Abstract

The longitudinal and transverse correlation functions for the fluctuations in the angle of arrival on the entrance pupil of a solar telescope have been estimated. The results are found to be consistent with the inertial model of turbulence. Values of the integral CN2dh of the structure constant over the lower atmospheric layers and of Fried’s seeing parameter r0 are deduced. They are found to be consistent with other independent estimations made with the same telescope.

© 1977 Optical Society of America

Full Article  |  PDF Article

Corrections

J. Borgnino and F. Martin, "Errata: Correlation between angle-of-arrival fluctuations in the entrance pupil of a solar telescope," J. Opt. Soc. Am. 68, 277_1-277 (1978)
https://www.osapublishing.org/josa/abstract.cfm?uri=josa-68-2-277_1

References

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).
  2. R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
    [Crossref]
  3. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [Crossref]
  4. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
    [Crossref]
  5. C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).
    [Crossref]
  6. J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
    [Crossref]
  7. J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
    [Crossref]
  8. R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
    [Crossref]
  9. R. F. Lutomirski and R. G. Buser, Appl. Opt. 13, 2869 (1974).
    [Crossref] [PubMed]
  10. D. L. Fried, Radio Sci. 10, 71 (1975).
    [Crossref]
  11. P. E. Barnhart, G. Keller, and W. E. Mitchell, Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).
  12. J. Vernin and F. Roddier, J. Soc. Am. 63, 270 (1973).
  13. A. Rocca, F. Roddier, and J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
    [Crossref]
  14. A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).
  15. A. Consortini, L. Ronchi, and L. Stefanuti, Appl. Opt. 9, 2543 (1970).
    [Crossref] [PubMed]
  16. D. A. Wolf, J. Opt. Soc. Am. 63, 657 (1973).
    [Crossref]
  17. A. Consortini, P. Pandolfini, and R. Vanni, in Proceedings of the Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, 1974.
  18. C. Roddier and F. Roddier, J. Opt. Soc. Am. 63, 661 (1973).
    [Crossref]
  19. J. C. Dainty, Opt. Commun. 7, 129 (1973).
    [Crossref]
  20. E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.
  21. R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.
  22. R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.
  23. D. P. Greenwood, in Program of the OSA, Topical Meeting on Imaging in Astronomy, 1974.
  24. C. E. Coulman, Solar Phys. 7, 122 (1969).
    [Crossref]
  25. C. E. Coulman, Solar Phys. 34, 491 (1974).
    [Crossref]
  26. C. E. Coulman, Boundary-Layer Meteorol. 4, 169 (1973).
    [Crossref]
  27. G. Ricort, Thesis (3rd cycle) Nice University, France, 1973 (unpublished).
  28. C. Aime, Thesis, Nice University, France, 1977 (unpublished).
  29. P. N. Brandt, Solar Phys. 7, 187 (1969).
    [Crossref]
  30. P. N. Brandt, Solar Phys. 13, 243 (1970).
    [Crossref]
  31. J. Borgnino and F. Martin, “Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 1st part; Description of the method—First results,” Journal of Optics, (in press, 1977) (in French).
    [Crossref]
  32. N. V. Bystrova and A. N. Demidova, Soln. Dannye 7, n° 3 (1973).
  33. R. E. Hufnagel, Proceedings of AGARD Conference, Ankara, 1967, in Phase and Frequency Instabilities in Electromagnetic Wave Propagation, edited by K. Davies (Technivision Services, Slough, England, 1970).
  34. A. Danjon, A. Couder, and Lunettes et Télescopes. Editions de la Revue d’Optique Théorique et Instrumental Paris (1935).
  35. P. Beckmann, Probability in Communication Engineering (Harcourt, Brace and World, New York, 1967).
  36. R. Fante, J. Opt. Soc. Am. 66, 730 (1976).
    [Crossref]
  37. M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.
  38. F. Martin and J. Borgnino, “Statistical analysis of wave-front random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimationbynumericalprocessing,” Journal of Optics, (in press, 1977) (in French).
  39. J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
    [Crossref]
  40. K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
    [Crossref]
  41. D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
    [Crossref]
  42. M. Aubry, Les sondages acoustiques de l’Atmosphere XVIII ième Assemblée Générale de L’U.R.S.I., Lima, 1975.
  43. J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
    [Crossref]
  44. J. W. Deadorff, Boundary-Layer Meteorol. 7, 199 (1974).
  45. C. Roddier, Thesis, Nice University, France, 1976 (unpublished).
  46. J. W. Goodman, Introduction à l’Optique de Fourier et à l’ Holographie (Masson, Paris, 1972).

