Abstract

We investigate a method for widening the compensated field of view of an adaptive-optical telescope with multiple deformable mirrors and an array of artificial guide stars. An ensemble of wavefront sensor measurements, made with the individual guide stars in the array, is used to estimate the contribution of a region of the atmosphere to the cumulative phase distortion. Our analysis includes the effects of measurement noise, wavefront-sensor sampling, and reconstruction of the wave front from slope measurements. We performed numerical computations for an atmosphere consisting of two turbulent layers: one at 1% of the guide-star altitude with 90% of the total turbulence strength and one at 10% of the guide-star altitude with the remaining 10% of the total turbulence strength. If we assume that r0 = 0.15 m and that a photon-limited wave-front sensor detecting 50 photons/r0-sized subaperture is used, the results indicate that a 0.9-m-square telescope with a diagonal field of view of ~92 μrad ≈ 19 arcsec can use two deformable mirrors, four laser guide stars, and a natural tilt reference star to achieve an rms residual phase error that is <λ/7 over its entire field of view.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236, (1953).
    [CrossRef]
  2. G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).
  3. R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
    [CrossRef]
  4. D. V. Murphy, “Atmospheric-turbulence compensation experiments using cooperative beacons,” Lincoln Lab. J. 5, 25–44 (1992).
  5. R. R. Parenti, “Adaptive optics for astronomy,” Lincoln Lab. J. 5, 93–114 (1992).
  6. R. H. Dicke, “Phase-contrast detection of telescope seeing errors and their correction,” Astrophys. J. 198, 605–615 (1975).
    [CrossRef]
  7. J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Proceedings of the ESO Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.
  8. D. L. Fried, “Adaptive optics for imaging within the atmosphere: reference generation and field-of-view widening,” (Optical Sciences Company, Placentia, Calif., 1977).
  9. R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 129–131 (1985).
  10. L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
    [CrossRef]
  11. C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
    [CrossRef]
  12. R. A. Humphreys, C. A. Primmerman, L. C. Bradley, J. Herrman, “Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer,” Opt. Lett. 16, 1367–1369 (1991).
    [CrossRef] [PubMed]
  13. B. G. Zollars, “Atmospheric-turbulence compensation experiments using synthetic beacons,” Lincoln Lab. J. 5, 67–92 (1992).
  14. M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).
  15. E. P. Wallner, “Optimal wave-front correction using slope measurements,”J. Opt. Soc. Am. 73, 1771–1776 (1983).
    [CrossRef]
  16. B. M. Welsh, C. S. Gardner, “Performance analysis of adaptive-optics systems using laser guide stars and slope sensors,” J. Opt. Soc. Am. A 6, 1913–1923 (1989).
    [CrossRef]
  17. B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
    [CrossRef]
  18. J. Vernin, F. Roddier, “Experimental determination of two-dimensional spatiotemporal power spectra of stellar light scintillation. Evidence for a multilayer structure of the air turbulence in the upper troposphere,”J. Opt. Soc. Am. 63, 270–273 (1973).
    [CrossRef]
  19. F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
    [CrossRef]
  20. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  21. T. S. McKechnie, “Light propagation through the atmosphere and the properties of images formed by large ground-based telescopes,” J. Opt. Soc. Am. A 8, 346–365 (1991).
    [CrossRef]
  22. F. Roddier, “Astronomical adaptive optics with natural reference stars,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.
  23. R. Foy, “Work in France in the field of the laser artificial guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.
  24. F. Rigaut, “Dual adaptive optics: a solution to the tilt determination problem using laser guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.
  25. D. C. Johnston, “Increasing the corrected field of view of an adaptive optical telescope,” Ph.D. dissertation (School of Engineering, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1992).
  26. D. L. Fried, “Statistics of a geometric representation of wavefront distortion,”J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
  27. T. J. Kane, B. M. Welsh, C. S. Gardner, “Wavefront detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1114, 160–171 (1989).
    [CrossRef]

1992 (3)

D. V. Murphy, “Atmospheric-turbulence compensation experiments using cooperative beacons,” Lincoln Lab. J. 5, 25–44 (1992).

R. R. Parenti, “Adaptive optics for astronomy,” Lincoln Lab. J. 5, 93–114 (1992).

B. G. Zollars, “Atmospheric-turbulence compensation experiments using synthetic beacons,” Lincoln Lab. J. 5, 67–92 (1992).

1991 (5)

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

T. S. McKechnie, “Light propagation through the atmosphere and the properties of images formed by large ground-based telescopes,” J. Opt. Soc. Am. A 8, 346–365 (1991).
[CrossRef]

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

R. A. Humphreys, C. A. Primmerman, L. C. Bradley, J. Herrman, “Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer,” Opt. Lett. 16, 1367–1369 (1991).
[CrossRef] [PubMed]

1990 (2)

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

1989 (1)

1987 (1)

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

1985 (1)

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 129–131 (1985).

