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 ∫ <i>C</i><sub><i>N</i></sub><sup>2</sup>dh of the structure constant over the lower atmospheric layers and of Fried’s seeing parameter <i>r</i><sub>0</sub> are deduced. They are found to be consistent with other independent estimations made with the same telescope.

© 1977 Optical Society of America

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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. (1964).
  3. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
  4. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
  5. C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).
  6. J. W. Strohbehn and S. F. Clifford, IEEE Trans. Antennas Propagat. 15, 416 (1967).
  7. J. W. Strohbehn, J. Geophys. Res. 75, 1067 (1970).
  8. R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
  9. R. F. Lutomirski and R. G. Buser, Appl. Opt. 13 2869 (1974).
  10. D. L. Fried, Radio Sci. 10, 71 (1975).
  11. P. E. Barnhart, G. Keller, and W. E. Mitchell Jr., Report N Tr 59–291 (Air Force Cambridge Research Center, Bedford, Mass., 1959).
  12. J. Vernin and F. Roddier, J. Opt. Soc. Am. 63, 270 (1973).
  13. A. Rocca, F. Roddier, and J. Vernin, J. Opt. Sc. Am. 64, 1000 (1974).
  14. A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radiofizika 11, 1360 (1968).
  15. A. Consortini, L. Ronchi, and L. Stefanutl, Appl. Opt. 9, 2543 (1970).
  16. D. A. Wolf, J. Opt. Soc. Am. 63, 657 (1973).
  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).
  19. J. C. Dainty, Opt. Commun. 7, 129 (1973).
  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, 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, obtain 1974.
  23. D. P. Greenwood, in Program of the OSA, Topical Meeting on Imaging in Astronomy, 1974.
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  38. F. Martin and J. Borgnino, "Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimation by numerical processing," 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).
  40. K. A. Browning, J. R. Starr, and A. J. Whyman, Boundary-Layer Meteorol. 4, 91 (1973).
  41. D. W. Beran, W. M. Hooke, and S. F. Clifford, Boundary-Layer Meteorol. 4, 133 (1973).
  42. M. Aubry, Les sondages acoustiques de l'Atmosphére XVIII iéme 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).
  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).

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).

Aubry, M.

M. Aubry, Les sondages acoustiques de l'Atmosphére XVIII iéme 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, obtain 1974.

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

Barnhart, P. E.

P. E. Barnhart, G. Keller, and W. E. Mitchell Jr., 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).

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.

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).

F. Martin and J. Borgnino, "Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimation by numerical processing," Journal of Optics, (in press, 1977) (in French).

Brandt, P. N.

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

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

Browning, K. A.

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

Buser, R. G.

R. F. Lutomirski and R. G. Buser, Appl. Opt. 13 2869 (1974).

Bystrova, N. V.

N. V. Bystrova, and A. N. Demidova, Soln. Dannye 7, nº 3 (1973).

Ceppatelli, G.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, 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, obtain 1974.

Clifford, S. F.

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

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

Consortini, A.

A. Consortini, L. Ronchi, and L. Stefanutl, Appl. Opt. 9, 2543 (1970).

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

Coulman, C E.

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

Coulman, C. E.

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

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

Dainty, J. C.

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

Danjon, A.

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

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, nº 3 (1973).

Fante, R.

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

Fried, D. L.

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

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

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, Radiofizika 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).

Hufnagel, R. E.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. (1964).

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).

Kallistratova, M. A.

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radiofizika 11, 1360 (1968).

Keller, G.

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

Korff, D.

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

Lacarrere, P.

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

Lawrence, R. S.

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

Lutomirski, R. F.

R. F. Lutomirski and R. G. Buser, Appl. Opt. 13 2869 (1974).

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.

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).

F. Martin and J. Borgnino, "Statistical analysis of wavefront random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimation by numerical processing," Journal of Optics, (in press, 1977) (in French).

Mitchell Jr., W. E.

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

Moor, G. De

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

Moroder, E.

R. Barletti, G. Ceppatelli, E. Moroder, L. Paterno, and A. Righini, 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).

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, E. Moroder, L. Paterno, and A. Righini, 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, obtain 1974.

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).

Richter, J. H.

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

Ricort, G.

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

Righini, A.

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, 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, obtain 1974.

Rocca, A.

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Sc. Am. 64, 1000 (1974).

Roddier, C.

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

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

C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).

Roddier, F.

C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).

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

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

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Sc. Am. 64, 1000 (1974).

Ronchi, L.

A. Consortini, L. Ronchi, and L. Stefanutl, Appl. Opt. 9, 2543 (1970).

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, obtain 1974.

Stanley, N. R.

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. (1964).

Starr, J. R.

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

Stefanutl, L.

A. Consortini, L. Ronchi, and L. Stefanutl, Appl. Opt. 9, 2543 (1970).

Strohbehn, J. W.

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

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

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

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, Radiofizika 11, 1360 (1968).

Vachat, R. Du

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

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. Sc. Am. 64, 1000 (1974).

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

Whyman, A. J.

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

Wolf, D. A.

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

Other (46)

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

R. E. Hufnagel and N. R. Stanley, J. Opt. Soc. (1964).

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).

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

C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).

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

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

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

R. F. Lutomirski and R. G. Buser, Appl. Opt. 13 2869 (1974).

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

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

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

A. Rocca, F. Roddier, and J. Vernin, J. Opt. Sc. Am. 64, 1000 (1974).

A. S. Gurvich, M. A. Kallistratova, and N. S. Time, Radiofizika 11, 1360 (1968).

A. Consortini, L. Ronchi, and L. Stefanutl, Appl. Opt. 9, 2543 (1970).

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

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

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

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

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, 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, obtain 1974.

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

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

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

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

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

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

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

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

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).

N. V. Bystrova, and A. N. Demidova, Soln. Dannye 7, nº 3 (1973).

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).

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

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

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

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 wavefront random deformations produced by atmospheric turbulence near the ground. 2nd part: Correlation function estimation by numerical processing," Journal of Optics, (in press, 1977) (in French).

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

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

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

M. Aubry, Les sondages acoustiques de l'Atmosphére XVIII iéme Assemblée Générale de L'U. R.S.I., Lima, 1975.

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

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

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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