1976 (2)

R. Fante, J. Opt. Soc. Am. 66, 730 (1976).
[Crossref]

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

1975 (2)

1974 (6)

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
[Crossref]

R. F. Lutomirski and R. G. Buser, Appl. Opt. 13, 2869 (1974).
[Crossref] [PubMed]

J. W. Deadorff, Boundary-Layer Meteorol. 7, 199 (1974).

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

D. P. Greenwood, in Program of the OSA, Topical Meeting on Imaging in Astronomy, 1974.

C. E. Coulman, Solar Phys. 34, 491 (1974).
[Crossref]

1973 (11)

C. E. Coulman, Boundary-Layer Meteorol. 4, 169 (1973).
[Crossref]

N. V. Bystrova and A. N. Demidova, Soln. Dannye 7, n° 3 (1973).

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
[Crossref]

D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
[Crossref]

D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
[Crossref]

J. Vernin and F. Roddier, J. Soc. Am. 63, 270 (1973).

D. A. Wolf, J. Opt. Soc. Am. 63, 657 (1973).
[Crossref]

C. Roddier and F. Roddier, J. Opt. Soc. Am. 63, 661 (1973).
[Crossref]

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

1972 (1)

E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.

1970 (4)

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[Crossref]

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[Crossref]

P. N. Brandt, Solar Phys. 13, 243 (1970).
[Crossref]

A. Consortini, L. Ronchi, and L. Stefanuti, Appl. Opt. 9, 2543 (1970).
[Crossref] [PubMed]

1969 (2)

C. E. Coulman, Solar Phys. 7, 122 (1969).
[Crossref]

P. N. Brandt, Solar Phys. 7, 187 (1969).
[Crossref]

1968 (1)

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).

1967 (1)

J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
[Crossref]

1966 (1)

1964 (1)

1935 (1)

A. Danjon, A. Couder, and Lunettes et Télescopes. Editions de la Revue d’Optique Théorique et Instrumental Paris (1935).

Aime, C.

C. Aime, Thesis, Nice University, France, 1977 (unpublished).

Andre, J. C.

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

Aubry, M.

M. Aubry, Les sondages acoustiques de l’Atmosphere XVIII ième Assemblée Générale de L’U.R.S.I., Lima, 1975.

Auvergne, M.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Barletti, R.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

Barnhart, P. E.

P. E. Barnhart, G. Keller, and W. E. Mitchell, Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).

Beckmann, P.

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace and World, New York, 1967).

Beran, D. W.

D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
[Crossref]

Bijaoui, A.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Borgnino, J.

F. Martin and J. Borgnino, “Statistical analysis of wave-front random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimationbynumericalprocessing,” Journal of Optics, (in press, 1977) (in French).

J. Borgnino and F. Martin, “Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 1st part; Description of the method—First results,” Journal of Optics, (in press, 1977) (in French).
[Crossref]

Brandt, P. N.

P. N. Brandt, Solar Phys. 13, 243 (1970).
[Crossref]

P. N. Brandt, Solar Phys. 7, 187 (1969).
[Crossref]

Browning, K. A.

K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
[Crossref]

Buser, R. G.

Bystrova, N. V.

N. V. Bystrova and A. N. Demidova, Soln. Dannye 7, n° 3 (1973).

Ceppatelli, G.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

Clifford, S. F.

D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
[Crossref]

J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
[Crossref]

Consortini, A.

A. Consortini, L. Ronchi, and L. Stefanuti, Appl. Opt. 9, 2543 (1970).
[Crossref] [PubMed]

A. Consortini, P. Pandolfini, and R. Vanni, in Proceedings of the Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, 1974.

Couder, A.

A. Danjon, A. Couder, and Lunettes et Télescopes. Editions de la Revue d’Optique Théorique et Instrumental Paris (1935).

Coulman, C. E.

C. E. Coulman, Solar Phys. 34, 491 (1974).
[Crossref]

C. E. Coulman, Boundary-Layer Meteorol. 4, 169 (1973).
[Crossref]

C. E. Coulman, Solar Phys. 7, 122 (1969).
[Crossref]

Dainty, J. C.

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

Danjon, A.

A. Danjon, A. Couder, and Lunettes et Télescopes. Editions de la Revue d’Optique Théorique et Instrumental Paris (1935).

De Moor, G.

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

Deadorff, J. W.

