Abstract

Conventional theory of imaging through the atmosphere is based on two main assumptions: (1) atmospheric turbulence is assumed to follow a Kolmogorov spectrum and (2) the outer scale, Lo, is assumed to be much larger than any telescope. There are numerous reports in the literature, however, of image properties that are not consistent with this theory—for example, cores in star images and lack of expected image motion. In almost every case these reports are consistent with a smaller value of Lo. There is also evidence of smaller Lo from other, more direct sources such as balloonborne temperature probes and long-baseline interferometry. If Lo is smaller than previously thought, as is suggested here, many long-held ideas about imaging with ground-based telescopes will have to be modified. A much more favorable picture emerges, especially at near-infrared wavelengths. At these wavelengths, resolution in the range 0.03–0.1 arcsec should be routinely attainable with 4–10-m telescopes, even though seeing at visible wavelengths is only 1 arcsec. To attain such high levels of resolution, telescopes must be built to diffraction-limited standards rather than to the currently accepted standards, which fall well short of this limit. Recent images obtained at 2.2 μm with the 4-m Kitt Peak telescope show that very high resolution (0.1 arcsec) is attainable. The images also show that telescope aberrations prevent even higher resolution (0.05 arcsec). A further benefit of a smaller Lo is that the isoplanatic angle of the atmosphere at near-infrared wavelengths is likely to be much larger than previously thought. Thus much wider angular regions are available from which to select suitably bright stars for guiding and tracking. A small Lo also means that ground-based infrared laser beams may be focused to diffraction-limited accuracy on targets in space without necessarily having to use wave-front compensation.

© 1992 Optical Society of America

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References

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  1. R. E. Hufnagel, N. R. Stanley, “Modulation transfer function associated with image transmission through the atmosphere,”J. Opt. Soc. Am. 54, 52–61 (1964), Eqs. (7.2) and (7.6).
    [CrossRef]
  2. 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]
  3. R. F. Griffin, “On image structure, and the value and challenge of very large telescopes,” Observatory 93, 3–8 (1973).
  4. R. F. Griffin, “Giant telescopes, tiny images,” Sky Telescope 79, 469–470 (1990).
  5. A. B. Meinel, “Astronomical seeing and observatory site selection,” in Telescopes, G. P. Kuiper, B. M. Middlehurst, eds. (U. Chicago Press, Chicago, Ill., 1960).
  6. J. M. Beckers, J. T. Williams, “Performance of the MMT III: seeing experiments with the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 16–23 (1982).
    [CrossRef]
  7. N. J. Woolf, D. W. McCarthy, J. R. P. Angel, “Performance of the MMT VII: image shrinkage in sub-arc second seeing at the MMT and 2.3 meter telescopes,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 50–56 (1982).
    [CrossRef]
  8. T. S. McKechnie, “Light propagation through the atmosphere and the properties of images formed by large ground-based telescopes,” J. Opt. Soc. Am. A 8, 346–365 (1991).
    [CrossRef]
  9. C. E. Coulman, J. Vernin, Y. Coqueugniot, J. L. Caccia, “Outer scale of turbulence appropriate to modeling refractive-index structure profiles,” Appl. Opt. 27, 155–160 (1988).
    [CrossRef] [PubMed]
  10. C. E. Coulman, J. Vernin, “Significance of anistropy and the outer scale of turbulence for optical and radio seeing,” Appl. Opt. 30, 118–126 (1991).
    [CrossRef] [PubMed]
  11. J. L. Bufton, “Comparison of vertical profile turbulence structure with stellar observations,” Appl. Opt. 12, 1785–1793 (1973).
    [CrossRef] [PubMed]
  12. J. M. Mariotti, G. P. Di Benedetto, “Pathlength stability of synthetic aperture telescopes. The case of the 25 cm Cerga interferometer,” in Proceedings of International Astronomical Union Colloquium 79, M. H. Ulrich, K. Jaer, eds. (European Southern Observatory, Garching bei MiInchen, Germany, 1984), pp. 257–265.
  13. T. S. McKechnie, “Focusing infrared laser beams on targets in space without using adaptive optics,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 119–135 (1991).
    [CrossRef]
  14. T. S. McKechnie, “Diffraction limited imaging using large ground-based telescopes,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 164–178 (1990).
    [CrossRef]
  15. R. L. Ulich, “Performance of the multi-mirror telescope (MMT) V: pointing and tracking of the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 33–41 (1982).
    [CrossRef]
  16. R. L. Ulich, “Overview of acquisition, tracking, and pointing system technologies,” in Acquisition, Tracking, and Pointing II, J. E. Kimbrell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.887, 40–63 (1988).
    [CrossRef]
  17. R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).
  18. T. S. McKechnie, seminar presented at Air Force Weapons Laboratory, Albuquerque, N.M., September 1989. Attendees: D. W. McCarthy, Jr., K. Hege (Steward Observatory); G. Loos, B. Venet (U.S. Air Force); and R. Haddock (Lentec Corp.).
  19. D. W. McCarthy, B. Mcleod, D. J. Barlow, “Infrared array camera for interferometry with the cophased multiple-mirror telescope,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckenridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 496–507 (1990).
    [CrossRef]
  20. D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
    [CrossRef]
  21. J. C. Christou, “Infrared speckle imaging with application to binary stars,” Exp. Astron. 2, 22–56 (1991).
    [CrossRef]
  22. J. C. Christou, “Image quality, tip-tilt correction and shift-and-add infrared imaging,” Publ. Astron. Soc. Pac. 103, 1040–1048 (1991).
    [CrossRef]
  23. M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.
  24. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1970).
  25. D. Anderson, R. Crawford, “The MMT7 mirror: analysis of the rms difference specifications and their impact on fabrication and testing,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 332–340 (1988).
    [CrossRef]
  26. R. F. Griffin, The Observatories, Madingley Road, Cambridge CB3 OHA, England, UK (personal communication, 1989).
  27. R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369 (1980).
    [CrossRef]
  28. E. Wolf, Progress in Optics (North-Holland, Amsterdam, 1980), Vol. 19, Sec. 5.3, pp. 281–376.
  29. J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).
  30. J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
    [CrossRef]
  31. T. S. McKechnie, “Propagation of the spectral correlation function in a homogeneous medium,” J. Opt. Soc. Am. A 8, 339–345 (1991), Eqs. (26) and (28).
    [CrossRef]
  32. R. Crawford, D. Anderson, “Polishing and aspherizing a 1.8-meter F/2.7 paraboloid,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 322–331 (1988).
    [CrossRef]
  33. Beckers and Williams6do not actually use the word “core.” Instead they refer to “elements” in the image “which remain stationary” in good seeing conditions. This description suggests a core formed by a telescope with less than diffraction-limited performance.
  34. R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).
  35. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Sec. 9.1.3, Eq. (22).