1983 (1)

1975 (1)

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

1973 (1)

1965 (1)

1953 (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236, (1953).
[CrossRef]

Ameer, G. A.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Azouit, M.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236, (1953).
[CrossRef]

Barclay, H. T.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Beckers, J. M.

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Proceedings of the ESO Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.

Beland, S.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Boeke, B. R.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Boyer, C.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Bradley, L. C.

Browne, S. L.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Caccia, J. L.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Cowie, L.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Cowley, D.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Dicke, R. H.

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

Fontanella, J. C.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Foy, R.

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 129–131 (1985).

R. Foy, “Work in France in the field of the laser artificial guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

Fried, D. L.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

D. L. Fried, “Statistics of a geometric representation of wavefront distortion,”J. Opt. Soc. Am. 55, 1427–1435 (1965).
[CrossRef]

D. L. Fried, “Adaptive optics for imaging within the atmosphere: reference generation and field-of-view widening,” (Optical Sciences Company, Placentia, Calif., 1977).

Fugate, R. Q.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Gaffard, J. P.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Gardner, C. S.

B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Performance analysis of adaptive-optics systems using laser guide stars and slope sensors,” J. Opt. Soc. Am. A 6, 1913–1923 (1989).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

T. J. Kane, B. M. Welsh, C. S. Gardner, “Wavefront detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1114, 160–171 (1989).
[CrossRef]

Gigan, P.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Graves, J. E.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Herrman, J.

Hill, S.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Humphreys, R. A.

Jagourel, P.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Johnston, D. C.

D. C. Johnston, “Increasing the corrected field of view of an adaptive optical telescope,” Ph.D. dissertation (School of Engineering, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1992).

Kane, T. J.

T. J. Kane, B. M. Welsh, C. S. Gardner, “Wavefront detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1114, 160–171 (1989).
[CrossRef]

Kern, P.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Labeyrie, A.

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 129–131 (1985).

Léna, P.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Limburg, E.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

McKechnie, T. S.

McKenna, D.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Merkle, F.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Murphy, D. V.

D. V. Murphy, “Atmospheric-turbulence compensation experiments using cooperative beacons,” Lincoln Lab. J. 5, 25–44 (1992).

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Page, D. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Parenti, R. R.

R. R. Parenti, “Adaptive optics for astronomy,” Lincoln Lab. J. 5, 93–114 (1992).

Primmerman, C. A.

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

R. A. Humphreys, C. A. Primmerman, L. C. Bradley, J. Herrman, “Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer,” Opt. Lett. 16, 1367–1369 (1991).
[CrossRef] [PubMed]

Rigaut, F.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

F. Rigaut, “Dual adaptive optics: a solution to the tilt determination problem using laser guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

Roberts, P. H.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Roddier, C.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Roddier, F.

J. Vernin, F. Roddier, “Experimental determination of two-dimensional spatiotemporal power spectra of stellar light scintillation. Evidence for a multilayer structure of the air turbulence in the upper troposphere,”J. Opt. Soc. Am. 63, 270–273 (1973).
[CrossRef]

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

F. Roddier, “Astronomical adaptive optics with natural reference stars,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

Rousset, G.

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

Ruane, R. E.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Salmon, D.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Songaila, A.

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Tallon, M.

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

Thompson, L. A.

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

Tyler, G. A.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Vernin, J.

J. Vernin, F. Roddier, “Experimental determination of two-dimensional spatiotemporal power spectra of stellar light scintillation. Evidence for a multilayer structure of the air turbulence in the upper troposphere,”J. Opt. Soc. Am. 63, 270–273 (1973).
[CrossRef]

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

Wallner, E. P.

Welsh, B. M.

Wopat, L. M.

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

Zollars, B. G.

B. G. Zollars, “Atmospheric-turbulence compensation experiments using synthetic beacons,” Lincoln Lab. J. 5, 67–92 (1992).

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Astron. Astrophys. (3)

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Léna, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, 129–131 (1985).

M. Tallon, R. Foy, “Adaptive telescope with laser probe: isoplanatism and cone effect,” Astron. Astrophys. 235, 549–557 (1990).

Astrophys. J. (1)

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

J. Opt. Soc. Am. (3)

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

Lincoln Lab. J. (3)

B. G. Zollars, “Atmospheric-turbulence compensation experiments using synthetic beacons,” Lincoln Lab. J. 5, 67–92 (1992).

D. V. Murphy, “Atmospheric-turbulence compensation experiments using cooperative beacons,” Lincoln Lab. J. 5, 25–44 (1992).