J. W. Deadorff, Boundary-Layer Meteorol. 7, 199 (1974).

Demidova, A. N.

N. V. Bystrova and A. N. Demidova, Soln. Dannye 7, n° 3 (1973).

Du Vachat, R.

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

Fante, R.

Fried, D. L.

Goodman, J. W.

J. W. Goodman, Introduction à l’Optique de Fourier et à l’ Holographie (Masson, Paris, 1972).

Greenwood, D. P.

D. P. Greenwood, in Program of the OSA, Topical Meeting on Imaging in Astronomy, 1974.

Gurvich, A. S.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).

Heudier, J. L.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Hooke, W. M.

D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
[Crossref]

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. Am. 54, 52 (1964).
[Crossref]

R. E. Hufnagel, Proceedings of AGARD Conference, Ankara, 1967, in Phase and Frequency Instabilities in Electromagnetic Wave Propagation, edited by K. Davies (Technivision Services, Slough, England, 1970).

Jensen, O. R.

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).

Keller, G.

P. E. Barnhart, G. Keller, and W. E. Mitchell, Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).

Korff, D.

Lacarrere, P.

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[Crossref]

Lutomirski, R. F.

Marchal, J.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Martin, F.

F. Martin and J. Borgnino, “Statistical analysis of wave-front random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimationbynumericalprocessing,” Journal of Optics, (in press, 1977) (in French).

J. Borgnino and F. Martin, “Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 1st part; Description of the method—First results,” Journal of Optics, (in press, 1977) (in French).
[Crossref]

Mitchell, W. E.

P. E. Barnhart, G. Keller, and W. E. Mitchell, Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).

Moroder, E.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.

Noonkester, V. R.

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

Ounas, C.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Pandolfini, P.

A. Consortini, P. Pandolfini, and R. Vanni, in Proceedings of the Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, 1974.

Paterno, L.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.

Postel, J.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Rappert, R. A.

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

Richter, J. H.

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

Ricort, G.

G. Ricort, Thesis (3rd cycle) Nice University, France, 1973 (unpublished).

Righini, A.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.

Rocca, A.

Roddier, C.

Roddier, F.

Ronchi, L.

Schneider, M.

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

Speroni, N.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

Stanley, N. R.

Starr, J. R.

K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
[Crossref]

Stefanuti, L.

Strohbehn, J. W.

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[Crossref]

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[Crossref]

J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
[Crossref]

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

Time, N. S.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).

Vanni, R.

A. Consortini, P. Pandolfini, and R. Vanni, in Proceedings of the Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, 1974.

Vernin, J.

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Soc. Am. 64, 1000 (1974).
[Crossref]

J. Vernin and F. Roddier, J. Soc. Am. 63, 270 (1973).

Whyman, A. J.

K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
[Crossref]

Wolf, D. A.

Annual Program of the Optical Society of America (3)

E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1972.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, in Annual Program of the Optical Society of America, 1973.

R. Barletti, G. Ceppatelli, L. Paterno, A. Righini, and N. Speroni, Annual Program of the Optical Society of America, 1974.

Appl. Opt. (2)

Boundary-Layer Meteorol. (5)

C. E. Coulman, Boundary-Layer Meteorol. 4, 169 (1973).
[Crossref]

J. H. Richter, O. R. Jensen, R. A. Rappert, and V. R. Noonkester, Boundary-Layer Meteorol. 4, 179 (1973).
[Crossref]

K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
[Crossref]

D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
[Crossref]

J. W. Deadorff, Boundary-Layer Meteorol. 7, 199 (1974).

Editions de la Revue d’Optique Théorique et Instrumental Paris (1)

A. Danjon, A. Couder, and Lunettes et Télescopes. Editions de la Revue d’Optique Théorique et Instrumental Paris (1935).

IEEE Trans. Antennas Propagat. (1)

J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
[Crossref]

J. Atm. Sci. (1)

J. C. Andre, G. De Moor, P. Lacarrere, and R. Du Vachat, J. Atm. Sci. 33, 482 (1976).
[Crossref]

J. Geophys. Res. (1)

J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
[Crossref]

J. Opt. Soc. Am. (8)

J. Soc. Am. (1)

J. Vernin and F. Roddier, J. Soc. Am. 63, 270 (1973).

Opt. Commun. (1)

J. C. Dainty, Opt. Commun. 7, 129 (1973).
[Crossref]

Proc. IEEE (1)

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
[Crossref]

Program of the OSA, Topical Meeting on Imaging in Astronomy (1)

D. P. Greenwood, in Program of the OSA, Topical Meeting on Imaging in Astronomy, 1974.

Radio Sci. (1)

D. L. Fried, Radio Sci. 10, 71 (1975).
[Crossref]

Radio-fizika (1)

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radio-fizika 11, 1360 (1968).

