Abstract

We discuss the design of laser-guided adaptive-optics systems for the large, 8–10-m-class telescopes. Through proper choice of system components and optimized system design, the laser power that is needed at the astronomical site can be kept to a minimum.

© 1994 Optical Society of America

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  1. R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
    [CrossRef]
  2. R. Racine, R. McClure, “An image stabilization experiment at the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 731–736 (1989).
    [CrossRef]
  3. R. 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]
  4. D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
    [CrossRef]
  5. R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
    [CrossRef]
  6. C. Primmerman, D. Murphy, D. Page, B. Zollars, H. Barclay, “Compensation of atmospheric optical distortion using a synthetic beacon,” Nature (London) 353, 141–143 (1991).
    [CrossRef]
  7. G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. Gaffard, F. Merkle, “First diffraction-limited astronomical images with adaptive optics,” Astron. Astrophys. 230, L29–L32, 1990.
  8. 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, 243–250 (1990).
    [CrossRef]
  9. F. Merkel, N. Hubin, “Adaptive optics for the European Very Large Telescope,”ESO Tech. Preprint 32 (European Southern Observatory, Garching, Germany, 1991).
  10. J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.
  11. C. Gardner, B. Welsh, L. Thompson, “Design and performance analysis of adaptive optical telescopes using laser guide stars,” Proc. IEEE 78, 1721–1743 (1990).
    [CrossRef]
  12. L. Thompson, C. Gardner, “Experiments on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature (London) 328, 229–231 (1987).
    [CrossRef]
  13. B. Welsh, C. Gardner, “Nonlinear resonant absorption effects on the design of resonance fluorescence lidars and laser guide stars,” Appl. Opt. 28, 4141–4153 (1989).
    [CrossRef] [PubMed]
  14. D. Fried, “Optical resolution through a randomly inhomogeneous medium for very long and very short exposures,”J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  15. G. Tyler, “Turbulence-induced adaptive-optics performance degradation: evaluation in the time domain,” J. Opt. Soc. Am. A 1, 251–262 (1984).
    [CrossRef]
  16. J. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8, p. 407.
  17. D. Fried, “Statistics of a geometric representation of wavefront distortion,”J. Opt. Soc. Am. 55, 1427–1435 (1965).
    [CrossRef]
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  19. D. Greenwood, D. Fried, “Power spectra requirements for wave-front-compensative systems,”J. Opt. Soc. Am. 66, 193–206 (1976).
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  20. D. Greenwood, “Bandwidth specification for adaptive optics systems,”J. Opt. Soc. Am. 67, 390–393 (1977).
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  21. D. Sandler, ThermoTrex Corporation, 9550 Distribution Avenue, San Diego, Calif. 92121–2306 (personal communication, 1992).
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    [CrossRef]
  23. B. Welsh, “Imaging performance analysis of adaptive optical telescopes using laser guide stars,” Appl. Opt. 30, 5021–5030 (1991).
    [CrossRef] [PubMed]
  24. R. Vernon (while working for United Technologies Optical Systems, East Hartford, Conn.), Science Applications International Corporation, Palm Beach Gardens, Fla. 33410 (personal communication, 1991).
  25. G. Tyler, D. Fried, “Image-position error associated with a quadrant detector,”J. Opt. Soc. Am. 72, 804–808 (1982).
    [CrossRef]
  26. T. Kane, B. Welsh, C. Gardner, “Wavefront detector optimization for laser guided adaptive telescopes,” in Active Telescope Systems, F. J. Roddier, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1114, 160–171 (1989).
    [CrossRef]
  27. R. Noll, “Phase estimates from slope-type wave-front sensors,”J. Opt. Soc. Am. 68, 139–140 (1978).
    [CrossRef]
  28. R. Frost, C. Rushforth, B. Baxter, “Fast FFT-based algorithm for phase estimation in speckle imaging,” Appl. Opt. 18, 2056–2061 (1979).
    [CrossRef] [PubMed]
  29. J. Herrmann, “Least-squares wave front errors of minimum norm,”J. Opt. Soc. Am. 70, 28–35 (1980).
    [CrossRef]
  30. W. Southwell, “Wave-front estimation from wave-front slope measurements,”J. Opt. Soc. Am. 70, 28–35 (1980).
    [CrossRef]
  31. D. Fried, “Anisoplanatism in adaptive optics,”J. Opt. Soc. Am. 72, 52–61 (1982).
    [CrossRef]
  32. B. Welsh, C. 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]
  33. D. Fried, “Analysis of focus anisoplanatism: the fundamental limit in performance of artificial guide star adaptive optics system,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 37–80.
  34. R. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” (MIT Lincoln Laboratory, Lexington, Mass., 1988).
  35. G. Tyler, “Summary of theoretical performance and limitations of laser guide star adaptive optics for astronomical applications,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 405–440.
  36. F. Rigaut, E. Gendron, “Laser guide star in adaptive optics: the tilt determination problem,” Astron. Astrophys. 261, 677–684 (1992).
  37. S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

