Abstract

Measurements of atmospheric turbulence structure and multiwavelength scintillation statistics are described. The scintillation measurements use coincident virtual point sources, and include log-amplitude variances and covariances, spectra, and receiver-aperture smoothing. These are related to turbulence strength, spectral slope, and inner scale. The saturation of scintillations is found to be wavelength independent. The Kolmogorov atmospheric model breaks down under weak turbulence conditions, and hence the commonly used atmospheric and propagation theories tend to apply under mutually contradictory conditions. The transverse amplitude-correlation length and resultant receiver-aperture smoothing depart from theoretical predictions under strong scintillations. Scintillation spectra show much data spread but averages support the Taylor hypothesis. Short-path optical determinations of turbulence strength are seriously affected by nonzero inner scales of turbulence. Correlations of multiwavelength scintillations vs time indicate nonuniformity of both turbulence spectra and strength over the path.

© 1972 Optical Society of America

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  1. R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).Familiarity with this review of scintillation phenomena is assumed in this paper.
    [Crossref]
  2. J. R. Kerr and R. Eiss, J. Opt. Soc. Am. 62, 682 (1972).
    [Crossref]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  4. A. Ishimaru, Radio Sci. 4, 295 (1969).
    [Crossref]
  5. F. P. Carlson, J. Opt. Soc. Am. 59, 1343 (1969).
    [Crossref]
  6. P. M. Livingston, P. H. Deitz, and E. C. Alcaraz, J. Opt. Soc. Am. 60, 925 (1970).
    [Crossref]
  7. The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated.Pertinent references areD. A. Gray and A. T. Waterman, J. Geophys. Res. 75, 1077 (1970)and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
    [Crossref]
  8. R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
    [Crossref]
  9. The measured scintillation variance may be reduced up to 20% (Sec. II E) owing to the nonzero receiver aperture. However, because of the (3/7) dependence in obtaining l0, the maximum effect on these points is to reduce the ordinate by 9%.
  10. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
    [Crossref]
  11. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
    [Crossref]
  12. A. T. Young, Astron. J. 72, 747 (1967).
    [Crossref]
  13. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  14. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
    [Crossref]
  15. V. I. Tatarski, Propagation of Waves in a Turbulent Atmosphere (Nauka, Moscow, 1967).
  16. D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).Note that independently scintillating patches equal to the diffraction scale of a finite transmitter aperture would result in improved aperture averaging, since this scale is smaller than (λL)12. Hence, it appears that transmitter-aperture effects cannot explain observations of poor receiver smoothing.
    [Crossref]
  17. G. R. Ochs, Measurements of 0.63 μm Laser-Beam Scintillation in Strong Atmospheric Turbulence, ESSA Technical Report No. ERL 154-WPL 10 (U. S. Government Printing Office, Washington, D. C., 1969).
  18. R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
    [Crossref]
  19. This qualitative rule is suggested by an unpublished analysis by D. L. Fried, in which he derives the relationship between equipment dynamic range and maximum measured (i.e., apparent) log-amplitude variances.
  20. M. W. Fitzmaurice and J. L. Bufton, J. Opt. Soc. Am. 59, 462 (1969).
    [Crossref]
  21. Receiver-aperture smoothing was apparently a significant factor in the results of Ref. 8. The scaling of finite receiver sizes by λ12 is not well justified under saturated conditions, in which covariances depart from those predicted by first-order theory.
  22. G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).
  23. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).
  24. G. E. Modesitt, J. Opt. Soc. Am. 61, 797 (1971).
    [Crossref]
  25. H. T. Yura, J. Opt. Soc. Am. 59, 111 (1969).
    [Crossref]
  26. K. Mano, Proc. IEEE (Corresp.) 58, 1168 (1970).
    [Crossref]
  27. K. Mano, Proc. IEEE (Corresp.) 58, 1405 (1970).
    [Crossref]
  28. M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 60, 654 (1970).
    [Crossref]
  29. W. P. Brown, J. Opt. Soc. Am. 61, 981 (1971).
    [Crossref]
  30. M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 61, 982 (1971).
    [Crossref]
  31. L. S. Taylor and D. J. Torrieri, J. Opt. Soc. Am. 62, 145 (1972).
    [Crossref]
  32. W. P. Brown, J. Opt. Soc. Am. 62, 45 (1972).
    [Crossref]
  33. D. A. deWolf, J. Opt. Soc. Am. 62, 730A (1972).
  34. R. F. Lutomirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).
    [Crossref] [PubMed]
  35. A. T. Young, Appl. Opt. 8, 869 (1969).
    [Crossref] [PubMed]
  36. A. T. Young, J. Opt. Soc. Am. 60, 248 (1970).
    [Crossref]
  37. A. T. Young, J. Opt. Soc. Am. 60, 1495 (1970).
    [Crossref]
  38. C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
    [Crossref]
  39. W. H. Dungey, D. O. Tarazano, and J. C. Wyngaard, J. Opt. Soc. Am. 61, 1552A (1971).
  40. J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).
  41. L. R. Zwang, Izv. Geophys. Series 8, 1252 (1960).
  42. L. R. Zwang, Izv. Geophys. Series 8, 1674 (1960).
  43. H. A. Panofsky, Radio Sci. 4, 1143 (1969).
    [Crossref]
  44. V. M. Koprov and L. R. Zwang, Izv. Atmos. Oceanic Phys. 2, 1142 (1966).
  45. V. M. Koprov, Izv. Atmos. Oceanic Phys. 1, 1151 (1965).
  46. S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
    [Crossref]
  47. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, and M. H. Ackley, J. Opt. Soc. Am. 61, 1279 (1971).
    [Crossref]
  48. R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
    [Crossref]
  49. D. J. Portman, E. Ryznar, and A. A. Waqif, Laser Scintillation Caused by Turbulence Near the Ground, University of Michigan Research Report No. 225 (available as AD 666 798,Clearinghouse, Springfield, Va., 1968).
  50. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
    [Crossref]
  51. T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmospheric Temperature Fluctuations, ECOM-5387 (available as AD 729 791, Clearinghouse, Springfield, Va., 1971).
  52. P. G. Saffman, in Topics in Nonlinear Physics, edited by N. J. Zabusky, (Springer, New York, 1968), p. 485.
    [Crossref]
  53. E. Brookner, IEEE Trans COM-18, 396 (1970).
    [Crossref]
  54. J. L. Lumley, Phys. Fluids 8, 1056 (1965).
    [Crossref]
  55. G. Heskestad, J. Appl. Mech. 32, 735 (1965).
    [Crossref]
  56. H. R. Carlon, Appl. Opt. 4, 1089 (1965).
    [Crossref]
  57. R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).
    [Crossref]

