Abstract

Because of the finite speed of light, a laser guide Star that is seen from the side is not exactly a straight line. When such a laser guide star is used to sense tip–tilt with some of the perspective-based techniques that are used to retrieve an absolute tip–tilt laser, such nonstraightness introduces an error. We estimate this effect for various diameters of a laser projector, assuming a Kolmogorov turbulence spectrum and figuring the maximum achievable Strehl ratio. We found that under poor seeing conditions the effect is not negligible and that laser projectors larger than those currently used are required.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
    [CrossRef]
  2. S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
    [CrossRef]
  3. M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, J. C. Dainty, ed., Proc. SPIE2956, 206–217 (1996).
    [CrossRef]
  4. R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).
  5. V. P. Lukin, “Laser beacon and full aperture tilt measurement,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 1–5.
  6. R. Ragazzoni, “Absolute tip–tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).
  7. R. Ragazzoni, “Propagation delay of a laser beacon as a tool to retrieve absolute tilt measurements,” Astrophys. J. 465, L73–L75 (1996).
    [CrossRef]
  8. F. Rigaut, E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  9. R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).
  10. R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).
  11. R. Ragazzoni, S. Esposito, “Additional telescope techniques for laser guide star tip–tilt retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 94–100 (1997).
    [CrossRef]
  12. E. Marchetti, R. Ragazzoni, “Sky coverage with the auxiliary telescopes laser guide star tilt recovery technique,” Astron. Astrophys. Suppl. Ser. 125, 551–556 (1997).
    [CrossRef]
  13. W. Happer, G. J. MacDonald, C. E. Max, E. J. Dyson, “Atmospheric turbulence compensation by resonant optical backscattering from the sodium layer in the upper atmosphere,” J. Opt. Soc. Am. A 11, 263–276 (1994).
    [CrossRef]
  14. J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
    [CrossRef]
  15. C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
    [CrossRef]
  16. H. M. Martin, “Image motion as a measure of seeing quality,” Publ. Astron. Soc. Pac. 99, 1360–1370 (1987).
    [CrossRef]
  17. D. G. Sandler, S. Stahl, J. R. P. Angel, M. Lloyd-Hart, D. McCarthy, “Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes,” J. Opt. Soc. Am. A 11, 925–938 (1994).
    [CrossRef]

1997

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

E. Marchetti, R. Ragazzoni, “Sky coverage with the auxiliary telescopes laser guide star tilt recovery technique,” Astron. Astrophys. Suppl. Ser. 125, 551–556 (1997).
[CrossRef]

1996

R. Ragazzoni, “Absolute tip–tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

R. Ragazzoni, “Propagation delay of a laser beacon as a tool to retrieve absolute tilt measurements,” Astrophys. J. 465, L73–L75 (1996).
[CrossRef]

1995

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

J.-M. Conan, G. Rousset, P.-Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A 12, 1559–1570 (1995).
[CrossRef]

1994

1993

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

1992

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

1987

J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

H. M. Martin, “Image motion as a measure of seeing quality,” Publ. Astron. Soc. Pac. 99, 1360–1370 (1987).
[CrossRef]

1976

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Angel, J. R. P.

Belen’kii, M. S.

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, J. C. Dainty, ed., Proc. SPIE2956, 206–217 (1996).
[CrossRef]

Biraben, F.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Brase, J. M.

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

Butts, R. R.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Conan, J.-M.

Dyson, E. J.

Esposito, S.

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

R. Ragazzoni, S. Esposito, “Additional telescope techniques for laser guide star tip–tilt retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 94–100 (1997).
[CrossRef]

Foy, R.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Gardner, C.

J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Gavel, D. T.

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

Gendron, E.

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

Grynberg, G.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Happer, W.

Hogge, C. B.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

Lloyd-Hart, M.

Lukin, V. P.

V. P. Lukin, “Laser beacon and full aperture tilt measurement,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 1–5.

MacDonald, G. J.

Madec, P.-Y.

Marchetti, E.

E. Marchetti, R. Ragazzoni, “Sky coverage with the auxiliary telescopes laser guide star tilt recovery technique,” Astron. Astrophys. Suppl. Ser. 125, 551–556 (1997).
[CrossRef]

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

Martin, H. M.

H. M. Martin, “Image motion as a measure of seeing quality,” Publ. Astron. Soc. Pac. 99, 1360–1370 (1987).
[CrossRef]

Max, C. E.

W. Happer, G. J. MacDonald, C. E. Max, E. J. Dyson, “Atmospheric turbulence compensation by resonant optical backscattering from the sodium layer in the upper atmosphere,” J. Opt. Soc. Am. A 11, 263–276 (1994).
[CrossRef]

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

McCarthy, D.

McCullough, P. R.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Migus, A.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Olivier, S. S.

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

Pilkington, J. D. H.

J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Ragazzoni, R.