Solar Phys. (4)

C. E. Coulman, Solar Phys. 7, 122 (1969).
[Crossref]

C. E. Coulman, Solar Phys. 34, 491 (1974).
[Crossref]

P. N. Brandt, Solar Phys. 7, 187 (1969).
[Crossref]

P. N. Brandt, Solar Phys. 13, 243 (1970).
[Crossref]

Soln. Dannye 7, n° 3 (1)

N. V. Bystrova and A. N. Demidova, Soln. Dannye 7, n° 3 (1973).

Other (13)

R. E. Hufnagel, Proceedings of AGARD Conference, Ankara, 1967, in Phase and Frequency Instabilities in Electromagnetic Wave Propagation, edited by K. Davies (Technivision Services, Slough, England, 1970).

P. Beckmann, Probability in Communication Engineering (Harcourt, Brace and World, New York, 1967).

M. Aubry, Les sondages acoustiques de l’Atmosphere XVIII ième Assemblée Générale de L’U.R.S.I., Lima, 1975.

J. Borgnino and F. Martin, “Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 1st part; Description of the method—First results,” Journal of Optics, (in press, 1977) (in French).
[Crossref]

G. Ricort, Thesis (3rd cycle) Nice University, France, 1973 (unpublished).

C. Aime, Thesis, Nice University, France, 1977 (unpublished).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961).

A. Consortini, P. Pandolfini, and R. Vanni, in Proceedings of the Topical Meeting on Optical Propagation Through Turbulence, Boulder, Colorado, 1974.

P. E. Barnhart, G. Keller, and W. E. Mitchell, Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).

M. Auvergne, A. Bijaoui, J. L. Heudier, J. Marchal, C. Ounas, J. Postel, and M. Schneider, Le Centre de Dépouillement de Clichés Astronomiques, in Image Processing Techniques in Astronomy, Vol. 54, edited by C. de Jager and H. Nieuwenshuljzen, Proceedings of a Conference held in Utrecht on March 25–27, 1975.

F. Martin and J. Borgnino, “Statistical analysis of wave-front random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimationbynumericalprocessing,” Journal of Optics, (in press, 1977) (in French).

C. Roddier, Thesis, Nice University, France, 1976 (unpublished).

J. W. Goodman, Introduction à l’Optique de Fourier et à l’ Holographie (Masson, Paris, 1972).

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Figures (7)

FIG. 1
FIG. 1

Principle of angle-of-arrival measurements, {S}, sun; {}, unperturbed light wave; {T.A.}, terrestrial atmosphere; {∑′}, perturbed light wave after propagation through terrestrial atmosphere; {P}, entrance pupil of the solar telescope; {D}, diaphragm in the objective image plane.

FIG 2
FIG 2

Photograph of the entrance pupil through the diaphragm placed on solar limb image. Angular diameter of the diaphragm, 10 arc sec. Exposure time, 1 ms. ↔, direction parallel to the edge of the sun.

FIG. 3
FIG. 3

Longitudinal (×) and transverse (●) autocorrelations of angle-of-arrival fluctuations. Date, March 18, 1976; local time, 15h13m; angular diameter of the diaphragm, 32 arc sec.

FIG. 4
FIG. 4

Influence of low-frequency filtering. Ě0 is the estimated mean value of the signal, E0 the true mean value of the signal, and K the energy lost by filtering.

FIG. 5
FIG. 5

Longitudinal autocorrelations of angle-of-arrival fluctuations: dashed line, experimental autocorrelations; solid line, theoretical autocorrelations (inertial model of turbulence). The slope of the straight line is 1 3. (a) Date, April 18, 1975; local time, 10h30m; angular diameter of the diaphragm, 10 arc sec. (b) Date, March 18, 1976; local time, 15h10m; angular diameter of the diaphragm, 20 arc sec. (c) Date, March 18, 1976; local time, 15h13m; angular diameter of the diaphragm, 32 arc sec.