R. R. Parenti, “Adaptive optics for astronomy,” Lincoln Lab. J. 5, 93–114 (1992).

Nature (London) (3)

R. Q. Fugate, D. L. Fried, G. A. Ameer, B. R. Boeke, S. L. Browne, P. H. Roberts, R. E. Ruane, G. A. Tyler, L. M. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide-star,” Nature (London) 353, 144–146 (1991).
[CrossRef]

L. A. Thompson, C. S. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
[CrossRef]

C. A. Primmerman, D. V. Murphy, D. A. Page, B. G. Zollars, H. T. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
[CrossRef]

Opt. Lett. (1)

Publ. Astron. Soc. Pac. (1)

H. W. Babcock, “The possibility of compensating astronomical seeing,” Publ. Astron. Soc. Pac. 65, 229–236, (1953).
[CrossRef]

Other (9)

J. M. Beckers, “Increasing the size of the isoplanatic patch with multiconjugate adaptive optics,” in Proceedings of the ESO Conference on Very Large Telescopes and their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1988), pp. 693–703.

D. L. Fried, “Adaptive optics for imaging within the atmosphere: reference generation and field-of-view widening,” (Optical Sciences Company, Placentia, Calif., 1977).

F. Roddier, “Astronomical adaptive optics with natural reference stars,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

R. Foy, “Work in France in the field of the laser artificial guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

F. Rigaut, “Dual adaptive optics: a solution to the tilt determination problem using laser guide star,” presented at the Laser Guide Star Adaptive Optics Workshop, Kirtland Air Force Base, N.M., 1992.

D. C. Johnston, “Increasing the corrected field of view of an adaptive optical telescope,” Ph.D. dissertation (School of Engineering, U.S. Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1992).

T. J. Kane, B. M. Welsh, C. S. Gardner, “Wavefront detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1114, 160–171 (1989).
[CrossRef]

F. Roddier, L. Cowie, J. E. Graves, A. Songaila, D. McKenna, J. Vernin, M. Azouit, J. L. Caccia, E. Limburg, C. Roddier, D. Salmon, S. Beland, D. Cowley, S. Hill, “Seeing at Mauna Kea: a joint UH-UN-NOAO-CFHT study,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 485–491 (1990).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

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 (13)

Fig. 1
Fig. 1

Schematic comparison between single-DM correction and two-DM correction when atmospheric distortion is caused by two thin turbulent layers.

Fig. 2
Fig. 2

Geometry.

Fig. 3
Fig. 3

Single-DM, open-loop adaptive-optical telescope.

Fig. 4
Fig. 4

Two-DM, open-loop adaptive-optical telescope.

Fig. 5
Fig. 5

Size of DM k weighting function.

Fig. 6
Fig. 6

Square telescope aperture divided into N/2 square subapertures.

Fig. 7
Fig. 7

Telescope aperture and FOV projected onto the guide-star plane on which a constellation of four guide stars has been projected.

Fig. 8
Fig. 8

Size of DM k.

Fig. 9
Fig. 9

Portion of the atmosphere assigned to DM k.

Fig. 10
Fig. 10

DM sizes when DM is conjugated to the turbulent layers that are described in Table 1.

Fig. 11
Fig. 11

Rms residual phase error averaged over the object wave front versus the object position for a two-DM adaptive telescope with four guide stars compared with conventional single-DM system.

Fig. 12
Fig. 12

Performance of a two-DM system with multiple WFS reference sources providing overall tilt information compared with a system that uses laser guide stars providing only higher-order phase information.

Fig. 13
Fig. 13

Rms residual phase error averaged over the object wave front versus the object position for a single-DM adaptive telescope and various choices of DM position compared with a two-DM system. For the single-DM cases in which the DM was conjugated to the strongest layer and the turbulence center of gravity, the four-guide-star constellation was used.

Tables (1)

Tables Icon

Table 1 Parameters for Multiconjugate Adaptive-Optics Problem

Equations (55)

