Abstract

Calculations of backscatter emission of mesospheric sodium atoms in a laser guide star that is excited by pulses ranging from 30-ns to 0.9-μs duration are described. The efficient use of such pulses at saturating irradiance values is shown to require ~3 GHz of spectral broadening to provide access to the full absorption spectrum of the D2 line. The broadening is provided by frequency modulation. A set of density matrices was used to account for all 24 hyperfine states and inhomogeneous Doppler broadening. At the broadband (3-GHz) saturation irradiance of 4 W/cm2, both linearly and circularly polarized laser beams are shown to produce emission rates exceeding 60% of the maximum possible rate-equation rate for the 0.9-μs pulses. As expected, circular polarization produced more backscatter than did linear polarization, but the enhancement never exceeded 1/3 in the calculations that are reported. A brief estimate of state precession in the Earth’s magnetic field suggests that achieving even this enhancement will require that the time scale for optical pumping be held to less than 1 μs, which will require the use of irradiances greater than 0.7 W/cm2 and spectral coverage of the full 3-GHz hyperfine-plus-Doppler absorption profile, at least until most of the population is pumped out of the F = 1 ground states.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Astronomy and Astrophysics Survey Committee, National Research Council, The Decade of Discovery in Astronomy and Astrophysics (National Academy Press, Washington, D.C., 1991), pp. 5–6 and 82–83.
  2. H. W. Babcock, “Adaptive optics revisited,” Science 249, 253–257 (1990).
    [CrossRef] [PubMed]
  3. G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Lena, C. Boyer, P. Jagourel, J. P. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32 (1990).
  4. F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
    [CrossRef]
  5. P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
    [CrossRef]
  6. F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
    [CrossRef]
  7. F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).
  8. R. Racine, R. D. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
    [CrossRef]
  9. F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
    [CrossRef]
  10. P. Wizinowich, B. McLeod, M. Lloyd-Hart, J. R. P. Angel, D. Colocci, R. Dekany, D. McCarthy, D. Wittman, I. Scott-Fleming, “Adaptive optics for array telescopes using piston-and-tilt wave-front sensing,” Appl. Opt. 31, 6036–6048 (1992).
    [CrossRef] [PubMed]
  11. R. B. Dunn, “NSO/SP adaptive optics program,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 216–231 (1990).
    [CrossRef]
  12. F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  13. S. S. Oliver, D. T. Gavel, “Tip–tilt compensation for astronomical imaging,” J. Opt. Soc. Am. A 11, 368–378 (1994).
    [CrossRef]
  14. R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).
  15. W. Happer, G. J. MacDonald, C. E. Max, F. 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]
  16. G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
    [CrossRef]
  17. 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]
  18. R. Q. Fugate, D. L. Fried, G. A. Amer, 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]
  19. D. V. Murphy, C. A. Primmerman, B. G. Zollars, H. T. Barclay, “Experimental demonstration of atmospheric compensation using multiple synthetic beacons,” Opt. Lett. 16, 1797–1799 (1991).
    [CrossRef] [PubMed]