1991 (6)

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

C. E. Coulman, J. Vernin, “Significance of anistropy and the outer scale of turbulence for optical and radio seeing,” Appl. Opt. 30, 118–126 (1991).
[CrossRef] [PubMed]

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

J. C. Christou, “Infrared speckle imaging with application to binary stars,” Exp. Astron. 2, 22–56 (1991).
[CrossRef]

J. C. Christou, “Image quality, tip-tilt correction and shift-and-add infrared imaging,” Publ. Astron. Soc. Pac. 103, 1040–1048 (1991).
[CrossRef]

T. S. McKechnie, “Propagation of the spectral correlation function in a homogeneous medium,” J. Opt. Soc. Am. A 8, 339–345 (1991), Eqs. (26) and (28).
[CrossRef]

1990 (1)

R. F. Griffin, “Giant telescopes, tiny images,” Sky Telescope 79, 469–470 (1990).

1988 (1)

1986 (1)

J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
[CrossRef]

1980 (1)

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369 (1980).
[CrossRef]

1973 (2)

J. L. Bufton, “Comparison of vertical profile turbulence structure with stellar observations,” Appl. Opt. 12, 1785–1793 (1973).
[CrossRef] [PubMed]

R. F. Griffin, “On image structure, and the value and challenge of very large telescopes,” Observatory 93, 3–8 (1973).

1966 (1)

1964 (1)

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1970).

Anderson, D.

D. Anderson, R. Crawford, “The MMT7 mirror: analysis of the rms difference specifications and their impact on fabrication and testing,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 332–340 (1988).
[CrossRef]

R. Crawford, D. Anderson, “Polishing and aspherizing a 1.8-meter F/2.7 paraboloid,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 322–331 (1988).
[CrossRef]

Angel, J. R. P.