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

D i ( x , x ) = [ ψ l i ( x ) - ψ l i ( x ) ] 2 ,
f ( 1 2 λ ¯ L ) 1 / 2 ,
p i = x + ( z l i z s ) { [ ( r s - x ) · x ^ ] x ^ + [ ( r s - x ) · y ^ ] y ^ } ,
p i = x ( 1 - z l i z s ) + z l i θ s .
ψ t ( x ) = i = 1 I ψ l i [ x ( 1 - z l i z s ) + z l i θ s ] ,
θ m = tan - 1 ( tan 2 θ m x + tan 2 θ m y ) 1 / 2 .
ψ t m ( x ) = i = 1 I ψ l i [ x ( 1 - z l i z g ) + z l i θ m ] .
φ t m ( x ) = ψ t m ( x ) - ψ ¯ t m ,
ψ ¯ t m = d 2 x W a ( x ) ψ t m ( x )
d 2 x W a ( x ) = 1 .
s m n = - d 2 x [ W n ( x ) · a ^ ] φ t m ( x ) - ν m a + α m n ,
ν m a = d 2 x W p ( x ) a φ t m ( x ) d 2 x W p ( x ) a 2 ,
α m n α m n = σ α 2 δ m m δ n n ,
α m n ψ l i ( x ) 0 ,
ϕ d k ( x ) = ψ d k ( x ) - d 2 x W d k ( x ) ψ d k ( x ) - ( ν d k x x + ν d k y y ) ,
c j k = m = 1 M n = 1 N M j k m n s m n ,
c k = M k s ,
ϕ ˜ d k ( x ) = c k · r k ( x ) = M k s · r k ( x ) ,
k ( x ) = ϕ ˜ d k ( x ) - ϕ d k ( x ) .
k 2 = d 2 x W d k ( x ) [ ϕ ˜ d k ( x ) - ϕ d k ( x ) ] 2 = d 2 x W d k ( x ) ϕ ˜ d k 2 ( x ) + d 2 x W d k ( x ) ϕ d k 2 ( x ) - 2 d 2 x W d k ( x ) ϕ ˜ d k ( x ) ϕ d k ( x ) ,
d 2 x W d k ( x ) ϕ ˜ d k 2 ( x ) = tr [ M k T R k M k Σ s s ] ,
Σ s s = ss T ,
R k = d 2 x W d k ( x ) r k ( x ) r k T ( x ) .
0 k 2 = d 2 x W d k ( x ) ϕ d k 2 ( x ) .
d 2 x W d k ( x ) ϕ ˜ d k ( x ) ϕ d k ( x ) = tr [ A k T M k ] ,
A k = d 2 x W d k ( x ) r k ( x ) s T ϕ d k ( x ) .
k 2 = o k 2 + tr [ M k T R k M k Σ s s ] - 2 tr [ A k T M k ] .
M k * = R k - 1 A k Σ s s - 1 ,
k 2 min = 0 k 2 - tr [ Σ s s - 1 A k T R k - 1 A k ] .
φ b ( x , θ b ) = i = 1 I φ l i ( x + z l i θ b ) ,
( x , θ b ) = i = 1 I φ l i ( x + z l i θ b ) - k = 1 K φ ˜ d k ( x + z d k θ b ) - ψ ^ τ ( x ) ,
2 ( θ b ) = d 2 x W a ( x ) 2 ( x , θ b ) .
2 ( θ b ) = 0 2 ( θ b ) + k = 1 K k = 1 K tr [ M k * T R k k ( θ b ) M k * Σ s s ] - 2 i = 1 I k = 1 K tr [ A i k T ( θ b ) M k * ] + d 2 x W a ( x ) ψ ^ τ 2 ( x ) - 2 i = 1 I d 2 x W a ( x ) ψ ^ τ ( x ) φ l i ( x + z l i θ b ) + 2 k = 1 K d 2 x W a ( x ) M k * s ψ ^ τ ( x ) · r k ( x + z d k θ b ) .
0 2 ( θ b ) = d 2 x W a ( x ) φ b 2 ( x , θ b ) .
R k k ( θ b ) = d 2 x W a ( x ) [ r k ( x + z d k q b ) r k T ( x + z d k θ b ) ] - r ¯ k ( x + z d k θ b ) r ¯ k T ( x + z d k θ b ) ,
r ¯ k ( x ) = d 2 x W a ( x ) r k ( x ) .
A i k ( θ b ) = d 2 x W a ( x ) r k ( x + z d k θ b ) s T φ l i ( x + z l i θ b ) .
r j k ( x , y ) exp { - [ ( x - x j k ) 2 + ( y - y j k ) 2 ρ m 2 } ,
x g m = z g θ m x ,
y g m = z g θ m y .
x ˜ g m = x g m d ,
y ˜ g m = y g m d .
x ˜ b = z g θ b x d ,
y ˜ b = z g θ b y d ,
x ˜ β = y ˜ β = z g β 2 d .
x ˜ g = D 2 d + x ˜ β ,
y ˜ g = D 2 d + y ˜ β .
z ˜ d k = z d k z g .
D k = D + 2 d z ˜ d k x ˜ β ,
ϕ d k ( x ) = i S k ϕ l i ( x ) .
D i ( x , x ) = [ ϕ l i ( x ) - ϕ l i ( x ) ] 2 = 6.88 ( x - x r i ) 5 / 3 ,
r 0 - 5 / 3 = i = 1 I r i - 5 / 3 .
q i = ( r i r 0 ) - 5 / 3
z ˜ l i = z l i / z g .
σ α = { 0.86 π η N ph 1 / 2 r 0 , d > r 0 0.74 π η N ph 1 / 2 d , d r 0 ,             ( rad / m ) ,

Metrics