Abstract

The adaptive-optics (AO) system at the W. M. Keck Observatory is characterized. We calculate the error budget of the Keck AO system operating in natural guide star mode with a near-infrared imaging camera. The measurement noise and bandwidth errors are obtained by modeling the control loops and recording residual centroids. Results of sky performance tests are presented: The AO system is shown to deliver images with average Strehl ratios of as much as 0.37 at 1.58 μm when a bright guide star is used and of 0.19 for a magnitude 12 star. The images are consistent with the predicted wave-front error based on our error budget estimates.

© 2004 Optical Society of America

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2003 (1)

2002 (2)

S. E. Winters, “Modeling and control of a deformable mirror,” J. Dynamic Syst. Meas. Control 124, 297–302 (2002).
[CrossRef]

L. C. Roberts, C. R. Neyman, “Characterization of the AEOS system,” Publ. Astron. Soc. Pac. 114, 1260–1266 (2002).
[CrossRef]

2000 (3)

P. L. 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]

J.-P. Véran, G. Herriot, “Centroid gain compensation in Shack-Hartmann adaptive optics systems with natural or laser guide star,” J. Opt. Soc. Am. A 17, 1430–1439 (2000).
[CrossRef]

G. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes. II. The narrowband phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
[CrossRef]

1998 (1)

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 (1)

N. F. Law, R. G. Lane, “Wavefront estimation at low light levels,” Opt. Commun. 126, 19–24 (1996).
[CrossRef]

1994 (1)

M. G. Loefdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys. Suppl. Ser. 107, 243–264 (1994).

1987 (1)

R. G. Lane, W. R. Fright, R. H. T. Bates, “Direct phase retrieval,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–526 (1987).
[CrossRef]

1977 (1)

1976 (1)

1972 (1)

R. Gerchberg, W. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane picture,” Optik 35, 237–246 (1972).

1966 (1)

Acton, D. S.

P. L. 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]

D. S. Acton, P. L. Wizinowich, P. J. Stomski, J. C. Shelton, O. Lai, J. M. Brase, “Laboratory calibration of the W. M. Keck Observatory adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 125–131 (1998).
[CrossRef]

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

An, J.

P. L. 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.

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[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. L. 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]

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

Bates, R. H. T.

R. G. Lane, W. R. Fright, R. H. T. Bates, “Direct phase retrieval,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–526 (1987).
[CrossRef]

Bauman, B.

D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optics system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 354–359 (2003).
[CrossRef]

Beeman, B. V.

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

Bloemhof, E. E.

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

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. L.

M. Troy, R. G. Dekany, G. L. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. R. 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. R.

M. Troy, R. G. Dekany, G. L. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. R. 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. L. 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.

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

D. S. Acton, P. L. Wizinowich, P. J. Stomski, J. C. Shelton, O. Lai, J. M. Brase, “Laboratory calibration of the W. M. Keck Observatory adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 125–131 (1998).
[CrossRef]

Brown, C.

D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optics system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 354–359 (2003).
[CrossRef]

Carrano, C. J.

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

Chanan, G.

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.

D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optics system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 354–359 (2003).
[CrossRef]

Dekany, R. G.

B. R. Oppenheimer, D. Palmer, R. G. Dekany, A. Sivaramakrishnan, M. A. Ealey, T. R. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–580 (1997).
[CrossRef]

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

Ealey, M. A.

B. R. Oppenheimer, D. Palmer, R. G. Dekany, A. Sivaramakrishnan, M. A. Ealey, T. R. Price, “Investigating a Xinetics Inc. deformable mirror,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 569–580 (1997).
[CrossRef]

Ellerbroek, B. L.

B. L. Ellerbroek, A.U.R.A., 950 North Cherry Avenue, Tucson, Ariz., 85719 (personal communication, 2002).

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]

Fried, D. L.

Fright, W. R.

R. G. Lane, W. R. Fright, R. H. T. Bates, “Direct phase retrieval,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–526 (1987).
[CrossRef]

Gates, E.

D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optics system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 354–359 (2003).
[CrossRef]

Gathright, J.

P. L. 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]

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

Gavel, D.

P. L. 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]

D. Gavel, E. Gates, C. Max, S. Olivier, B. Bauman, D. Pennington, B. Macintosh, J. Patience, C. Brown, P. Danforth, R. Hurd, S. Severson, J. Lloyd, “Recent science and engineering results with the laser guidestar adaptive optics system at Lick Observatory,” in Adaptive Optical System Technologies II, P. L. Wizinowich, D. Bonaccini, eds., Proc. SPIE4839, 354–359 (2003).
[CrossRef]

Gavel, D. T.

E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
[CrossRef]

Gerchberg, R.

