Abstract

A method is described for the calibration of power spectra of nonstellar astronomical objects, by the use of changes in seeing conditions during speckle-interferometric measurements. Results are given for an application of this technique to solar granulation. The correction of 40 analyses, determined with Fried’s parameter r0 ranging between 2.5 and 11.5 cm, provides satisfactory convergence, and thus permits estimation of the solar granulation power spectrum for frequencies up to 2.5 arc sec−1.

© 1978 Optical Society of America

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References

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  1. A. Labeyrie, Astron. Astrophys. 6, 85–87 (1970).
  2. D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
    [Crossref]
  3. D. R. Beddoes, J. C. Dainty, B. L. Morgan, and R. J. Scaddan, J. Opt. Soc. Am. 66, 1247 (1976).
    [Crossref]
  4. D. P. Karo and A. M. Schneiderman, J. Opt. Soc. Am. 66, 1252 (1976).
    [Crossref]
  5. C. Aime, J. Opt. Soc. Am. 64, 1129 (1974).
    [Crossref]
  6. D. Korff, J. Opt. Soc. Am. 63, 971 (1973).
    [Crossref]
  7. J. C. Dainty, Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975).
  8. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [Crossref]
  9. C. Aime, Sol. Phys. 30, 15 (1973).
    [Crossref]
  10. D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
    [Crossref]
  11. C. Roddier and F. Roddier, J. Opt. Soc. Am. 65, 664 (1975).
    [Crossref]
  12. C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).
  13. C. Aime, Thesis (University of Nice, France, 1977) (unpublished).

1977 (1)

C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).

1976 (2)

1975 (1)

1974 (1)

1973 (3)

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

D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
[Crossref]

C. Aime, Sol. Phys. 30, 15 (1973).
[Crossref]

1972 (1)

D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

1970 (1)

A. Labeyrie, Astron. Astrophys. 6, 85–87 (1970).

1966 (1)

Aime, C.

C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).

C. Aime, J. Opt. Soc. Am. 64, 1129 (1974).
[Crossref]

C. Aime, Sol. Phys. 30, 15 (1973).
[Crossref]

C. Aime, Thesis (University of Nice, France, 1977) (unpublished).

Beddoes, D. R.

Dainty, J. C.

D. R. Beddoes, J. C. Dainty, B. L. Morgan, and R. J. Scaddan, J. Opt. Soc. Am. 66, 1247 (1976).
[Crossref]

J. C. Dainty, Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975).

Dryder, G.

D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Fried, D. L.

Gezari, D. V.

D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
[Crossref]

Grec, G.

C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).

Karo, D. P.

Korff, D.

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

D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Labeyrie, A.

D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
[Crossref]

A. Labeyrie, Astron. Astrophys. 6, 85–87 (1970).

Miller, M. G.

D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Morgan, B. L.

Ricort, G.

C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).

Roddier, C.

Roddier, F.

Scaddan, R. J.

Schneiderman, A. M.

Stachnik, R. V.

D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
[Crossref]

Astron. Astrophys. (2)

A. Labeyrie, Astron. Astrophys. 6, 85–87 (1970).

C. Aime, G. Ricort, and G. Grec, Astron. Astrophys. 54, 505 (1977).

Astrophys. J. Lett. (1)

D. V. Gezari, A. Labeyrie, and R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1973).
[Crossref]

J. Opt. Soc. Am. (6)

Opt. Commun. (1)

D. Korff, G. Dryder, and M. G. Miller, Opt. Commun. 5, 187 (1972).
[Crossref]

Sol. Phys. (1)

C. Aime, Sol. Phys. 30, 15 (1973).
[Crossref]

Other (2)

J. C. Dainty, Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, Berlin, 1975).

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

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Figures (3)

FIG. 1
FIG. 1

Theoretical ratios R1/2(f) for the atmospheric-lens MTF as a function of spatial frequency in cycles per arc sec for r1 = 4, 6, 8, and 10 cm, and r2 = 11 cm. r1 and r2 are the values of Fried’s parameter. Full line, log-normal model; dashed line, normal model.

FIG. 2
FIG. 2

Example of a comparison between the experimental ratio W1(f)/W2(f) and the theoretical ratio R1/2(f). Full line, experimental; dashed line, theoretical. The log-normal assumption is used for the comparison. The x axis is graduated in cycles per arc-sec.

FIG. 3
FIG. 3

Power spectrum per unit area, corrected for seeing, expressed as a function of the spatial frequency in cycles per arc sec (2 c/s corresponds to 0.5 arc sec). The y axis is graduated logarithmically. The corrected spectra were obtained from 40 analyses of solar granulation, with r0 varying between 2.5 and 11.5 cm.

Equations (10)

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W i ( f ) = W R ( f ) T i ( f ) 2 ,
R 1 / 2 ( f ) = W 1 ( f ) W 2 ( f ) = T 1 ( f ) 2 T 2 ( f ) 2
T ( f ) 2 ( 1 / N ) τ 0 ( f ) ,
R 1 / 2 ( f ) N 2 / N 1 = r 1 2 / r 2 2 = α 2 ,
T i ( f ) 2 N T i ( f ) 2 le = τ 0 2 ( f ) exp [ - 6.88 ( λ f / r i ) 5 / 3 ]
R 1 / 2 ( f ) N exp [ - 6.88 ( λ f ) 5 / 3 ( r 1 - 5 / 3 - r 2 - 5 / 3 ) ] .
T i ( f ) 2 ln T i ( f ) 2 se = τ 0 2 ( f ) exp { - 6.88 ( λ f / r i ) 5 / 3 [ 1 - ( λ f / D ) 1 / 3 ] } ,
R 1 / 2 ( f ) ln exp { - 6.88 ( λ f ) 5 / 3 [ 1 - ( λ f / D ) 1 / 3 ] × ( r 1 - 5 / 3 - r 2 - 5 / 3 ) } .
r 1 - 5 / 3 - r 2 - 5 / 3 = β - 5 / 3 ,
r 1 = α r 2 ,             r 2 = β ( α - 5 / 3 - 1 ) 3 / 5 .