N. J. Woolf, D. W. McCarthy, J. R. P. Angel, “Performance of the MMT VII: image shrinkage in sub-arc second seeing at the MMT and 2.3 meter telescopes,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 50–56 (1982).
[CrossRef]

Barlow, D. J.

D. W. McCarthy, B. Mcleod, D. J. Barlow, “Infrared array camera for interferometry with the cophased multiple-mirror telescope,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckenridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 496–507 (1990).
[CrossRef]

Bates, R. H. T.

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369 (1980).
[CrossRef]

Beckers, J. M.

J. M. Beckers, J. T. Williams, “Performance of the MMT III: seeing experiments with the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 16–23 (1982).
[CrossRef]

Beland, R. R.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Sec. 9.1.3, Eq. (22).

Brown, J. H.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

Bufton, J. L.

Caccia, J. L.

Cady, F. M.

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369 (1980).
[CrossRef]

Carter, S. E.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Christou, J. C.

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

J. C. Christou, “Infrared speckle imaging with application to binary stars,” Exp. Astron. 2, 22–56 (1991).
[CrossRef]

J. C. Christou, “Image quality, tip-tilt correction and shift-and-add infrared imaging,” Publ. Astron. Soc. Pac. 103, 1040–1048 (1991).
[CrossRef]

J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
[CrossRef]

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

Coqueugniot, Y.

Coulman, C. E.

Crawford, R.

D. Anderson, R. Crawford, “The MMT7 mirror: analysis of the rms difference specifications and their impact on fabrication and testing,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 332–340 (1988).
[CrossRef]

R. Crawford, D. Anderson, “Polishing and aspherizing a 1.8-meter F/2.7 paraboloid,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 322–331 (1988).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).

Dewan, E. M.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

Di Benedetto, G. P.

J. M. Mariotti, G. P. Di Benedetto, “Pathlength stability of synthetic aperture telescopes. The case of the 25 cm Cerga interferometer,” in Proceedings of International Astronomical Union Colloquium 79, M. H. Ulrich, K. Jaer, eds. (European Southern Observatory, Garching bei MiInchen, Germany, 1984), pp. 257–265.

Freeman, J. D.

J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
[CrossRef]

Fried, D. L.

Good, R. E.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

Griffin, R. F.

R. F. Griffin, “Giant telescopes, tiny images,” Sky Telescope 79, 469–470 (1990).

R. F. Griffin, “On image structure, and the value and challenge of very large telescopes,” Observatory 93, 3–8 (1973).

R. F. Griffin, The Observatories, Madingley Road, Cambridge CB3 OHA, England, UK (personal communication, 1989).

Haas, M.

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

Hege, E. K.

J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
[CrossRef]

Henry, T. J.

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

Hufnagel, R. E.

Lanier, T. V.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Leinert, Ch.

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

Mariotti, J. M.

J. M. Mariotti, G. P. Di Benedetto, “Pathlength stability of synthetic aperture telescopes. The case of the 25 cm Cerga interferometer,” in Proceedings of International Astronomical Union Colloquium 79, M. H. Ulrich, K. Jaer, eds. (European Southern Observatory, Garching bei MiInchen, Germany, 1984), pp. 257–265.

McCarthy, D. W.

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

D. W. McCarthy, B. Mcleod, D. J. Barlow, “Infrared array camera for interferometry with the cophased multiple-mirror telescope,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckenridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 496–507 (1990).
[CrossRef]

N. J. Woolf, D. W. McCarthy, J. R. P. Angel, “Performance of the MMT VII: image shrinkage in sub-arc second seeing at the MMT and 2.3 meter telescopes,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 50–56 (1982).
[CrossRef]

McKechnie, T. S.

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

T. S. McKechnie, “Propagation of the spectral correlation function in a homogeneous medium,” J. Opt. Soc. Am. A 8, 339–345 (1991), Eqs. (26) and (28).
[CrossRef]

T. S. McKechnie, seminar presented at Air Force Weapons Laboratory, Albuquerque, N.M., September 1989. Attendees: D. W. McCarthy, Jr., K. Hege (Steward Observatory); G. Loos, B. Venet (U.S. Air Force); and R. Haddock (Lentec Corp.).

