Abstract

A technique is proposed allowing estimation of the spatial coherence outer scale, from simultaneous measurements of Fried’s parameter r0 and of the variance of angle-of-arrival fluctuations. This optical parameter must be differentiated from the classical geophysical parameter called the outer scale of turbulence; its knowledge is important for long baseline interferometry and imaging in optical astronomy.

© 1990 Optical Society of America

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References

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  1. C. Roddier, “Measurements of the Atmospheric Attenuation of the Spectral Components of Astronomical Images,” J. Opt. Soc. Am. 66, 478–482 (1976).
    [CrossRef]
  2. J. Borgnino, J. Vernin, “Experimental Verification of the Inertial Model of Atmospheric Turbulence from Solar Limb Motion,” J. Opt. Soc. Am. 68, 1056–1062 (1978).
    [CrossRef]
  3. M. Azouit, J. Borgnino, J. Vernin, “Use of a Linear Photodiode Array in Order to Estimate in Real Time the Contribution of the Lower Atmospheric Layers in Astronomical-Image Degradation,” J. Opt. Paris 9, 291–299 (1978).
    [CrossRef]
  4. F. Roddier, “Special Requirements for High Angular Resolution Interferometry,” in Proceedings, ESO Workshop on Site Testing for Future Large Telescopes, La Silla (4–6 Oct. 1983), p. 193.
  5. F. F. Forbes, N. J. Woolf, “Atmospheric Turbulence Effects on Large Telescope Image Motion and Size,” Proc. Soc. Photo-Opt. Instrum. Eng. 444, 175–182 (1983).
  6. 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]
  7. J. M. Mariotti, G. P. Di Benedetto, “Pathlength Stability of Synthetic Aperture Telescopes. The Case of the 25 cm Cerga Interferometer,” in Proceedings, IAU Colloquium 79, Garching (9–12 Apr. 1984), p. 257.
  8. J. W. Strohbehn, S. F. Clifford, “Polarization and Angle-of-Arrival Fluctuations for a Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
    [CrossRef]
  9. F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
    [CrossRef]
  10. V. I. Tatarski, “Effects of the Turbulent Atmosphere on Wave Propagation,” Israel Program of Scientific Translation, Jerusalem (1971).
  11. D. L. Fried, “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” J. Opt. Soc. Am. 56, 1372–1380 (1966).
    [CrossRef]
  12. M. Neiburger, J. G. Edinger, W. D. Bonner, Understanding Our Atmospheric Environment (Freeman, San Francisco, 1973).
  13. M. Sarazin, “ESO VLT Site Evaluation—II,” in Proceedings, Second Workshop on ESO’s Very Large Telescope, Venice (29 Sept.–2 Oct. 1986), p. 229.
  14. M. Sarazin, F. Roddier, “The ESO Differential Image Motion Monitor,” preprint of a paper submitted to Astron. Astrophys. (1989).
  15. J. C. Bortz, “Wave-Front Sensing by Optical Phase Differentiation,” J. Opt. Soc. Am. A 1, 35–39 (1984).
    [CrossRef]

1988 (1)

1984 (1)

1983 (1)

F. F. Forbes, N. J. Woolf, “Atmospheric Turbulence Effects on Large Telescope Image Motion and Size,” Proc. Soc. Photo-Opt. Instrum. Eng. 444, 175–182 (1983).

1981 (1)

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
[CrossRef]

1978 (2)

M. Azouit, J. Borgnino, J. Vernin, “Use of a Linear Photodiode Array in Order to Estimate in Real Time the Contribution of the Lower Atmospheric Layers in Astronomical-Image Degradation,” J. Opt. Paris 9, 291–299 (1978).
[CrossRef]

J. Borgnino, J. Vernin, “Experimental Verification of the Inertial Model of Atmospheric Turbulence from Solar Limb Motion,” J. Opt. Soc. Am. 68, 1056–1062 (1978).
[CrossRef]

1976 (1)

1971 (1)

V. I. Tatarski, “Effects of the Turbulent Atmosphere on Wave Propagation,” Israel Program of Scientific Translation, Jerusalem (1971).

1967 (1)

J. W. Strohbehn, S. F. Clifford, “Polarization and Angle-of-Arrival Fluctuations for a Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
[CrossRef]

1966 (1)

Azouit, M.

M. Azouit, J. Borgnino, J. Vernin, “Use of a Linear Photodiode Array in Order to Estimate in Real Time the Contribution of the Lower Atmospheric Layers in Astronomical-Image Degradation,” J. Opt. Paris 9, 291–299 (1978).
[CrossRef]

Bonner, W. D.

M. Neiburger, J. G. Edinger, W. D. Bonner, Understanding Our Atmospheric Environment (Freeman, San Francisco, 1973).

Borgnino, J.

M. Azouit, J. Borgnino, J. Vernin, “Use of a Linear Photodiode Array in Order to Estimate in Real Time the Contribution of the Lower Atmospheric Layers in Astronomical-Image Degradation,” J. Opt. Paris 9, 291–299 (1978).
[CrossRef]

J. Borgnino, J. Vernin, “Experimental Verification of the Inertial Model of Atmospheric Turbulence from Solar Limb Motion,” J. Opt. Soc. Am. 68, 1056–1062 (1978).
[CrossRef]

Bortz, J. C.

Caccia, J. L.

Clifford, S. F.

J. W. Strohbehn, S. F. Clifford, “Polarization and Angle-of-Arrival Fluctuations for a Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
[CrossRef]

Coqueugniot, Y.

Coulman, C. E.

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, IAU Colloquium 79, Garching (9–12 Apr. 1984), p. 257.

Edinger, J. G.

M. Neiburger, J. G. Edinger, W. D. Bonner, Understanding Our Atmospheric Environment (Freeman, San Francisco, 1973).

Forbes, F. F.