1992 (1)

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

1991 (5)

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

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

B. Welsh, C. 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. Welsh, “Imaging performance analysis of adaptive optical telescopes using laser guide stars,” Appl. Opt. 30, 5021–5030 (1991).
[CrossRef] [PubMed]

1990 (2)

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

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

1989 (4)

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

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

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

B. Welsh, C. 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 (1)

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

1984 (1)

1982 (2)

1980 (2)

1979 (1)

1978 (1)

1977 (1)

1976 (1)

1966 (1)

1965 (1)

Ameer, G.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Barclay, H.

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

Barrett, T.

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

Baxter, B.

Boeke, B.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Boyer, C.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Brase, J.

S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

Browne, S.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Dunn, R.

R. 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]

Fletcher, J.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

Fontanella, J.

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

Fontanella, J. C.

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, 243–250 (1990).
[CrossRef]

Fried, D.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

D. Fried, “Anisoplanatism in adaptive optics,”J. Opt. Soc. Am. 72, 52–61 (1982).
[CrossRef]

G. Tyler, D. Fried, “Image-position error associated with a quadrant detector,”J. Opt. Soc. Am. 72, 804–808 (1982).
[CrossRef]

D. Greenwood, D. Fried, “Power spectra requirements for wave-front-compensative systems,”J. Opt. Soc. Am. 66, 193–206 (1976).
[CrossRef]

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

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

D. Fried, “Analysis of focus anisoplanatism: the fundamental limit in performance of artificial guide star adaptive optics system,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 37–80.

Frost, R.

Fugate, R.

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Gaffard, J.

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

Gaffard, J.-P.

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, 243–250 (1990).
[CrossRef]

Gardner, C.

B. Welsh, C. 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]

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

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

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

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

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

Gavel, D.

S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

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. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Goodman, J.

J. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8, p. 407.

Graves, J.

J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.

Greenwood, D.

Grundmann, W.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

Herrmann, J.

Hubin, N.

F. Merkel, N. Hubin, “Adaptive optics for the European Very Large Telescope,”ESO Tech. Preprint 32 (European Southern Observatory, Garching, Germany, 1991).

Jagourel, P.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Kane, T.

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

Kern, P.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Lena, P.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Max, C.

S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

McClure, R.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

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

McKenna, D.

J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.

Merkel, F.

F. Merkel, N. Hubin, “Adaptive optics for the European Very Large Telescope,”ESO Tech. Preprint 32 (European Southern Observatory, Garching, Germany, 1991).

Merkle, F.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Murphy, D.

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

Noll, R.

Northcott, M.

J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.

Olivier, S.

S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

Page, D.

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

Palmer, D.

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

Primmerman, C.

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

Racine, R.