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M. Schoeck, D. Le Mignant, G. Chanan, P. L. Wizinowich, M. A. van Dam, “Atmospheric characterization with the Keck adaptive optics system. I. Open-loop data,” Appl. Opt. 42, 3705–3720 (2003).
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M. A. van Dam, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 1–10 (2003).
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E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
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E. M. Johansson, D. S. Acton, J. R. An, K. Avicola, B. V. Beeman, J. M. Brase, C. J. Carrano, J. Gathright, D. T. Gavel, R. L. Hurd, O. Lai, W. Lupton, B. A. Macintosh, C. E. Max, S. S. Olivier, J. C. Shelton, P. J. Stomski, K. Tsubota, K. E. Waltjen, J. A. Watson, P. L. Wizinowich, “Initial performance of the Keck AO wavefront controller system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 600–607 (2000). 30
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P. L. 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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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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M. A. van Dam, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory,” in Astronomical Adaptive Optics Systems and Applications, R. K. Tyson, M. Lloyd-Hart, eds., Proc. SPIE5169, 1–10 (2003).
[CrossRef]

M. Troy, R. G. Dekany, G. L. Brack, B. R. Oppenheimer, E. E. Bloemhof, T. Trinh, F. G. Dekens, F. Shi, T. L. Hayward, B. R. 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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P. J. Stomski, J. C. Shelton, “Compensating for pupil rotation in the W. M. Keck Observatory adaptive optics system,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 608–619 (2000).
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[CrossRef]

D. S. Acton, P. L. Wizinowich, P. J. Stomski, J. C. Shelton, O. Lai, J. M. Brase, “Laboratory calibration of the W. M. Keck Observatory adaptive optics facility,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 125–131 (1998).
[CrossRef]

M. D. Oliker, “Alignment techniques for DM, lenslet, and WFS camera at the SOR,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 595–604 (1997).
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P.-Y. Madec, “Control techniques,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, UK, 1999), pp. 131–154.
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[CrossRef]

F. J. Rigaut, J.-P. Véran, O. Lai, “Analytical model for Shack-Hartmann-based adaptive optics systems,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 1038–1048 (1998).
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[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Transfer curve between the angle of arrival in arc seconds and the mean centroids. The plot is generated by displacement of the white-light source in the y direction.

Fig. 2
Fig. 2

Phase map of the residual error after image sharpening.

Fig. 3
Fig. 3

Schematic of the control loop. The diagnostics measure the centroids immediately after addition of the noise, and the mirror is driven by the signal coming from the zero-order hold.

Fig. 4
Fig. 4

Logarithm of the power spectral density (in square nanometers per hertz) for the (a) TT and (b) the DM. The smooth curves represent the noise power on the diagnostics.

Fig. 5
Fig. 5

(a) Strehl ratio at 1.58 μm and (b) the rms wave-front error obtained from the Maréchal approximation. The points represent the mean of ∼10 images, and the error bars represent the 1σ spread about the mean.

Fig. 6
Fig. 6

Left, diffraction-limited image at 1.58 μm; center, best bright star image; right, best image of a magnitude 12 star.

Equations (27)

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

Idark=AT3/2 exp-Eg/2kT,
FWHM=2×2.355/2πm.
Sx, y=w12πσ12exp-x2+y22σ12+w22πσ22exp-x2+y22σ220.470 μm.
R=HTW-1H+αCϕ-1-1HTW-1.
yn=yn-1+0.8kTTun,
HTTz=0.8kTTzz-1,
en=-wen-1+kDMun,
yn=lyn-1+en,
HDMz=kDMz2z-lz+w.
S=exp-σϕ2exp-σχ2,
σχ2=0.288λh/r05/3.
σFIT=afdr05/6λ2π,
HStares=HZOHs=1-exp-sTsT.
HDelays=exp-sτc.
Hf=HStarefHDelayfHTT/DMfHZOHf.
Mf=Hf1+HfXf+Nf,
Df=11+HfXf+Nf.
σNoise2=-Hf1+Hf2|Nf|2df.
σNoise2= Hf1+Hf2|Nf|2,
σBW2=-11+Hf2|Xf|2df=-|Df|2-11+Hf2|Nf|2df|Df|2-11+Hf2|Nf|2.
EI1=pT,
VarI1=p+d+bT+σr2,
Varcx=VarI14EI12=VarI14pT2=p+d+bT+σr24pT2.
|NTTf|2=224012.681.22Varcx.
|NDMf|2=1.252|RS|2Varcx.
|Df|2=|DFTdnwn|2,
σtotal=σCAM2+σFIT2+σTEL2+σTT-BW2+σDM-BW2+σTT-Noise2+σDM-Noise21/2=1132+1392+602+752+1032+92+1721/2=229 nm.

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