T. S. McKechnie, “Focusing infrared laser beams on targets in space without using adaptive optics,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 119–135 (1991).
[CrossRef]

T. S. McKechnie, “Diffraction limited imaging using large ground-based telescopes,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 164–178 (1990).
[CrossRef]

McLeod, B.

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

D. W. McCarthy, B. Mcleod, D. J. Barlow, “Infrared array camera for interferometry with the cophased multiple-mirror telescope,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckenridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 496–507 (1990).
[CrossRef]

Meinel, A. B.

A. B. Meinel, “Astronomical seeing and observatory site selection,” in Telescopes, G. P. Kuiper, B. M. Middlehurst, eds. (U. Chicago Press, Chicago, Ill., 1960).

Murphy, E. A.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

Ninneman, R. R.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Olives, M. L.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Reamy, P. C.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Ribak, E.

J. C. Christou, E. K. Hege, J. D. Freeman, E. Ribak, “Self-calibrating shift-and-add technique for speckle imaging,”J. Opt. Soc. Am. 3, 204–209 (1986).
[CrossRef]

Ridgway, S. T.

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

Stanley, N. R.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1970).

Sydney, P. F.

R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

Ulich, R. L.

R. L. Ulich, “Performance of the multi-mirror telescope (MMT) V: pointing and tracking of the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 33–41 (1982).
[CrossRef]

R. L. Ulich, “Overview of acquisition, tracking, and pointing system technologies,” in Acquisition, Tracking, and Pointing II, J. E. Kimbrell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.887, 40–63 (1988).
[CrossRef]

Vernin, J.

Williams, J. T.

J. M. Beckers, J. T. Williams, “Performance of the MMT III: seeing experiments with the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 16–23 (1982).
[CrossRef]

Wolf, E.

E. Wolf, Progress in Optics (North-Holland, Amsterdam, 1980), Vol. 19, Sec. 5.3, pp. 281–376.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Sec. 9.1.3, Eq. (22).

Woolf, N. J.

N. J. Woolf, D. W. McCarthy, J. R. P. Angel, “Performance of the MMT VII: image shrinkage in sub-arc second seeing at the MMT and 2.3 meter telescopes,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 50–56 (1982).
[CrossRef]

Zinnecker, H.

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

Appl. Opt. (3)

Astron. J. (1)

D. W. McCarthy, T. J. Henry, B. McLeod, J. C. Christou, “The low-mass companion of Gliese 22A: first results of the Steward Observatory infrared speckle camera,” Astron. J. 101, 214–219 (1991).
[CrossRef]

Exp. Astron. (1)

J. C. Christou, “Infrared speckle imaging with application to binary stars,” Exp. Astron. 2, 22–56 (1991).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Observatory (1)

R. F. Griffin, “On image structure, and the value and challenge of very large telescopes,” Observatory 93, 3–8 (1973).

Opt. Commun. (1)

R. H. T. Bates, F. M. Cady, “Towards true imaging by wideband speckle interferometry,” Opt. Commun. 32, 365–369 (1980).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

J. C. Christou, “Image quality, tip-tilt correction and shift-and-add infrared imaging,” Publ. Astron. Soc. Pac. 103, 1040–1048 (1991).
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Sky Telescope (1)

R. F. Griffin, “Giant telescopes, tiny images,” Sky Telescope 79, 469–470 (1990).

Other (21)

A. B. Meinel, “Astronomical seeing and observatory site selection,” in Telescopes, G. P. Kuiper, B. M. Middlehurst, eds. (U. Chicago Press, Chicago, Ill., 1960).

J. M. Beckers, J. T. Williams, “Performance of the MMT III: seeing experiments with the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 16–23 (1982).
[CrossRef]

N. J. Woolf, D. W. McCarthy, J. R. P. Angel, “Performance of the MMT VII: image shrinkage in sub-arc second seeing at the MMT and 2.3 meter telescopes,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 50–56 (1982).
[CrossRef]

M. Haas, J. C. Christou, H. Zinnecker, S. T. Ridgway, Ch. Leinert, “Z. C. Ma, a binary star,” submitted to Astron. Astrophys.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (U.S. Government Printing Office, Washington, D.C., 1970).