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

Rambold, W.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

Richardson, E.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

Rigaut, F.

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

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, 243–250 (1990).
[CrossRef]

Roberts, P.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Roddier, F.

J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.

Rousset, G.

G. Rousset, J. Fontanella, P. Kern, P. Gigan, P. Lena, C. Boyer, P. Jagourel, J. 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, 243–250 (1990).
[CrossRef]

Ruane, R.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Rushforth, C.

Sandler, D.

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

D. Sandler, ThermoTrex Corporation, 9550 Distribution Avenue, San Diego, Calif. 92121–2306 (personal communication, 1992).

Sasiela, R.

R. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” (MIT Lincoln Laboratory, Lexington, Mass., 1988).

Southwell, W.

Stilburn, J.

R. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

Tatarski, V.

V. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 3, p. 58.

Thompson, L.

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

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

Tyler, G.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

G. Tyler, “Turbulence-induced adaptive-optics performance degradation: evaluation in the time domain,” J. Opt. Soc. Am. A 1, 251–262 (1984).
[CrossRef]

G. Tyler, D. Fried, “Image-position error associated with a quadrant detector,”J. Opt. Soc. Am. 72, 804–808 (1982).
[CrossRef]

G. Tyler, “Summary of theoretical performance and limitations of laser guide star adaptive optics for astronomical applications,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 405–440.

Vernon, R.

R. Vernon (while working for United Technologies Optical Systems, East Hartford, Conn.), Science Applications International Corporation, Palm Beach Gardens, Fla. 33410 (personal communication, 1991).

Welsh, B.

Wild, W.

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

Wopat, L.

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

Zollars, B.

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

Appl. Opt. (3)

Astron. Astrophys. (2)

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

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

J. Opt. Soc. Am. (9)

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

Nature (London) (4)

D. Sandler, T. Barrett, D. Palmer, R. Fugate, W. Wild, “Use of a neural network to control an adaptive optics system for an astronomical telescope,” Nature (London) 351, 300–302 (1991).
[CrossRef]

R. Fugate, D. Fried, G. Ameer, B. Boeke, S. Browne, P. Roberts, R. Ruane, G. Tyler, L. Wopat, “Measurement of atmospheric wavefront distortion using scattered light from a laser guide star,” Nature (London) 353, 144–148 (1991).
[CrossRef]

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

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

Proc. IEEE (1)

C. Gardner, B. Welsh, L. 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. McClure, W. Grundmann, W. Rambold, J. Fletcher, E. Richardson, J. Stilburn, “An image-stabilization, high-resolution camera for the Canada–France–Hawaii Telescope,” Publ. Astron. Soc. Pac. 101, 1156–1165 (1989).
[CrossRef]

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

Other (13)

R. 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]

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, 243–250 (1990).
[CrossRef]

F. Merkel, N. Hubin, “Adaptive optics for the European Very Large Telescope,”ESO Tech. Preprint 32 (European Southern Observatory, Garching, Germany, 1991).

J. Graves, D. McKenna, M. Northcott, F. Roddier, “The UH prototype adaptive optics system,” in Adaptive Optics for Large Telescopes, Vol. 19 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), 173–175.

J. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8, p. 407.

V. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961), Chap. 3, p. 58.

D. Sandler, ThermoTrex Corporation, 9550 Distribution Avenue, San Diego, Calif. 92121–2306 (personal communication, 1992).

R. Vernon (while working for United Technologies Optical Systems, East Hartford, Conn.), Science Applications International Corporation, Palm Beach Gardens, Fla. 33410 (personal communication, 1991).

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

D. Fried, “Analysis of focus anisoplanatism: the fundamental limit in performance of artificial guide star adaptive optics system,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 37–80.

R. Sasiela, “A unified approach to electromagnetic wave propagation in turbulence and the evaluation of multiparameter integrals,” (MIT Lincoln Laboratory, Lexington, Mass., 1988).

