Abstract

Shack–Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2×2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).
  2. M. C. Roggemann, B. Welsh, Imaging through Turbulence (CRC Press, 1996).
  3. 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).
  4. M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Performance of the Keck Observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
    [CrossRef] [PubMed]
  5. 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]
  6. J. P. Véran, G. Herriot, “Centroid gain compensation in a Shack–Hartmann adaptive optics system: implementation issues,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 642–648 (2000).
  7. L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).
  8. A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).
  9. G. A. Tyler, “Reconstruction and assessment of the least-squares and slope discrepancy components of the phase,” J. Opt. Soc. Am. A 17, 1828–1839 (2000).
    [CrossRef]
  10. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
    [CrossRef]
  11. G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt Brace, 1988).
  12. M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory: part II,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 174–183 (2004).
  13. F. J. Rigaut, J. Veran, O. Lai, “Analytical model for Shack–Hartmann-based adaptive optics systems,” in Adaptive Optical System Technologies, D. Bonaccini and R. K. Tyson, eds., Proc. SPIE3353, 1038–1048 (1998).
  14. G. Chanan, C. Ohara, M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]

2004 (1)

2000 (3)

1977 (1)

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).

Bouchez, A. H.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

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).

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).

Chanan, G.

Chin, J.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

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).

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).

Dunn, J.

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

Hartman, S.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

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).

Herriot, G.

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]

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

J. P. Véran, G. Herriot, “Centroid gain compensation in a Shack–Hartmann adaptive optics system: implementation issues,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 642–648 (2000).

Hudgin, R. H.

Johansson, E.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

Lafon, R.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

Lai, O.

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

Le Mignant, D.

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Performance of the Keck Observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
[CrossRef] [PubMed]

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory: part II,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 174–183 (2004).

Macintosh, B. A.

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Performance of the Keck Observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
[CrossRef] [PubMed]

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory: part II,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 174–183 (2004).

Ohara, C.

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).

Rigaut, F. J.

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

Roggemann, M. C.

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

Saddlemyer, L. K.

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

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).

Smith, M.

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

Stomski, P.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

Strang, G.

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt Brace, 1988).

Summers, D.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

Trinh, T.

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).

Troy, M.

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

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).

Tyler, G. A.

van Dam, M. A.

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Performance of the Keck Observatory adaptive optics system,” Appl. Opt. 43, 5458–5467 (2004).
[CrossRef] [PubMed]

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory: part II,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 174–183 (2004).

Veran, J.

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

Véran, J. P.

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]

J. P. Véran, G. Herriot, “Centroid gain compensation in a Shack–Hartmann adaptive optics system: implementation issues,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 642–648 (2000).

Véran, J.-P.

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

Welsh, B.

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

Wizinowich, P. L.

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Other (9)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

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

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).

J. P. Véran, G. Herriot, “Centroid gain compensation in a Shack–Hartmann adaptive optics system: implementation issues,” in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007, 642–648 (2000).

L. K. Saddlemyer, G. Herriot, J.-P. Véran, M. Smith, J. Dunn, “Innovations within the Altair real-time wave-front reconstructor,” in Astronomical Adaptive Optics Systems and Applications, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 1384–1392 (2004).

A. H. Bouchez, D. Le Mignant, M. A. van Dam, J. Chin, S. Hartman, E. Johansson, R. Lafon, P. Stomski, D. Summers, P. L. Wizinowich, “Keck laser guide star adaptive optics: science verification results,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 321–330 (2004).

G. Strang, Linear Algebra and Its Applications, 3rd ed. (Harcourt Brace, 1988).

M. A. van Dam, D. Le Mignant, B. A. Macintosh, “Characterization of adaptive optics at Keck Observatory: part II,” in Advancements in Adaptive Optics, D. Bonaccini, B. L. Ellerbroek, and R. Ragazzoni, eds., Proc. SPIE5490, 174–183 (2004).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Slope discrepancy metric, g, measured with the calibration light source as a function of reference centroid scaling, α.

Fig. 2
Fig. 2

Slope discrepancy metric, g, measured with a star as a function of reference centroid scaling, α, on Keck II.

Fig. 3
Fig. 3

Plot of the mean x-centroid value as a function of displacement of the star (asterisks) and calibration light source (circles).

Fig. 4
Fig. 4

Slope discrepancy metric, g, measured with a star as a function of reference centroid scaling, α, on Keck I.

Equations (14)

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

s = w ,
s = H w .
w ̂ = ( H T H ) + H T s ,
s = H w ̂ ,
s = s s = [ I H ( H T H ) + H T ] s .
R = U S V T ,
s = Z Z T s .
s = r c .
s * = r * c * .
s * = β r α c ,
s * = β r α c .
E [ r ] = c ,
g = s * T c c T c .
E [ g ] = E [ ( β r α c ) ] T c c T c = ( β E [ r ] α c ) T c c T c = ( β α ) c T c c T c = β α .

Metrics