D. Anderson, R. Crawford, “The MMT7 mirror: analysis of the rms difference specifications and their impact on fabrication and testing,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 332–340 (1988).
[CrossRef]

R. F. Griffin, The Observatories, Madingley Road, Cambridge CB3 OHA, England, UK (personal communication, 1989).

J. M. Mariotti, G. P. Di Benedetto, “Pathlength stability of synthetic aperture telescopes. The case of the 25 cm Cerga interferometer,” in Proceedings of International Astronomical Union Colloquium 79, M. H. Ulrich, K. Jaer, eds. (European Southern Observatory, Garching bei MiInchen, Germany, 1984), pp. 257–265.

T. S. McKechnie, “Focusing infrared laser beams on targets in space without using adaptive optics,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, P. B. Ulrich, L. E. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1408, 119–135 (1991).
[CrossRef]

T. S. McKechnie, “Diffraction limited imaging using large ground-based telescopes,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1236, 164–178 (1990).
[CrossRef]

R. L. Ulich, “Performance of the multi-mirror telescope (MMT) V: pointing and tracking of the MMT,” in Advanced Technology Optical Telescopes, L. D. Barr, G. Burbridge, eds., Proc. Soc. Photo-Opt. Instrum. Eng.332, 33–41 (1982).
[CrossRef]

R. L. Ulich, “Overview of acquisition, tracking, and pointing system technologies,” in Acquisition, Tracking, and Pointing II, J. E. Kimbrell, ed., Proc. Soc. Photo-Opt. Instrum. Eng.887, 40–63 (1988).
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R. R. Ninneman, P. F. Sydney, P. C. Reamy, T. V. Lanier, S. E. Carter, M. L. Olives, Ambient Vibration Test Results of Proposed RME LSS Site at the Air Force Maui Optical Station (AMOS), engineering rep. (Air Force Weapons Laboratory, Kirtland AFB, N.M., December1987).

T. S. McKechnie, seminar presented at Air Force Weapons Laboratory, Albuquerque, N.M., September 1989. Attendees: D. W. McCarthy, Jr., K. Hege (Steward Observatory); G. Loos, B. Venet (U.S. Air Force); and R. Haddock (Lentec Corp.).

D. W. McCarthy, B. Mcleod, D. J. Barlow, “Infrared array camera for interferometry with the cophased multiple-mirror telescope,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckenridge, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1237, 496–507 (1990).
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E. Wolf, Progress in Optics (North-Holland, Amsterdam, 1980), Vol. 19, Sec. 5.3, pp. 281–376.

J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1984).

R. Crawford, D. Anderson, “Polishing and aspherizing a 1.8-meter F/2.7 paraboloid,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. Soc. Photo-Opt. Instrum. Eng.966, 322–331 (1988).
[CrossRef]

Beckers and Williams6do not actually use the word “core.” Instead they refer to “elements” in the image “which remain stationary” in good seeing conditions. This description suggests a core formed by a telescope with less than diffraction-limited performance.

R. E. Good, R. R. Beland, E. A. Murphy, J. H. Brown, E. M. Dewan, “Atmospheric models of optical turbulence,” in Modeling of the Atmosphere (Critical Reviews), L. S. Rothman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.928, 165–186 (1981).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Sec. 9.1.3, Eq. (22).

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Figures (16)

Fig. 1
Fig. 1

For the atmospheric MTF, the atmosphere can be represented exactly by an equivalent phase screen defined by Eq. (1). The equivalent wave at any given instant has three mean levels associated with it. When Lo is small and the telescope is large, the three mean levels converge to the absolute mean level. The rms waveheight variations associated with the three levels also converge: σsσlσ. For Lo ~ 20–40 cm and telescopes larger than 2 m, the short-exposure image centroid is, for all practical purposes, the same as the long-exposure centroid.

Fig. 2
Fig. 2

Detectability of the core for a diffraction-limited telescope in 1-arcsec visible seeing (σ = 0.3 μm, ωo = 0.25 m). Core detectability [Eq. (16)] increases as λ and D increase. With large telescopes and infrared wavelengths, cores dominate the center of the image.