  20. L. A. Thompson, R. M. Castle, “Experimental demonstration of a Rayleigh-scattered laser guide star at 351 nm,” Opt. Lett. 17, 1485–1487 (1992).
    [CrossRef] [PubMed]
  21. 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]
  22. C. S. Gardner, “Sodium resonance fluorescence lidar applications in atmospheric science and astronomy,” Proc. IEEE 77, 408–418 (1989).
    [CrossRef]
  23. B. M. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
    [CrossRef] [PubMed]
  24. R. A. Humphreys, C. A. Primmerman, L. C. Bradley, J. Herrmann, “Atmospheric turbulence measurements using a synthetic beacon in the mesospheric sodium layer,” Opt. Lett. 16, 1367–1369 (1991).
    [CrossRef] [PubMed]
  25. C. E. Max, K. Avicola, J. M. Brase, H. W. Friedman, H. D. Bissinger, J. Duff, D. T. Gavel, J. A. Horton, R. Kiefer, J. R. Morris, S. S. Olivier, R. W. Presta, D. A. Rapp, J. T. Salmon, K. E. Waltjen, “Design, layout, and early results of a feasibility experiment for sodium-layer laser guide star adaptive optics,” J. Opt. Soc. Am. A 11, 813–824 (1994).
    [CrossRef]
  26. K. Avicola, J. M. Brase, J. R. Morris, H. D. Bissinger, H. W. Friedman, D. T. Gavel, C. E. Max, S. S. Olivier, R. W. Presta, D. A. Rapp, J. T. Salmon, K. E. Waltjen, “Sodium-layer laser-guide-star experimental results,” J. Opt. Soc. Am. A 11, 825–831 (1994).
    [CrossRef]
  27. D. T. Gavel, J. R. Morris, R. G. Vernon, “Systematic design and analysis of laser-guide-star adaptive-optics systems for large telescopes,” J. Opt. Soc. Am. A 11, 914–924 (1994).
    [CrossRef]
  28. G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
    [CrossRef]
  29. K. H. Fricke, U. von Zahn, “Mesophase temperatures derived from probing the hyperfine structure of the D2resonance line of sodium by lidar,”J. Atmos. Terr. Phys. 47, 499–512 (1985).
    [CrossRef]
  30. C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
    [CrossRef]
  31. C. S. Gardner, D. G. Voelz, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 2. Gravity waves,”J. Geophys. Res. 92, 4673–4694 (1987).
    [CrossRef]
  32. D. L. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,”J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  33. P. W. Milonni, L. E. Thode, “Theory of mesospheric sodium fluorescence excited by pulse trains,” Appl. Opt. 31, 785–800 (1992).
    [CrossRef] [PubMed]
  34. L. C. Bradley, “Pulse-train excitation of sodium for use as a synthetic beacon,” J. Opt. Soc. Am. B 9, 1931–1944 (1992).
    [CrossRef]
  35. See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
    [CrossRef]
  36. R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981), pp. 507–509. The alternative form, B′, of the hyperfine Bcoefficient given in footnote 36 on p. 509, is employed here.
  37. Ref. 36, pp. 313–314.
  38. Ref. 36, pp. 307–310.
  39. E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, London, 1953), pp. 90–91.
  40. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.
  41. Ref. 36, pp. 402–403.
  42. M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
    [CrossRef]
  43. W. B. Hawkins, “Orientation and alignment of sodium atoms by means of polarized resonance radiation,” Phys. Rev. 98, 478–486 (1955).
    [CrossRef]
  44. A. Kastler, “Optical methods of atomic orientation and of magnetic resonance,”J. Opt. Soc. Am. 47, 460–465 (1957).
    [CrossRef]
  45. J. A. Abate, “Preparation of atomic sodium as a two-level atom,” Opt. Commun. 10, 269–272 (1974).
    [CrossRef]
  46. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1960), Chap. 4.