FIG. 6
FIG. 6

Difference between longitudinal and transverse autocorrelations of angle-of-arrival fluctuations. Dashed line, experimental results; solid line, theoretical results (inertial model of turbulence). (a) Date, April 18, 1975; local time, 10h30m; angular diameter of the diaphragm, 10 arc sec; slope of the straight line 1 = 1 3. (b) Date, March 18, 1976; local time = 15h10m; angular diameter of the diaphragm, 20 arc sec; slope of the straight line 1 = 1 3; slope of the straight line 2 = 2 5. (c) Date, March 18, 1976; local time = 15h13m; angular diameter of the diaphragm, 32 arc sec; slope of the straight line 1 = 1 3.

FIG. 7
FIG. 7

Determination of k/E0.

Tables (2)

Tables Icon

TABLE I Values of r0 and C N 2 d h obtained by the first method.

Tables Icon

TABLE II Values of r0 and C N 2 d h obtained by the second method.

Equations (30)

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E ( x , y ) = E 0 + k y φ ( x , y ) ,
δ max = ( a / f ) ξ ,
φ max = 2 π λ a f ξ .
E ( x , y ) E ( x x 0 , y y 0 ) = E 0 2 + k E 0 ( y φ ( x , y ) + y φ ( x x 0 , y y 0 ) ) + k 2 y φ ( x y ) x y φ ( x x 0 , y y 0 ) ,
E ( x , y ) E ( x x 0 , y y 0 ) = E 0 2 + k 2 y 0 2 φ ( x , y ) φ ( x x 0 , y y 0 ) .
D φ ( x 0 , y 0 ) = 6.88 ( r r 0 ) 5 / 3 ,
D φ ( x 0 , y 0 ) = 2 [ φ 2 ( x , y ) φ ( x x 0 , y y 0 ) ] .
φ 2 ( x , y ) φ ( x x 0 , y y 0 ) = φ 2 ( x , y ) 3.44 ( r r 0 ) 5 / 3 .
C E ( x 0 , y 0 ) = E ( x , y ) E ( x x 0 , y y 0 ) = E 0 2 + 5.73 k 2 r 0 5 / 3 [ ( x 0 2 + y 0 2 ) 1 / 6 1 3 y 0 2 ( x 0 2 + y 0 2 ) 7 / 6 ] .
C E L ( x 0 , 0 ) = 5.73 k 2 r 0 5 / 3 x 0 1 / 3 ,
C E T ( 0 , y 0 ) = 2 3 × ( 5.73 k 2 r 0 5 / 3 y 0 1 / 3 ) .
D φ ( x 0 , y 0 ) = 2.91 ( 4 π 2 / λ 2 ) ( cos θ ) 1 ( x 0 2 + y 0 2 ) 5 / 6 C N 2 d h ,
C E L ( x 0 , 0 ) = 97 k 2 λ 2 ( cos θ ) 1 { C N 2 d h } x 0 1 / 3 ,
C E T ( 0 , y 0 ) = 2 3 × 97 ( k 2 / λ 2 ) ( cos θ ) 1 { C N 2 d h } y 0 1 / 3 .
D ( x , y ) = A + γ log E ( x , y ) ,
E ( x , y ) = exp ( A γ ) exp ( D ( x , y ) γ ) .
Δ C E ( x 0 ) = 1 3 × 5.73 k 2 r 0 5 / 3 x 0 1 / 3 ,
Δ C E ( x 0 ) = 1 3 × 97 k 2 λ 2 ( cos θ ) 1 ( C N 2 d h ) x 0 1 / 3 .
Δ E E 0 = E ( x , y ) E 0 E 0 k E 0 y φ ( x , y ) .
E 0 π 1 2 a 2 .
Δ E π 1 2 a 2 1 2 C a ( ρ ) ,
C a ( 2 f α ) = { 2 a 2 { cos 1 ( f α a ) f α a [ 1 ( f α a ) 2 ] 1 / 2 if α a f 0 if α > a f .
Δ E E 0 = { 1 2 π { cos 1 ( f α a ) f α a [ 1 ( f α a ) 2 ] 1 / 2 if α a f 1 if α > a f .
φ ( x , y ) = ( 2 π / λ ) δ .
y φ ( x , y ) = 2 π λ d δ d ξ = 2 π λ α .
k E 0 = { λ 2 π α ( 1 2 π { cos 1 ( f α a ) f α a [ 1 ( f α a ) 2 ] 1 / 2 } ) if α a f λ 2 π α if α > a f .
lim α 0 ( k / E 0 ) = 2 λ f π 2 a = 0.63 λ f π a .
k E 0 = λ f 2 π a = 0.5 λ f π a .
0.5 λ f π a k E 0 0.63 λ f π a .
k E 0 = 0.565 λ f π a ,