Fig. 3
Fig. 3

Predicted PSF’s for a diffraction-limited 4-m ground-based telescope in 1-arcsec visible seeing conditions (σ = 0.3 μm, ωo = 0.25 m). At infrared wavelengths, core and halo structure is evident, and diffraction-limited resolution is attainable because of the presence of the core. At 2.2 μm, 0.1-arcsec resolution is possible. At visible wavelengths in these seeing conditions, negligible energy resides in the core. Because the volumes (total light energy) under all curves are identical, the curve widths give directly comparable measures of resolution at the different wavelengths. Strehl intensities are given by multiplying the number on the left-hand scale by (λ/0.55)2.

Fig. 4
Fig. 4

Predicted PSF’s for a diffraction-limited 8-m ground-based telescope in 1-arcsec visible seeing conditions (σ = 0.3 μm, ωo = 0.25 m). At infrared wavelengths, diffraction-limited resolution is attainable because of the presence of the core. At 2.2 μm, 0.05-arcsec resolution is possible. At 1.1 μm, 0.03-arcsec resolution is possible. At visible wavelengths in these seeing conditions, negligible energy resides in the core. Because the volumes (total light energy) under all curves are identical, the curve widths give directly comparable measures of resolution at the different wavelengths. Strehl intensities are given by multiplying the number on the left-hand scale by (λ/0.55)2.

Fig. 5
Fig. 5

Images showing the star Zeta Ophiuchi, obtained at 2.2 μm with the 4-m Kitt Peak telescope: A, with image motion removed by using shift-and-add with respect to the core; B, with image motion removed by using shift-and-add with respect to the centroid of light energy; C, with image motion not removed—i.e., a standard long-exposure image. The core structure seen in A is the PSF inherently associated with the telescope. The disproportionately bright rings and lobes indicate significant telescope aberrations. The central diffraction-limited feature is ~0.1 arcsec across (FWHM). Visible seeing was approximately 1–1.5 arcsec. Photographs by courtesy of J. Christou (NOAO).

Fig. 6
Fig. 6

Images showing the 0.48-arcsec binary star Eta Ophiuchi, obtained at 2.2 μm with the 4-m Kitt Peak telescope: A, with image motion removed by using shift-and-add with respect to the core; B, with image motion removed using shift-and-add with respect to the centroid of light energy; C, with image motion not removed—i.e., a standard long-exposure image. Image A is simply the convolution of the image shown in Fig. 5A with two delta functions separated by 0.48 arcsec [Eq. (30)]. The binary pair are easily resolved in spite of their close separation. In C the cores appear to be smeared in the direction 7 o’clock to 1 o’clock, possibly indicating a progressive telescope drive error or perhaps a preferred telescope vibration direction. Visible seeing was approximately 1–1.5 arcsec. Photographs by courtesy of J. Christou (NOAO).

Fig. 7
Fig. 7

Star images obtained at 3.4 μm with the 4-m Kitt Peak telescope, based on a sequence of 500 short-exposure frames. Images obtained: A, after the 10th frame; B, after the 250th frame; C, after the 500th frame. In all three images: top left, instantaneous short-exposure image; bottom left, sum of all previous frames with shift-and-add to the light-energy centroid; bottom right, sum of all previous frames with shift-and-add to the core; top right, direct sum of all previous images—i.e., the standard long-exposure image. The core, which contains approximately 75% of the light energy, is clearly depicted even in the individual short-exposure images. The severe coma is possibly due to misalignment of the secondary mirror. Photographs by courtesy of J. Christou (NOAO).

Fig. 8
Fig. 8

Effect of aberrations on star images at 2.2 μm for a telescope similar to the 4-m telescope at Kitt Peak. Seeing at 0.5 μm is assumed to be 1 arcsec (σ = 0.3125 μm, ωo = 0.25 m). The aberrations were generated by introducing appropriate amounts of spherical aberration and then choosing best focus [Eq. (13)]. The residual P-V wave-front aberrations are as indicated. The volumes under all curves are identical. The Strehl intensities for the 2.2-μm images can be read from the vertical scale. However, the number given for the 0.5-μm image must be multiplied by (0.5/2.2)2 because of the wavelength change. The blurring effect of the pixels has not been included. The 0.058-arcsec pixel interval used by Christou would reduce the core brightness levels shown by 0.63×.

Fig. 9
Fig. 9

Resolution of large diffraction-limited telescopes in 1-arcsec visible seeing conditions (σ = 0.3 μm, ωo = 0.25 m). At infrared wavelengths where σ/λ is small (<0.3), the presence of the core means that resolution is limited only by telescope aperture.