1994 (5)

1992 (5)

1991 (6)

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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. Q. Fugate, D. L. Fried, G. A. Amer, 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. V. Murphy, C. A. Primmerman, B. G. Zollars, H. T. Barclay, “Experimental demonstration of atmospheric compensation using multiple synthetic beacons,” Opt. Lett. 16, 1797–1799 (1991).
[CrossRef] [PubMed]

F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

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

1990 (3)

G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

H. W. Babcock, “Adaptive optics revisited,” Science 249, 253–257 (1990).
[CrossRef] [PubMed]

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

1989 (3)

R. Racine, R. D. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
[CrossRef]

C. S. Gardner, “Sodium resonance fluorescence lidar applications in atmospheric science and astronomy,” Proc. IEEE 77, 408–418 (1989).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
[CrossRef] [PubMed]

1987 (2)

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. S. Gardner, D. G. Voelz, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 2. Gravity waves,”J. Geophys. Res. 92, 4673–4694 (1987).
[CrossRef]

1986 (1)

C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

1985 (2)

K. H. Fricke, U. von Zahn, “Mesophase temperatures derived from probing the hyperfine structure of the D2resonance line of sodium by lidar,”J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

1978 (1)

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

1977 (1)

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

1974 (1)

J. A. Abate, “Preparation of atomic sodium as a two-level atom,” Opt. Commun. 10, 269–272 (1974).
[CrossRef]

1966 (1)

1957 (1)

1955 (2)

W. B. Hawkins, “Orientation and alignment of sodium atoms by means of polarized resonance radiation,” Phys. Rev. 98, 478–486 (1955).
[CrossRef]

See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
[CrossRef]

Abate, J. A.

J. A. Abate, “Preparation of atomic sodium as a two-level atom,” Opt. Commun. 10, 269–272 (1974).
[CrossRef]

Amer, G. A.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Angel, J. R. P.

Avicola, K.

Babcock, H. W.

H. W. Babcock, “Adaptive optics revisited,” Science 249, 253–257 (1990).
[CrossRef] [PubMed]

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]

D. V. Murphy, C. A. Primmerman, B. G. Zollars, H. T. Barclay, “Experimental demonstration of atmospheric compensation using multiple synthetic beacons,” Opt. Lett. 16, 1797–1799 (1991).
[CrossRef] [PubMed]

Bissinger, H. D.

Blamont, J. E.

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

Boeke, B. R.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Bos, F.

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

Boyer, C.

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Bradley, L. C.

Brase, J. M.

Browne, S. L.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Castle, R. M.

Chanin, M. L.

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

Citron, M. L.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

Colocci, D.

Condon, E. U.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, London, 1953), pp. 90–91.

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981), pp. 507–509. The alternative form, B′, of the hyperfine Bcoefficient given in footnote 36 on p. 509, is employed here.

Dekany, R.

Duff, J.

Dunn, R. B.

R. B. Dunn, “NSO/SP adaptive optics program,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 216–231 (1990).
[CrossRef]

Dyson, F. J.

Edmonds, A. R.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1960), Chap. 4.

Elon-Graves, J.

F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.

Fontanella, J. C.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Foy, R.

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Fricke, K. H.

K. H. Fricke, U. von Zahn, “Mesophase temperatures derived from probing the hyperfine structure of the D2resonance line of sodium by lidar,”J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

Fried, D. L.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,”J. Opt. Soc. Am. 56, 1372–1379 (1966).
[CrossRef]

Friedman, H. W.

Fugate, R. Q.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Gabel, C. W.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

Gaffard, J. P.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
[CrossRef]

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Gardner, C. S.

C. S. Gardner, “Sodium resonance fluorescence lidar applications in atmospheric science and astronomy,” Proc. IEEE 77, 408–418 (1989).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
[CrossRef] [PubMed]

C. S. Gardner, D. G. Voelz, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 2. Gravity waves,”J. Geophys. Res. 92, 4673–4694 (1987).
[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. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

Gardner, G. S.

G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

Gavel, D. T.

Gendron, E.

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

Gigan, P.

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Gray, H. R.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

Happer, W.

Hawkins, W. B.

W. B. Hawkins, “Orientation and alignment of sodium atoms by means of polarized resonance radiation,” Phys. Rev. 98, 478–486 (1955).
[CrossRef]

Herrmann, J.

Horton, J. A.

Humphreys, R. A.

Jagourel, P.

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Kastler, A.

Kern, P.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
[CrossRef]

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

Kiefer, R.

Labeyrie, A.

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

Lena, P.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

Lloyd-Hart, M.

MacDonald, G. J.

Max, C. E.

McCarthy, D.

McClure, R. D.

R. Racine, R. D. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
[CrossRef]

McLeod, B.

Megie, G.

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

Merkle, F.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
[CrossRef]

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

Milonni, P. W.

Morris, J. R.

Murphy, D. V.