F. F. Forbes, N. J. Woolf, “Atmospheric Turbulence Effects on Large Telescope Image Motion and Size,” Proc. Soc. Photo-Opt. Instrum. Eng. 444, 175–182 (1983).

Fried, D. L.

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, IAU Colloquium 79, Garching (9–12 Apr. 1984), p. 257.

Neiburger, M.

M. Neiburger, J. G. Edinger, W. D. Bonner, Understanding Our Atmospheric Environment (Freeman, San Francisco, 1973).

Roddier, C.

Roddier, F.

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
[CrossRef]

F. Roddier, “Special Requirements for High Angular Resolution Interferometry,” in Proceedings, ESO Workshop on Site Testing for Future Large Telescopes, La Silla (4–6 Oct. 1983), p. 193.

M. Sarazin, F. Roddier, “The ESO Differential Image Motion Monitor,” preprint of a paper submitted to Astron. Astrophys. (1989).

Sarazin, M.

M. Sarazin, “ESO VLT Site Evaluation—II,” in Proceedings, Second Workshop on ESO’s Very Large Telescope, Venice (29 Sept.–2 Oct. 1986), p. 229.

M. Sarazin, F. Roddier, “The ESO Differential Image Motion Monitor,” preprint of a paper submitted to Astron. Astrophys. (1989).

Strohbehn, J. W.

J. W. Strohbehn, S. F. Clifford, “Polarization and Angle-of-Arrival Fluctuations for a Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, “Effects of the Turbulent Atmosphere on Wave Propagation,” Israel Program of Scientific Translation, Jerusalem (1971).

Vernin, J.

Woolf, N. J.

F. F. Forbes, N. J. Woolf, “Atmospheric Turbulence Effects on Large Telescope Image Motion and Size,” Proc. Soc. Photo-Opt. Instrum. Eng. 444, 175–182 (1983).

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (1)

J. W. Strohbehn, S. F. Clifford, “Polarization and Angle-of-Arrival Fluctuations for a Plane Wave Propagated Through a Turbulent Medium,” IEEE Trans. Antennas Propag. AP-15, 416–421 (1967).
[CrossRef]

Israel Program of Scientific Translation, Jerusalem (1)

V. I. Tatarski, “Effects of the Turbulent Atmosphere on Wave Propagation,” Israel Program of Scientific Translation, Jerusalem (1971).

J. Opt. Paris (1)

M. Azouit, J. Borgnino, J. Vernin, “Use of a Linear Photodiode Array in Order to Estimate in Real Time the Contribution of the Lower Atmospheric Layers in Astronomical-Image Degradation,” J. Opt. Paris 9, 291–299 (1978).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

F. F. Forbes, N. J. Woolf, “Atmospheric Turbulence Effects on Large Telescope Image Motion and Size,” Proc. Soc. Photo-Opt. Instrum. Eng. 444, 175–182 (1983).

Prog. Opt. (1)

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
[CrossRef]

Other (5)

J. M. Mariotti, G. P. Di Benedetto, “Pathlength Stability of Synthetic Aperture Telescopes. The Case of the 25 cm Cerga Interferometer,” in Proceedings, IAU Colloquium 79, Garching (9–12 Apr. 1984), p. 257.

F. Roddier, “Special Requirements for High Angular Resolution Interferometry,” in Proceedings, ESO Workshop on Site Testing for Future Large Telescopes, La Silla (4–6 Oct. 1983), p. 193.

M. Neiburger, J. G. Edinger, W. D. Bonner, Understanding Our Atmospheric Environment (Freeman, San Francisco, 1973).

M. Sarazin, “ESO VLT Site Evaluation—II,” in Proceedings, Second Workshop on ESO’s Very Large Telescope, Venice (29 Sept.–2 Oct. 1986), p. 229.

M. Sarazin, F. Roddier, “The ESO Differential Image Motion Monitor,” preprint of a paper submitted to Astron. Astrophys. (1989).

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Figures (3)

Fig. 1
Fig. 1

Components of the angle of arrival: 1, part of the perturbed wavefront and 2, normal to the incident plane wave.

Fig. 2
Fig. 2

Theoretical variation of the spatial coherence outer scale 0 as a function of the variance σ2 of the angle-of-arrival fluctuations for different values of Fried’s parameter r0.

Fig. 3
Fig. 3

(a) Hufnagel’s average C N 2 profile corresponding to nighttime conditions with a constant value for heights between 0 and 40 m. r0 was computed for a wavelength equal to 500 nm. (b) Corresponding vertical profile for atmospheric turbulence outer scale in the lower atmosphere obtained using relation (6) and the U.S. Standard Atmosphere. 0 was deduced from relation (4).

Equations (7)

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α ( x , y ) = - ( λ / 2 π ) x ϕ ( x , y ) , β ( x , y ) = - ( λ / 2 π ) y ϕ ( x , y ) ,
σ 2 = α 2 = β 2 0 d h C N 2 ( h ) L 0 ( h ) - 1 D - 1 d f f - 2 / 3 ,
σ 2 3 [ D - 1 / 3 0 d h C N 2 ( h ) - 0 d h L 0 ( h ) - 1 / 3 C N 2 ( h ) ] .
L 0 - 1 / 3 = [ 0 d h L 0 ( h ) - 1 / 3 C N 2 ( h ) ] / [ 0 d h C N 2 ( h ) ] .
σ 2 0.18 λ 2 r 0 - 5 / 3 [ D - 1 / 3 - L 0 - 1 / 3 ] .
L 0 ( h ) 4 / 3 = K M ( h ) - 2 C N 2 ( h ) ,
r 0 - 5 / 3 = 16.7 λ - 2 0 d h C N 2 ( h ) .

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