Fig. 10
Fig. 10

The core and the centroid of light energy exhibit different amounts of motion. In both cases, motions reduce with telescope diameter D, but the core is always the more stable of the two entities. At infrared wavelengths, tracking should be carried out by using the core, rather than the light energy centroid, as reference.

Fig. 11
Fig. 11

Image stabilization with a servo-driven tip/tilt mirror. The quadrant detector locks on to the core of the reference object. At near-infrared wavlengths, long-exposure images with diffraction-limited resolution can be obtained directly with this arrangement.

Fig. 12
Fig. 12

In the absence of suitable reference stars or glints, tracking can be carried out by using two edges lying approximately at right angles to each other. The plots show the edge-spread function for a 4-m diffraction-limited telescope in 1-arcsec visible seeing conditions (σ = 0.3 μm, σo = 0.25 m). At near-infrared wavelengths, this function changes abruptly in the vicinity of the edge (x = 0), thereby permitting diffraction-limited location of the edge.

Fig. 13
Fig. 13

The isoplanatic angle in 1-arcsecond visible seeing conditions (σ = 0.3 μm, ωo = 0.25 m). Although the isoplanatic angle is only a few arcsec at visible wavelengths, at infrared wavelengths the presence of the core—an extremely stable feature—increases the isoplanatic angle to many arcmin (and perhaps even larger angles).

Fig. 14
Fig. 14

Variation of the turbulence outer-scale limit, Lo, with altitude as measured by Coulman et al. The plot is based on data measured in France, the United States, and Chile. Because most of the atmospheric turbulence lies in the first 4 or 5 km (see Fig. 15), the effective Lo for the entire atmosphere is only approximately 30–40 cm (see Fig. 16).

Fig. 15
Fig. 15

Typical variation of the atmospheric refractive-index-structure constants Cn2(z) with altitude. The plot is based on the SLC night model. Most of the turbulence strength is located in the first 4 or 5 km.

Fig. 16
Fig. 16

Average turbulence size in the atmosphere described by the autocorrelation function ρ(ω). The width of this function is a measure of Lo. Measurements of ρ(ω) by the author at the RGO and by Coulman et al. indicate small Lo values (20–40 cm). These measurements contradict the conventional assumption that Lo is large. They are clearly inconsistent with the function shown for the 5-m Lo value—a conservative Lo estimate, according to conventional wisdom.

Tables (2)

Tables Icon

Table 1 Telescope Strehl Intensity P(0; λ) Caused by Various Amounts of Telescope Aberration for a Range of Wavelengths (0.5–5.0 μm)a

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Table 2 Fraction of Light Energy in the Core, exp(−4π2σ2/λ2), for a Number of Wavelengths over a Range of visible Seeing Conditions between 0.0 arcsec (Perfect Seeing) and 2.5 arcsec (Poor Seeing)a

Equations (50)