D. V. Murphy, C. A. Primmerman, B. G. Zollars, H. T. Barclay, “Experimental demonstration of atmospheric compensation using multiple synthetic beacons,” Opt. Lett. 16, 1797–1799 (1991).
[CrossRef] [PubMed]

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]

Northcott, M.

F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Oliver, S. S.

Olivier, S. S.

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]

Perl, M. L.

See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.

Presta, R. W.

Primmerman, C. A.

Rabi, I. I.

See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
[CrossRef]

Racine, R.

R. Racine, R. D. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
[CrossRef]

Rapp, D. A.

Rigaut, F.

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

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Roberts, P. H.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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, F.

F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Rousset, G.

F. Rigaut, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

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

F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
[CrossRef]

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

Ruane, R. E.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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, J. T.

Scott-Fleming, I.

Sechrist, C. F.

C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

Segal, A. C.

C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

Senitsky, B.

See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
[CrossRef]

Shortley, G. H.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, London, 1953), pp. 90–91.

Stroud, C. R.

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.

Thode, L. E.

Thompson, L. A.

L. A. Thompson, R. M. Castle, “Experimental demonstration of a Rayleigh-scattered laser guide star at 351 nm,” Opt. Lett. 17, 1485–1487 (1992).
[CrossRef] [PubMed]

G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[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]

Tyler, G. A.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Vernon, R. G.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.

Voelz, D. G.

C. S. Gardner, D. G. Voelz, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 2. Gravity waves,”J. Geophys. Res. 92, 4673–4694 (1987).
[CrossRef]

C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

von Zahn, U.

K. H. Fricke, U. von Zahn, “Mesophase temperatures derived from probing the hyperfine structure of the D2resonance line of sodium by lidar,”J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

Waltjen, K. E.

Welsh, B. M.

G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

B. M. Welsh, C. S. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
[CrossRef] [PubMed]

Wittman, D.

Wizinowich, P.

Wopat, L. M.

R. Q. Fugate, D. L. Fried, G. A. Amer, 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.

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]

D. V. Murphy, C. A. Primmerman, B. G. Zollars, H. T. Barclay, “Experimental demonstration of atmospheric compensation using multiple synthetic beacons,” Opt. Lett. 16, 1797–1799 (1991).
[CrossRef] [PubMed]

Appl. Opt. (3)

Astron. Astrophys. (4)

R. Foy, A. Labeyrie, “Feasibility of adaptive telescope with laser probe,” Astron. Astrophys. 152, L29–L31 (1985).

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

G. Rousset, J. C. Fontanella, P. Kern, P. Gigan, F. Rigaut, P. Lena, 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, G. Rousset, P. Kern, J. C. Fontanella, J. P. Gaffard, F. Merkle, P. Lena, “Adaptive optics on a 3.6-m telescope: results and performance,” Astron. Astrophys. 250, 280–290 (1991).

J. Atmos. Terr. Phys. (1)

K. H. Fricke, U. von Zahn, “Mesophase temperatures derived from probing the hyperfine structure of the D2resonance line of sodium by lidar,”J. Atmos. Terr. Phys. 47, 499–512 (1985).
[CrossRef]

J. Geophys. Res. (2)

C. S. Gardner, D. G. Voelz, C. F. Sechrist, A. C. Segal, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 1. Seasonal and nocturnal variations,”J. Geophys. Res. 91, 13,659–13,673 (1986).
[CrossRef]

C. S. Gardner, D. G. Voelz, “Lidar studies of the nighttime sodium layer over Urbana, Illinois. 2. Gravity waves,”J. Geophys. Res. 92, 4673–4694 (1987).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (1)

Nature (London) (3)

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]

R. Q. Fugate, D. L. Fried, G. A. Amer, 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]

Opt. Commun. (1)

J. A. Abate, “Preparation of atomic sodium as a two-level atom,” Opt. Commun. 10, 269–272 (1974).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (2)

See, for example, M. L. Perl, I. I. Rabi, B. Senitsky, “Nuclear electric quadrupole moment of Na23by the atomic beam resonance method,” Phys. Rev. 98, 611–626 (1955), and references therein.
[CrossRef]

