m were omitted from the plot to decrease the plot range.

Fig. 13
Fig. 13

Values of r 0 obtained on 26 October 2002. The thin bars are results from telemetry data with the lengths of the bars indicating the lengths of the data sets. Thick bars are results from NIRC2 long-exposure images. The asterisks show r 0 values calculated from 1.5-s diagnostics data sets.

Fig. 14
Fig. 14

(a) Values of r 0 obtained from diagnostics data sets on 23 September 2002. The triangles show the results if no data conditioning is done, that is, if static aberrations are not removed. The squares show the results if the time average of a diagnostics data set is subtracted from this set. The diamonds, representing the most accurate estimates of r 0, are obtained if the averages of close-to-simultaneous telemetry data sets are subtracted. (b) We plot the ratio of the phase variances of the cases shown as squares and diamonds in (a). This quantity is the percentage of the turbulence strength that appears static in the 1.5-s data sets.

Tables (1)

Tables Icon

Table 1 Demonstration of the Iterative Method that Accounts for the WFS Spot-Size Dependence on Atmospheric Turbulencea

Equations (28)

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px=1/w-w/2xw/20otherwise..
sx=12πσexp-x22σ2,
ix=sx * px=12werf12σx+w2-erf12σx-w2,
erfx=2π0xexp-t2dt.
cx=I5+I8-I4+I7I4+I5+I7+I8.
I4+I7  erfx2σ-erfx-w2σ,
I5+I8  erfx+w2σ-erfx2σ.
cx=erfx+w2σ-2 erfx2σ+erfx-w2σerfx+w2σ-erfx-w2σ
CcentAA=π2 σ erfw2σ1-exp-w22σ2.
FWHMturb=0.98 λWFSr0λWFS,
BAAr=λ2  dff · u2WΦfGfexp2πif · r.
WΦf=0.0229r0-5/3f2+f02-11/6,
Gf=2J1πdfπdf2
Gf=sinπdfxπdfx2sinπdfyπdfy2
DAAr=2BAA0-BAAr.
DAAr=λ2r0-5/3d-1/3r, f0,
DAAΔr=αr-αr+Δr2,
DAAΔr=αr-αr+Δr2+2σN2Δr00Δr=0.
iCti+a-di2σi2.
C=SStd-StSdSStt-St2, a=Sd-CStS,
S=i1σi2, St=itiσi2, Sd=idiσi2,
Std=itidiσi2, Stt=iti2σi2.
αj=λ4πdϕur+ϕlr-ϕul-ϕll,
βj=λ4πdϕur+ϕul-ϕlr-ϕll,
CZ,i= drWrϕrZjr,
CM,j=i=0N-1 bijCZ,i,
bij= ZjrMirdr MirMirdr,
cZ=Rg=BMA-1g,

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