G. Tyler, “Summary of theoretical performance and limitations of laser guide star adaptive optics for astronomical applications,” in Laser Guide Star Adaptive Optics Workshop Proceedings, R. Q. Fugate, ed. (Phillips Laboratory, Albuquerque, N.M., 1992), pp. 405–440.

S. Olivier, D. Gavel, C. Max, J. Brase, “Resolution limits for ground based astronomical imaging using adaptive optics,” (Lawrence Livermore National Laboratory, Livermore, Calif., 1992).

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Figures (9)

Fig. 1
Fig. 1

Sodium response as a function of laser pulse fluence for the LLNL copper-vapor-pumped dye laser. Stretching the nominally 32-ns FWHM pulse by a factor of 64 brings the fluence essentially back into the linear regime. 2.5 μJ/cm2/unstretched pulse corresponds to 650-W average power irradiating a 1 = m2 spot. A 16× pulse stretcher is currently under construction at LLNL.

Fig. 2
Fig. 2

Number of guide stars necessary at a 10-m telescope for reduction of the cone-effect wave-front variance to less than 1 rad2. The Hufnagel–Valley turbulence model is used, with r0 = 15 cm at λ = 0.5 μm. The curves are for a, θ0 = 7 μrad; b, θ0 = 10 μrad; and c, θ0 = 15 μrad.

Fig. 3
Fig. 3

Optimum subaperture size as a function of laser power for the Keck system. The dashed curve indicates the analytic solution under assumptions 1–4 (see Subsection 4.B); the solid curve indicates the numerical optimization of the full error model.

Fig. 4
Fig. 4

Optimum wave-front sampling rate as a function of laser power for the Keck system. Dashed curve, the analytic solution; solid curve, the numerical solution.

Fig. 5
Fig. 5

Optimum laser power per spot that is necessary for achievement of a given Strehl ratio with a minimum of total laser power. Below 1 μm the optimum number of guide stars is fixed at 12. With the number of guide stars fixed, the cone effect dominates the wave-front error at shorter wavelengths, forcing other contributors toward 0, and laser power to infinity, to achieve a given Strehl ratio.

Fig. 6
Fig. 6

Optimum number of guide stars that is necessary for achievement of a given Strehl ratio with a minimum of total laser power, corresponding to the optimum laser power per spot shown in Fig. 5.

Fig. 7
Fig. 7

Strehl ratio versus wavelength for laser-guided adaptive-optics systems at the Keck telescope. The laser power is 20 W/spot. The 69-subaperture system has d = 1.1 m, fc = 50 Hz, and the 241-subaperture system has d = 58.8 cm, fc = 70 Hz. The other parameters are given in Table 1. Dashed curve, the analytic solution; solid curve, the numerical solution; subaps., subapertures.

Fig. 8
Fig. 8

Strehl ratio versus wavelength for laser-guided adaptive-optics sytems at the Lick 3-m telescope and at the LLNL 0.5-m telescope. The laser power in the Lick design is 40 W/spot, with d = 33 cm and fc = 60 Hz for the 69-subaperture system and d = 17.6 cm and fc = 50 Hz for the 241-subaperture system. The LLNL experiment uses 1000 W, with d = 10 cm and fc = 55 Hz. Dashed curve, the analytic solution; solid curve, the numerical solution.

Fig. 9
Fig. 9

Sample error budget for the Keck laser-guide-star system at λ = 1.5 μm, D = 10 m. The upper portion shows the higher-order wave-front contribution. The lower portion shows the tip–tilt system contribution. DM, deformable mirror.