W. B. Hawkins, “Orientation and alignment of sodium atoms by means of polarized resonance radiation,” Phys. Rev. 98, 478–486 (1955).
[CrossRef]

Phys. Rev. A (1)

M. L. Citron, H. R. Gray, C. W. Gabel, C. R. Stroud, “Experimental study of power broadening in a two-level system,” Phys. Rev. A 16, 1507–1512 (1977).
[CrossRef]

Planet. Space Sci. (1)

G. Megie, F. Bos, J. E. Blamont, M. L. Chanin, “Simultaneous nighttime lidar measurements of atmospheric sodium and potassium,” Planet. Space Sci. 26, 27–35 (1978).
[CrossRef]

Proc. IEEE (2)

C. S. Gardner, “Sodium resonance fluorescence lidar applications in atmospheric science and astronomy,” Proc. IEEE 77, 408–418 (1989).
[CrossRef]

G. S. Gardner, B. M. Welsh, L. A. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
[CrossRef]

Publ. Astron. Soc. Pac. (2)

R. Racine, R. D. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
[CrossRef]

F. Roddier, M. Northcott, J. Elon-Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Science (1)

H. W. Babcock, “Adaptive optics revisited,” Science 249, 253–257 (1990).
[CrossRef] [PubMed]

Other (12)

Astronomy and Astrophysics Survey Committee, National Research Council, The Decade of Discovery in Astronomy and Astrophysics (National Academy Press, Washington, D.C., 1991), pp. 5–6 and 82–83.

F. Merkle, G. Rousset, P. Kern, J. P. Gaffard, “First diffraction-limited astronomical images with adaptive optics,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 193–202 (1990).
[CrossRef]

P. Kern, P. Lena, P. Gigan, F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, C. Boyer, P. Jagourel, F. Merkle, “Adaptive optics prototype system for infrared astronomy, I: system description,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 243–251 (1990).
[CrossRef]

F. Merkle, P. Kern, F. Rigaut, P. Lena, G. Rousset, “Adaptive optics prototype system for infrared astronomy, II: first observing results,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 232–242 (1990).
[CrossRef]

R. B. Dunn, “NSO/SP adaptive optics program,” in Adaptive Optics and Optical Structures, J. Schulte in den Baeumen, R. K. Tyson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1271, 216–231 (1990).
[CrossRef]

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981), pp. 507–509. The alternative form, B′, of the hyperfine Bcoefficient given in footnote 36 on p. 509, is employed here.

Ref. 36, pp. 313–314.

Ref. 36, pp. 307–310.

E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. Press, London, 1953), pp. 90–91.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, New York, 1986), Chap. 15.

Ref. 36, pp. 402–403.

A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. Press, Princeton, N.J., 1960), Chap. 4.

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 (24)

Fig. 1
Fig. 1

Hyperfine states of the D2 line of Na23 showing the optical transitions for (a) linearly polarized light with the electric field along the quantization z axis and (b) left-circularly polarized light with the propagation direction along the quantization z axis. The frequencies shown are the differences between adjacent hyperfine sublevels.

Fig. 2
Fig. 2

Absorption cross section of the D2 line of Na23 in the mesosphere for a temperature of 173 K at which the Doppler FWHM is 1 GHz.

Fig. 3
Fig. 3

Excited-level populations versus time for illumination by a single strongly saturating (≈5 W/cm2, 0.167 μJ/cm2) 32-ns FWHM power Gaussian pulse tuned to 664.5 MHz below the centroid of the D2 line, which is at or near the peak of the 2S1/2 (F = 2) → 2P3/2 component of the Doppler-broadened D2 line. The solid curve is the total 2P3/2 level population; the dotted curve is the F = 3, MF = 0 hyperfine-state population.

