Abstract

Simple dimensional analysis shows that many scintillation phenomena can be interpreted in terms of aperture filtering. The saturation of stellar scintillation at large zenith angles cannot be accounted for by dispersion, but can be accounted for by a combination of dispersion and seeing-disk filtering.

© 1970 Optical Society of America

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References

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  1. S. H. Reiger, Astron. J. 68, 395 (1963).
    [Crossref]
  2. A. T. Young, Astron. J. 72, 747 (1967).
    [Crossref]
  3. A. T. Young, Appl. Opt. 8, 869 (1969).
    [Crossref] [PubMed]
  4. Tatarski says, “This spectral method of solving the problem is equivalent to the method based on structure or correlation functions, but is in many respects more convenient.” [Wave Propagation in a Turbuldent Medium (McGraw-Hill Book Co., New York, 1961), p. 106.]
  5. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
    [Crossref]
  6. L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), pp. 12–13.
  7. V. I. Tatarski, Ref. 4, pp. 256–257.
  8. J. B. Irwin, Astron. J. 71, 28 (1966).
    [Crossref]

1969 (1)

1967 (2)

1966 (1)

J. B. Irwin, Astron. J. 71, 28 (1966).
[Crossref]

1963 (1)

S. H. Reiger, Astron. J. 68, 395 (1963).
[Crossref]

Fried, D. L.

Irwin, J. B.

J. B. Irwin, Astron. J. 71, 28 (1966).
[Crossref]

Mertz, L.

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), pp. 12–13.

Reiger, S. H.

S. H. Reiger, Astron. J. 68, 395 (1963).
[Crossref]

Tatarski,

Tatarski says, “This spectral method of solving the problem is equivalent to the method based on structure or correlation functions, but is in many respects more convenient.” [Wave Propagation in a Turbuldent Medium (McGraw-Hill Book Co., New York, 1961), p. 106.]

Tatarski, V. I.

V. I. Tatarski, Ref. 4, pp. 256–257.

Young, A. T.

Appl. Opt. (1)

Astron. J. (3)

S. H. Reiger, Astron. J. 68, 395 (1963).
[Crossref]

A. T. Young, Astron. J. 72, 747 (1967).
[Crossref]

J. B. Irwin, Astron. J. 71, 28 (1966).
[Crossref]

J. Opt. Soc. Am. (1)

Other (3)

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York, 1965), pp. 12–13.

V. I. Tatarski, Ref. 4, pp. 256–257.

Tatarski says, “This spectral method of solving the problem is equivalent to the method based on structure or correlation functions, but is in many respects more convenient.” [Wave Propagation in a Turbuldent Medium (McGraw-Hill Book Co., New York, 1961), p. 106.]

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Figures (1)

Fig. 1
Fig. 1

Total modulation power of stellar scintillation for a small aperture as a function of air mass. For secz ≤ 1.5, the data fit the 11/6 power law expected for the diffraction-limited regime. Beyond 2 air masses, dispersion becomes important; the combined effects of diffraction and dispersion produce the upper curve to the right ( ~ sec 4 3 z / tan z). At large air masses, seeing is more important than diffraction, and the lower curve ( ~ sec 2 3 z / tan z) results. Note that seeing is required to produce the observed saturation at large air masses. Data are from Tatarski,4 p. 228 (his Fig. 34).

Equations (15)

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f a ( a k ) = [ 2 J 1 ( a k ) / a k ] 2 ,
P ~ d k x d k y · L 3 k 1 3 f a ( a k ) ,
P ~ L 3 0 k d k · k 1 3 J 1 2 ( a k ) / ( a k ) 2 = L 3 a - 2 0 k - 2 3 J 1 2 ( a k ) d k .
P ~ L 3 a - 7 / 3 0 u - 2 3 J 1 2 ( u ) d u .
P ~ L 3 [ ( λ L ) 1 2 ] - 7 / 3 = λ - 7 / 6 L 11 / 6 ,
P ~ L 3 0 ( λ L ) - 1 2 k 4 3 d k = 3 7 L 3 [ ( λ L ) - 1 2 ] 7 / 3 = 3 7 λ - 7 / 6 L 11 / 6 .
Δ V Δ μ h o tan z sec z ,
Δ k V 1 / Δ V .
Δ H ( λ h o sec z ) 1 2
Δ k H 1 / Δ H ,
P ~ L 3 d k V d k H k 1 3 · f ( k V , k H ) ~ ( h o sec z ) 3 0 Δ k V d k V 0 Δ k H d k H · k 1 3 .
P ~ ( h o sec z ) 3 Δ μ h o sec z tan z 0 Δ k H k H 1 3 d k H ~ ( h o sec z ) 2 Δ μ tan z ( Δ k H ) 4 3 ~ ( h o sec z ) 2 Δ μ tan z ( λ h o sec z ) - 2 3 ~ λ - 2 3 ( h o sec z ) 4 3 Δ μ tan z .
D ~ L ( sec z ) 1 2 = h o sec 3 2 z .
Δ k H ~ ( h o sec 3 2 z ) - 1 ,
P ~ ( h o sec z ) 2 Δ μ tan z ( h o sec 3 2 z ) - 4 3 = ( h o sec z ) 2 3 Δ μ tan z ,