Tables (3)

Tables Icon

Table 1 Parameters for the Keck Telescope

Tables Icon

Table 2 Parameters for the Telescope at Lick Observatory

Tables Icon

Table 3 Parameters for the LLNL Telescope

Equations (43)

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S = 4 π D 2 0 D d α K ( α ) exp [ - 1 / 2 D ( α ) ] ,
K ( α ) = 2 π { cos - 1 ( α D ) = α D [ 1 - ( α D ) 2 ] 1 / 2 }
D ( r 1 - r 2 ) = [ ϕ ( r 1 ) - ϕ ( r 2 ) ] 2 ,
D ( α ) = 6.88 ( α / r 0 ) 5 / 3 ,
r 0 = [ 0.422 ( 2 π / λ ) 2 sec ( ψ ) 0 d h C N 2 ( h ) ] - 3 / 5 ,
f g = [ 0.102 ( 2 π / λ ) 2 sec ( ψ ) 0 d h C N 2 ( h ) v 5 / 3 ( h ) ] 3 / 5 .
σ dm 2 = μ ( d r 0 ) 5 / 3 ,
σ servo 2 = κ ( f g f c ) 5 / 3 ,
σ SNR = 2 π 2 [ ( 3 / 16 ) 2 + ( n / 8 ) 2 ] 1 / 2 SNR ( λ gs λ ) ,
n = ( d b L ) ( λ gs d ) ,
d b = 1.27 L { [ λ gs r 0 ( λ gs ) ] 2 + ( λ gs d p ) 2 } 1 / 2 ,
SNR = N [ N + n pix ( σ r 2 + σ bg 2 ) ] 1 / 2 ,
N = ϕ ( π d 2 4 ) ( 1 f s ) η T o S subap ,
S subap = exp [ - 0.134 sec ( ψ ) ( d / r 0 ) 5 / 3 ] .
ϕ = T a ν l sec ( ψ ) 4 π L 2 R At [ I ( r , t ) ] ρ Na d r ,
R At [ I ( x , t ) ] = I ( x , t ) σ Na h ν = P σ T a h ν ν l A b ,
σ meas 2 = σ SNR 2 ( π f c f s ) + σ uncom 2 ,
θ 0 = [ 2.905 ( 2 π / λ ) 2 sec ( ψ ) 8 / 3 0 d h C N 2 ( h ) h 5 / 3 ] - 3 / 5 .
σ sep 2 = ( θ θ 0 ) 5 / 3 ,
σ cone 2 = 0.5 D 5 / 3 ( 2 π / λ ) 2 [ μ 5 / 3 ( L ) L 5 / 3 - 0.877 μ 2 ( L ) L 2 + 0.940 μ 3 ( L ) L 3 - 2.014 μ 4 ( L ) L 4 + 1.204 μ 5 ( L ) L 5 - 0.322 μ 6 ( L ) L 6 ] ,
μ n ( L ) = sec n + 1 ( ψ ) 0 L C N 2 ( z ) z n d z .
σ es 2 = ( 0.1014 d b L θ 0 ) 5 / 3 ,
σ wf 2 = σ servo 2 + σ dm 2 + [ σ meas 2 + σ sep 2 + ( σ cone 2 or σ es 2 ) ] ,
S exp ( - σ wf 2 ) ,
n gs = [ π 2 Ξ D 5 / 6 σ cone λ ] 12 / 5 ,
r ¯ 0 = [ 0.422 ( 2 π / λ ¯ ) 2 0 d h C N 2 ( h ) ] - 3 / 5 ,
f ¯ g = [ 0.102 ( 2 π / λ ¯ ) 2 0 d h C N 2 ( h ) v 5 / 3 ( h ) ] - 3 / 5 ,
θ ¯ 0 = [ 2.905 ( 2 π / λ ¯ ) 2 0 d h C N 2 ( h ) h 5 / 3 ] - 3 / 5 ,
μ ¯ n = 0 L C N 2 ( h ) h n d h ,