Fig. 4
Fig. 4

Population distribution of the hyperfine sublevels of the 2S1/2 ground level after illumination by a single strongly saturating pulse. The solid and the dotted curves are the F = 2 and F = 1 hyperfine sublevel populations, respectively. The population fraction is for 25-MHz intervals centered at the indicated Doppler shift.

Fig. 5
Fig. 5

Backscatter emission versus pulse fluence for an isolated 32-ns FWHM power Gaussian pulse. The dotted curve is for the unmodulated pulse described by the caption to Fig. 3. The solid curve is for a pulse whose frequency and frequency modulation are chosen to match its power spectral density approximately to the Doppler-broadened hyperfine profile of the D2 line.

Fig. 6
Fig. 6

Spectral power density of a 32-ns FWHM power pulse modulated with the DGFM format described in the text. The dotted curve is the D2-line absorption profile (arbitrary units) for comparison.

Fig. 7
Fig. 7

Conceptual diagram of an m-stage pulse stretcher that generates 2m subpulses with a delay of T between adjacent subpulses. The diagonal lines represent 50/50 beam splitters, and the boxes represent optical-delay lines. The two outputs can be combined at a polarizing beam combiner (linear polarization only) or can be separately propagated to and overlapped at the mesosphere.

Fig. 8
Fig. 8

Example of the electric-field amplitude format of the stretched-pulse model that is used in this paper. The component pulses are 32-ns FWHM power Gaussians; they are separated by 60 ns in this plot. Adjacent pulses alternate between constructive and destructive interference.

Fig. 9
Fig. 9

Spectral power density of a 32-ns FWHM power pulse modulated with the GFM format described in the text. The dotted curve is the D2-line absorption profile for comparison. The GFM format concentrates its energy in the spectral region associated with the F = 2 component of the ground level; the GFM format was designed for use with circular polarization at high pulse fluences.

Fig. 10
Fig. 10

Backscatter emission rate versus time for frequency-modulated 2.5-μJ/cm2 stretched pulses consisting of 15 subpulses spaced 60 ns apart, each of which is a 32-ns FWHM power Guassian. The frequency-modulation formats are DGFM (solid curve) and GFM (dotted curve).

Fig. 11
Fig. 11

Ground-level hyperfine populations versus time for the DGFM pulse described in the caption to Fig. 10. The solid curve represents the total population in the F = 2 states; the dotted curve represents that in the F = 1 states. The balanced spectrum of the DGFM pulse approximately preserves the ratio of these two populations.

Fig. 12
Fig. 12

Ground-level hyperfine populations versus time for the GFM pulse described in the caption to Fig. 10. The solid curve represents the total population in the F = 2 states; the dotted curve represents that in the F = 1 states. The spectral emphasis of the GFM format on the 2S1/2 (F = 2) → 2P3/2 transitions optically pumps the 2S1/2 (F = 1) states, reducing the effectiveness of this format for linear polarization.

Fig. 13
Fig. 13

Comparison of the backscatter-emission rates for stretched and unstreteched pulses frequency modulated with the DGFM format. The subpulse separation for the stretched case is much longer than 100 ns.

Fig. 14
Fig. 14

Comparison of backscatter-emission rates at various subpulse separations for stretched pulses that are frequency modulated with the DGFM format. From top to bottom the pulse separations are ≫100, 60, and 40 ns.

Fig. 15
Fig. 15

Comparison of backscatter-emission rates at various pulse-stretch factors. All the pulses are modulated with the DGFM format, and the subpulse separation is 60 ns.

Fig. 16
Fig. 16

Time dependence of the total population of the optically pumped manifold [(F, MF) = (2,2) and (3,3)] states for illumination by a circularly polarized pulse with 2.5-μJ/cm2 fluence. The stretched-pulse electric-field amplitude is that of Fig. 8, 15 sub-pulses with a 60-ns separation between subpulses: solid curve, GFM; dotted curve, DGFM.

Fig. 17
Fig. 17

Time dependence of the optically pumped (3,3) excited-state population for the conditions of Fig. 16: solid curve, GFM; dotted curve, DGFM.