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

E. Marchetti, R. Ragazzoni, “Sky coverage with the auxiliary telescopes laser guide star tilt recovery technique,” Astron. Astrophys. Suppl. Ser. 125, 551–556 (1997).
[CrossRef]

R. Ragazzoni, “Absolute tip–tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

R. Ragazzoni, “Propagation delay of a laser beacon as a tool to retrieve absolute tilt measurements,” Astrophys. J. 465, L73–L75 (1996).
[CrossRef]

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

R. Ragazzoni, S. Esposito, “Additional telescope techniques for laser guide star tip–tilt retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 94–100 (1997).
[CrossRef]

Rigaut, F.

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

Rousset, G.

Sandler, D. G.

Stahl, S.

Tallon, M.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

Thompson, L.

J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Astron. Astrophys.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. R. McCullough, M. Tallon, “The polychromatic artificial sodium star: a new concept for correcting the atmospheric tilt,” Astron. Astrophys. 111, 569–578 (1995).

R. Ragazzoni, “Absolute tip–tilt determination with laser beacons,” Astron. Astrophys. 305, L13–L16 (1996).

F. Rigaut, E. Gendron, “Laser guide star in adaptive optics—the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).

R. Ragazzoni, “Robust tilt determination from laser guide stars using a combination of different techniques,” Astron. Astrophys. 319, L9–L12 (1997).

Astron. Astrophys. Suppl. Ser.

E. Marchetti, R. Ragazzoni, “Sky coverage with the auxiliary telescopes laser guide star tilt recovery technique,” Astron. Astrophys. Suppl. Ser. 125, 551–556 (1997).
[CrossRef]

Astrophys. J.

R. Ragazzoni, “Propagation delay of a laser beacon as a tool to retrieve absolute tilt measurements,” Astrophys. J. 465, L73–L75 (1996).
[CrossRef]

S. S. Olivier, C. E. Max, D. T. Gavel, J. M. Brase, “Tip–tilt compensation—resolution limits for ground-based telescopes using laser guide stars adaptive optics,” Astrophys. J. 407, 428–439 (1993).
[CrossRef]

IEEE Trans. Antennas Propag.

C. B. Hogge, R. R. Butts, “Frequency spectra for the geometric representation of wavefront distortions due to atmospheric turbulence,” IEEE Trans. Antennas Propag. AP-24, 144–154 (1976).
[CrossRef]

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

R. Ragazzoni, S. Esposito, E. Marchetti, “Auxiliary telescopes for the absolute tip–tilt determination of a laser guide star,” Mon. Not. R. Astron. Soc. 276, L76–L78 (1995).

Nature (London)

J. D. H. Pilkington, L. Thompson, C. Gardner, “Artificial guide star for adaptive imaging,” Nature (London) 330, 116 (1987).
[CrossRef]

Publ. Astron. Soc. Pac.

H. M. Martin, “Image motion as a measure of seeing quality,” Publ. Astron. Soc. Pac. 99, 1360–1370 (1987).
[CrossRef]

Other

R. Ragazzoni, S. Esposito, “Additional telescope techniques for laser guide star tip–tilt retrieval,” in Adaptive Optics and Applications, R. K. Tyson, R. Q. Fugate, eds., Proc. SPIE3126, 94–100 (1997).
[CrossRef]

M. S. Belen’kii, “Tilt angular correlation and tilt sensing techniques with a laser guide star,” in Optics in Atmospheric Propagation, Adaptive Systems, and Lidar Techniques for Remote Sensing, J. C. Dainty, ed., Proc. SPIE2956, 206–217 (1996).
[CrossRef]

V. P. Lukin, “Laser beacon and full aperture tilt measurement,” in Adaptive Optics, Vol. 13 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 1–5.

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

Configuration adopted for the LGS tip–tilt retrieval.

Fig. 2
Fig. 2

Two power spectra for two different projector apertures d. One can easily note that the knee in each spectrum falls at different frequencies for the two cases.

Fig. 3
Fig. 3

Examples of tilt derivatives from two laser projector apertures.

Fig. 4
Fig. 4

Strehl degradation S versus laser projector diameter d for two main telescope diameters and two seeing conditions. The solid curves represent the fitting formula described in the text. The filled circles are for the D = 8.0-m main telescope aperture diameter and the open circles refer to the D = 3.5-m case. The highest Strehl ratios refer to the good-seeing conditions, whereas the two with lower Strehl ratios refer to the poor-seeing conditions described in the text.

Tables (1)

Tables Icon

Table 1 Strehl Degradation

Equations (5)

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

Δ t 2 τ c   cos   z ,
Δ ψ θ t   Δ t = θ t 2 τ c   cos   z .
σ θ = 0.427   λ d d r 0 5 / 6 ,
S = 1 + π 2 2 σ ψ λ / D 2 - 1 ,
σ ψ K / d ,

Metrics