σ dm 2 = μ sec ( ψ ) ( d r ¯ 0 ) 5 / 3 ( λ ¯ λ ) 2 ,
σ servo 2 = κ sec ( ψ ) ( f ¯ g β f s ) 5 / 3 ( λ ¯ λ ) 2 ,
σ meas 2 = 4 π 5 β [ ( 3 16 ) 2 + ( 1.27 d 8 d p ) 2 + [ 1.27 d sec ( ψ ) 3 / 5 8 r ¯ 0 ( λ g s / λ ¯ ) 6 / 5 ] 2 ] × [ 1 N + n pix ( σ r 2 + σ bf 2 ) N 2 ] ( λ gs λ ) 2 + σ ¯ uncom 2 ( λ ¯ λ ) 2 ,
N = [ P σ Na ρ Na T a 2 λ gs w d 2 η T o 16 H 2 sec ( ψ ) h c f s ] × exp [ - 0.134 sec ( ψ ) ( d / r ¯ 0 ) 5 / 3 ( λ g s / λ ¯ ) 2 ] ,
σ cone 2 = 0.5 n gs - 5 / 6 D 5 / 3 sec ( ψ ) ( 2 π λ ) 2 × [ μ ¯ 5 / 3 H 5 / 3 - 0.877 μ ¯ 2 H 2 + 0.940 μ ¯ 3 H 3 - 2.014 μ ¯ 4 H 4 + 1.20 μ ¯ 5 H 5 ] ,
d σ wf 2 = d σ dm 2 + d σ meas 2 = 0 , f c σ wf 2 = f c σ servo 2 + f c σ meas 2 = 0.
d * = ( 27 5 ) 3 / 14 π 15 / 14 h 3 / 14 c 3 / 1 κ 9 / 70 f ¯ g 3 / 14 λ gs 3 / 14 r ¯ 0 4 / 7 H 3 / 7 2 3 / 35 μ 12 / 35 λ ¯ 3 / 7 ( P ρ Na σ Na η T a 2 T o ) 3 / 14 , f c * = ( 5 27 ) 3 / 14 2 24 / 35 κ 33 / 70 f ¯ g 11 / 4 ( λ ¯ r ¯ 0 ) 3 / 7 ( P ρ Na σ Na η T 0 T a 2 ) 3 / 14 π 15 / 14 h 3 / 14 c 3 / 14 μ 9 / 35 λ gs 3 / 14 H 3 / 7 .
min d , f c , P s , n gs P t n g s P s             subject to             σ wf const . ,
δ σ wf 2 = ( σ dm 2 d + σ meas 2 d ) δ d + ( σ meas 2 f c + σ meas 2 f c ) δ f c + ( σ meas 2 P ) δ P + ( σ cone 2 n gs ) δ n gs
δ P t = P s δ n gs + n gs δ P s = 0.
P s σ meas 2 P s - n gs σ cone 2 n gs = 0.
σ wf 2 = σ dm 2 ( d ) = σ servo 2 ( f c ) + σ meas 2 ( d , f c , P s ) + σ cone 2 ( n gs ) .
P s * = sec ( ψ ) 14 / 5 ( 113 7 ) 14 / 5 3 1 / 5 π 5 h c κ 3 / 5 μ 6 / 5 f ¯ g H 2 λ gs λ ¯ 18 / 5 5 ( 2 16 / 5 ) η ρ Na σ Na T a 2 T o r ¯ 0 2 ( σ wf λ ) 28 / 5 , n gs * = sec ( ψ ) 6 / 5 ( 226 15 ) 16 / 5 π 12 / 5 D 2 Ξ 6 / 5 ( σ wf λ ) 12 / 5 .
P s * ( n gs ) = 3 1 / 5 7 14 / 5 π 5 h c μ 6 / 5 κ 3 / 5 H 2 f ¯ g λ gs λ ¯ 18 / 5 sec ( ψ ) 14 / 5 5 ( 2 2 / 5 ) [ σ wf 2 - σ cone 2 ( n gs , λ ) ] - 14 / 5 η ρ Na σ Na T a 2 T o r ¯ 0 2 λ 28 / 5

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