Fig. 18
Fig. 18

Time dependence of backscatter conditions of Fig. 16 at various pulse fluences: solid curve, GFM; dotted curve, DGFM.

Fig. 19
Fig. 19

Time dependence of the total population of the optically pumped manifold states [(2,2) and (3,3)] for various pulse fluences and for DGFM. The pulses are as for Fig. 16, except for the fluence and the frequency modulation. The curves are labeled with the Rabi rate, Ω, for thermal-equilibrium initial populations at the peak isolated subpulse irradiance; the corresponding fluence in μJ/cm2 is given by 2.51 Ω2.

Fig. 20
Fig. 20

Optical pumping time versus pulse fluence for the conditions of Fig. 19. The solid and the dotted curves are the times at which the pumped-manifold population reaches 50% and 80%, respectively. The times are measured from the half-maximum irradiance point on the leading edge of the pulse.

Fig. 21
Fig. 21

Comparison of backscatter emission for circular (upper curve) and linear (lower curve) polarization for stretched pulses with DGFM. The electric-field amplitude of the stretched pulse is described by Fig. 8.

Fig. 22
Fig. 22

Gaussian irradiance profile estimate of the effect of the laser spatial spot size on the observed backscatter emission for linearly polarized, unstretched, 32-ns FWHM power Gaussian pulses and DGFM. The laser power is at the ground, atmospheric transmission of 0.6 at 589 nm was used, and the sodium-column density was the Gardner et al. annual average value of 5 × 109 cm−2. The label on each curve is the FWHM of the irradiance profile.

Fig. 23
Fig. 23

Gaussian irradiance-profile estimate of the effect of the laser spatial spot size on the observed backscatter emission for a linearly polarized, stretched pulse and DGFM. The stretched pulse had 16 subpulses and 60-ns interpulse separation; the other conditions are as for Fig. 22.

Fig. 24
Fig. 24

Population remaining in the (1, 1)′ ground state at normalized time t/τz, where τz = 4π/μBBe for various angles between the laser propagation direction and the Earth’s magnetic field. From top to bottom the angles are 15°, 30°, 45°, 60°, 75°, and 90°. The atom is prepared in the (1, 1)′ ground state at time t = 0 and evolves in the presence of the Earth’s magnetic field but in the absence of the laser field. Collisions have been neglected so the population is a periodic function of time.

Tables (5)

Tables Icon

Table 1 Hyperfine Transition Dipole Matrix Elements Divided by 〈 αe, 3/2||P(1)||αg, 1/2〉

Tables Icon

Table 2 Spontaneous-Emission Branching Ratios

Tables Icon

Table 3 Backscatter-Emission Efficiencies

Tables Icon

Table 4 Frequency-Modulation Format Classes Used in This Paper

Tables Icon

Table 5 Frequency-Modulation Models Used in This Paper

Equations (24)