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H ( x ) = i = 1 n h i ( x ) .
σ 2 = H ( x ) 2 ,
ρ ( ω ) = H ( x + ω ) H ( x ) H ( x ) 2 ,
σ s σ l σ .
σ s = σ l = σ .
T ( ω ; λ ) = exp { - 4 π 2 σ 2 λ 2 [ 1 - ρ ( ω ) ] } .
ρ ( ω ) = exp ( - ω 2 ω o 2 ) .
I ( α ; λ ) = 2 π 0 D T ( ω ; λ ) T t ( ω ; λ ) J 0 ( 2 π α ω λ ) ω d ω ,
T t ( ω ; λ ) = 2 π cos - 1 ( ω D ) - 2 ω π D ( 1 - ω 2 D 2 ) 1 / 2 .
I ( α ; λ ) = 8 λ o 2 D 2 λ 2 0 D exp { - 4 π 2 σ 2 λ 2 [ 1 - exp ( - ω 2 ω o 2 ) ] } × [ 2 π cos - 1 ( ω D ) - 2 ω π D ( 1 - ω 2 D 2 ) 1 / 2 ] × J 0 ( 2 π α ω λ ) ω d ω .
I ( α ; λ ) = λ o 2 λ 2 exp ( - 4 π 2 σ 2 λ 2 ) × [ P ( α ; λ ) + 4 ω o 2 ( D 2 - d 2 ) n = 1 ( 2 π σ / λ ) 2 n n n ! exp ( - π 2 ω o 2 α 2 n λ 2 ) ] ,
S ( λ ) = λ 2 λ o 2 I ( 0 ; λ ) .
P ( α ; λ ) = 64 ( D 2 - d 2 ) 2 × | d / 2 D / 2 exp ( 8 i π ω 2 U f λ D 2 + 32 i π ω 4 U s λ D 4 ) J 0 ( 2 π ω α λ ) ω d ω | 2 ,
U f = 1 8 F 2 Z ,
P ( α ; λ ) = 4 [ J 1 ( π D α / λ ) π D α / λ ] 2 ,
E = ( D 2 - d 2 ) P ( 0 ; λ ) 4 ω o 2 n = 1 ( 2 π σ / λ ) 2 n n n ! .
S ( λ ) exp ( - 4 π 2 σ 2 λ 2 ) P ( 0 ; λ ) ,
σ = σ o ( cos β ) 1 / 2 .
R h 4 σ ω o .
R c = λ D .
λ m = 2 π σ .
λ m = 2 π ( σ 2 + σ t 2 ) 1 / 2 .
λ = 4 π σ .
ϕ c = 8 σ ω o D 2 .
ϕ h = [ ( 8 σ ω o D 2 ) 2 + ( λ π D ) 2 ] 1 / 2 .
ϕ cen = [ ϕ c 2 ( I c 2 + 2 I c I h ) + ϕ h 2 I h 2 ] 1 / 2 ,
I c = exp ( - 4 π 2 σ 2 λ 2 ) ,
I h = 1 - exp ( - 4 π 2 σ 2 λ 2 ) .
i ( α ; λ ) = o ( α ; λ ) I ( α ; λ ) .
i ( α ; λ ) = ψ 1 I ( α - ξ / 2 ; l ) + ψ 2 I ( α + ξ / 2 ; λ ) ,
L ( x ) = - I ( x , y ; λ ) d y .
G ( x ) = 0 L ( x - x ) d x ,
C ( θ ; λ ) = exp { - 4 π 2 σ 2 λ 2 [ 1 - exp ( - θ 2 10 8 ω o 2 ) ] } ,
θ = ω 10 , 000 ,
L o ( z ) = 4 1 + ( z - 8500 2500 ) 2 ,
σ i 2 = h i ( x ) 2 ,
ρ i ( ω ) = h i ( x + ω ) h i ( x ) h i ( x ) 2 .
σ 2 = i = 1 n σ i 2 ,
ρ ( ω ) = 1 σ 2 i = 1 n σ i 2 ρ i ( ω ) .
ρ i ( ω ) = 1 - ( ω L o ( z i ) ) 5 / 3 , ω L o ( z i ) , = 0 , otherwise ,
ρ ( ω ) = 0 z o C n 2 ( z ) ρ ( ω , z ) d z 0 z o C n 2 ( z ) d z ,
σ i 2 z i - 1 z i C n ( z ) 2 d z ,
σ 2 0 z o C n ( z ) 2 d z .
C n 2 ( z ) = 8.40 × 10 - 15 for 0 z 18.5 m = 2.87 × 10 - 12 / z 2 for 18.5 z 110 m = 8.40 × 10 - 15 for 110 z 1500 m = 8.87 × 10 - 7 / z 3 for 1500 z 7200 m = 2.00 × 10 - 16 / z 1 / 2 for 7200 z 20 , 000 m .
A ( α ) = - W / 2 W / 2 exp { - i k [ H ( x ) - α x ] } d x - W / 2 W / 2 d x ,
A ( α ) = - W / 2 W / 2 d x - k 2 2 - W / 2 W / 2 [ H ( x ) - α x ] 2 d x - i k - W / 2 W / 2 [ H ( x ) - α x ] d x - W / 2 W / 2 d x ,
I ( α ) = 1 - k 2 { - W / 2 W / 2 [ H ( x ) - α x ] 2 d x - W / 2 W / 2 d x - [ - W / 2 W / 2 [ H ( x ) - α x ] 2 d x - W / 2 W / 2 d x ] } ,
α I ( α ) = 0.
α c = 12 W 3 - W / 2 W / 2 x H ( x ) d x .
ϕ c = σ W 3 / 2 ( 12 ω o π ) 1 / 2 .

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