Abstract

We present generalized numerical predictions of the effects of transmitter-aperture size and divergence on the on-axis scintillations of a laser beam propagating through a turbulent stmosphere, utilizing analytical results obtained from the literature. The sharp reduction of scintillation that has been predicted for a large, focused beam is shown to depend very critically upon the focus adjustment; small misadjustments result in increases by orders of magnitude. This also implies that diffraction-limited optics may be required. This requirement, together with the implications of turbulent beam-wander and spreading effects, suggest that the predicted reduction is of little practical significance. We also present the conditions necessary for obtaining point-source results in scintillation experiments.

© 1972 Optical Society of America

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References

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  1. D. L. Fried and J. B. Seidman, J. Opt. Soc. Am. 57, 181 (1967).
    [Crossref]
  2. A. Ishimaru, Radio Sci. 4, 295 (1969).
    [Crossref]
  3. A. Ishimaru, Proc. IEEE 57, 407 (1969).
    [Crossref]
  4. F. P. Carlson, J. Opt. Soc. Am. 59, 1343 (1969).
    [Crossref]
  5. R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
    [Crossref]
  6. R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
    [Crossref]
  7. D. L. Fried, J. Opt. Soc. Am. 57, 980 (1967).
    [Crossref]
  8. E. C. Alcaraz and P. M. Livingston, in Proceedings of the Electro-Optical Systems Design Conference—West (Industrial and Scientific Conference Management, Inc., Chicago, 1971), p. 76.
  9. J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
    [Crossref]
  10. R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).
    [Crossref] [PubMed]
  11. H. T. Yura (private communication).
  12. P. J. Titterton (private communication).

1971 (2)

J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
[Crossref]

R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).
[Crossref] [PubMed]

1970 (1)

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

1969 (4)

F. P. Carlson, J. Opt. Soc. Am. 59, 1343 (1969).
[Crossref]

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

A. Ishimaru, Proc. IEEE 57, 407 (1969).
[Crossref]

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

1967 (2)

Alcaraz, E. C.

E. C. Alcaraz and P. M. Livingston, in Proceedings of the Electro-Optical Systems Design Conference—West (Industrial and Scientific Conference Management, Inc., Chicago, 1971), p. 76.

Carlson, F. P.

Curcio, J. A.

J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
[Crossref]

Dowling, J. A.

J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
[Crossref]

Fried, D. L.

Harp, J. C.

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

Ishimaru, A.

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

A. Ishimaru, Proc. IEEE 57, 407 (1969).
[Crossref]

Lawrence, R. S.

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

Lee, R. W.

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

Livingston, P. M.

E. C. Alcaraz and P. M. Livingston, in Proceedings of the Electro-Optical Systems Design Conference—West (Industrial and Scientific Conference Management, Inc., Chicago, 1971), p. 76.

Lutomirski, R. F.

Seidman, J. B.

Shenker, H.

J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
[Crossref]

Strohbehn, J. W.

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

Titterton, P. J.

P. J. Titterton (private communication).

Yura, H. T.

Appl. Opt. (1)

IEEE J. (1)

J. A. Dowling, J. A. Curcio, and H. Shenker, IEEE J. QE-7, 275 (1971).
[Crossref]

J. Opt. Soc. Am. (3)

Proc. IEEE (3)

R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
[Crossref]

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

A. Ishimaru, Proc. IEEE 57, 407 (1969).
[Crossref]

Radio Sci. (1)

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

Other (3)

E. C. Alcaraz and P. M. Livingston, in Proceedings of the Electro-Optical Systems Design Conference—West (Industrial and Scientific Conference Management, Inc., Chicago, 1971), p. 76.

H. T. Yura (private communication).

P. J. Titterton (private communication).

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Figures (4)

Fig. 1
Fig. 1

Normalized log amplitude variance vs transmitter focus conditions, for small and moderate apertures.

Fig. 2
Fig. 2

Normalized log amplitude variance vs transmitter focus conditions, for large apertures.

Fig. 3
Fig. 3

Normalized log amplitude variance vs transmitter-divergence conditions.

Fig. 4
Fig. 4

Normalized log amplitude variance vs transmitter inverse Fresnel number.

Equations (11)

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σ 2 = 2.18 k 7 / 6 L 11 / 6 C n 2 0 1 f ( x ) d x ,
f ( x ) = Re [ ( α 1 L ( 1 - x ) + i ( 1 - α 2 L + α 1 2 L 2 x + α 2 2 L 2 x - α 2 L x ) ( 1 - α 2 L ) 2 + ( α 1 L ) 2 ) ( 1 - x ) ] 5 / 6 - [ ( 1 - x ) 2 ( α 1 L ( 1 - α 2 L ) 2 + ( α 1 L ) 2 ) ] 5 / 6 ,
σ S 2 = 0.124 k 7 / 6 L 11 / 6 C n 2 .
- α 2 L = D R / D T , θ = - α 2 L ( D T / L ) .
α 2 L - 1 = Δ ( 1 ) .
δ = f 2 L Δ ,
L - R = L Δ ,
Δ α 1 L .
δ f α 1 L f L .
C n 2 const × ( D T ) 7 / 3 L 3 .
σ S 2 const × ( D T 2 λ L ) 7 / 6 = const × ( α i L ) - 7 / 6 ,