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

ρ m n t = - i - 1 ( H ρ - ρ H ) m n + Γ m n ; p q ρ p q ,
H m n = E m δ m n - ( ω L + δ ω D + φ ˙ ( t ) ) δ m n δ m e - p m n · ( E 0 ( t ) δ m e + E 0 * ( t ) δ n e ) / 2 ,
Γ m n ; p q = γ m n δ m p δ n q + μ m p δ m n δ p q ,
γ m n = - 1 / τ s for both m , n ( excited states ) = - 1 / 2 τ s for m ( an excited state ) and n ( a ground state ) or vice versa = 0 otherwise ,
μ m p = β m p / τ s for m ( a ground state ) and p ( an excited state ) = 0 otherwise ,
E m = h ν 0 + h f e ( I , J , F ) for m ( an excited state ) = h f g ( I , J , F ) for m ( a ground state ) ,
f α ( I , J , F ) = A α K / 2 + B α [ 3 K ( K + 1 ) - 4 I ( I + 1 ) × J ( J + 1 ) ] / [ 8 I ( 2 I - 1 ) J ( 2 J - 1 ) ] ,
K F ( F + 1 ) - I ( I + 1 ) - J ( J + 1 ) .
α e , 3 / 2 ; 3 / 2 ; F P ( 1 ) I ( 0 ) α g , 1 / 2 ; 3 / 2 ; F = ( - 1 ) F [ ( 2 F + 1 ) ( 2 F + 1 ) ] 1 / 2 { 3 2 3 2 F F 1 1 2 } × α e , 3 / 2 P ( 1 ) α g , 1 / 2 ,
α e , 3 / 2 ; 3 / 2 ; F , M F P q ( 1 ) I ( 0 ) α g , 1 / 2 ; 3 / 2 ; F , M F = ( - 1 ) F + F - M F [ ( 2 F + 1 ) ( 2 F + 1 ) ] 1 / 2 [ F 1 F - M F q M F ] × { 3 2 3 2 F F 1 1 2 } α e , 3 / 2 P ( 1 ) α g , 1 / 2 ,
β ( g ; F , M ) , ( e ; F , M ) = F , M P M - M ( 1 ) I ( 0 ) F , M 2 / F , M F , M P M - M ( 1 ) I ( 0 ) F , M 2 = ( 2 J e + 1 ) F , M P M - M ( 1 ) I ( 0 ) F , M 2 / α e , 3 / 2 P ( 1 ) α g , 1 / 2 2 ,
d S e d t = excited states ρ j j / τ s ,
d S b d t = excited states , j ρ j j j ( polarisation ) / 4 π τ s ,
j ( circular ) = p β p j × { 1.5 for Δ m = ± 1 transitions 0 for Δ m = 0 transitions , j ( linear ) = p β p j × { 0.75 for Δ m = ± 1 transitions 1.5 for Δ m = 0 transitions .
d P d Ω = { [ 1 + cos 2 ( θ ) ] ( 3 / 16 π ) for Δ m = ± 1 transitions [ sin 2 ( θ ) ] ( 3 / 8 π ) for Δ m = 0 transitions ,
{ S ¯ e ( t ) S ¯ b ( t ) ρ ¯ n n ( t ) } = - d u { S e ( t , u δ ω D / Δ D ) S b ( t , u δ ω D / Δ D ) ρ n n ( t , u δ ω D / Δ D ) } × ( 4 ln 2 / π ) 1 / 2 exp ( - u 2 4 ln 2 ) ,
α e , J e P ( 1 ) α g , J g 2 = 3 h λ 3 ( 2 J e + 1 ) / 64 π 4 τ s ,
p ¯ 2 = ( 2 F + 1 ) - 1 F , M F α e , 3 / 2 ; 3 / 2 ; F , M F + q × P q ( 1 ) α g , 1 / 2 ; 3 / 2 ; F , M F 2 = [ 3 ( 2 J g + 1 ) ] - 1 α e , 3 / 2 P ( 1 ) α g , 1 / 2 2 = h λ 3 ( 2 J e + 1 ) / [ 64 π 4 τ s ( 2 J g + 1 ) ] .
Ω ¯ ( t ) = p ¯ E 0 ( t ) / ,
Ω ¯ 2 ( t ) = I ( t ) λ 3 ( 2 J e + 1 ) / 2 π h c τ s ( 2 J g + 1 ) = I ( t ) λ 3 / π h c τ s .
I ¯ sat = π h c / 2 λ 3 τ s ,
ϕ m ( t ) = 2 π A σ { j = - W ( t j ) h m [ ( t - t j ) / σ ] - q m / τ } ,
E n ( t ) = E 1 ( t ) + j = 1 n ( - 1 ) j { E 1 [ t - ( 2 j - 1 ) τ s ] + E 1 ( t - 2 j τ s ) } ,
Ψ ( t ) = m = - 1 1 d m , 1 ( 1 ) ( θ ) exp ( - i 2 π m t / τ z ) d m , 1 ( 1 ) ( - θ ) ,

Metrics