1972 (4)

1971 (7)

1970 (13)

P. M. Livingston, P. H. Deitz, and E. C. Alcaraz, J. Opt. Soc. Am. 60, 925 (1970).
[Crossref]

The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated.Pertinent references areD. A. Gray and A. T. Waterman, J. Geophys. Res. 75, 1077 (1970)and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
[Crossref]

R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
[Crossref]

K. Mano, Proc. IEEE (Corresp.) 58, 1168 (1970).
[Crossref]

K. Mano, Proc. IEEE (Corresp.) 58, 1405 (1970).
[Crossref]

M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 60, 654 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[Crossref]

E. Brookner, IEEE Trans COM-18, 396 (1970).
[Crossref]

A. T. Young, J. Opt. Soc. Am. 60, 248 (1970).
[Crossref]

A. T. Young, J. Opt. Soc. Am. 60, 1495 (1970).
[Crossref]

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).Familiarity with this review of scintillation phenomena is assumed in this paper.
[Crossref]

1969 (8)

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

A. T. Young, Appl. Opt. 8, 869 (1969).
[Crossref] [PubMed]

H. A. Panofsky, Radio Sci. 4, 1143 (1969).
[Crossref]

M. W. Fitzmaurice and J. L. Bufton, J. Opt. Soc. Am. 59, 462 (1969).
[Crossref]

G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).

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

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

H. T. Yura, J. Opt. Soc. Am. 59, 111 (1969).
[Crossref]

1967 (4)

1966 (3)

V. M. Koprov and L. R. Zwang, Izv. Atmos. Oceanic Phys. 2, 1142 (1966).

C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
[Crossref]

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

1965 (4)

V. M. Koprov, Izv. Atmos. Oceanic Phys. 1, 1151 (1965).

J. L. Lumley, Phys. Fluids 8, 1056 (1965).
[Crossref]

G. Heskestad, J. Appl. Mech. 32, 735 (1965).
[Crossref]

H. R. Carlon, Appl. Opt. 4, 1089 (1965).
[Crossref]

1960 (2)

L. R. Zwang, Izv. Geophys. Series 8, 1252 (1960).

L. R. Zwang, Izv. Geophys. Series 8, 1674 (1960).

Ackley, M. H.

Alcaraz, E. C.

Bouricius, G. M. B.

Brookner, E.

E. Brookner, IEEE Trans COM-18, 396 (1970).
[Crossref]

Brown, W. P.

Bufton, J. L.

Burling, R. W.

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

Campbell, G. S.

T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmospheric Temperature Fluctuations, ECOM-5387 (available as AD 729 791, Clearinghouse, Springfield, Va., 1971).

Carlon, H. R.

Carlson, F. P.

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).

Clifford, S. F.

Coulman, C. E.

Deitz, P. H.

deWolf, D. A.

D. A. deWolf, J. Opt. Soc. Am. 62, 730A (1972).

Dungey, W. H.

W. H. Dungey, D. O. Tarazano, and J. C. Wyngaard, J. Opt. Soc. Am. 61, 1552A (1971).

Eiss, R.

Fitzmaurice, M. W.

Fried, D. L.

Gray, D. A.

The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated.Pertinent references areD. A. Gray and A. T. Waterman, J. Geophys. Res. 75, 1077 (1970)and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
[Crossref]

Hamblin, P. F.

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

Harp, J. C.

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

Heskestad, G.

G. Heskestad, J. Appl. Mech. 32, 735 (1965).
[Crossref]

Ishimaru, A.

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

Keister, M. P.

Kerr, J. R.

Kleen, R. H.

Koprov, V. M.

V. M. Koprov and L. R. Zwang, Izv. Atmos. Oceanic Phys. 2, 1142 (1966).

V. M. Koprov, Izv. Atmos. Oceanic Phys. 1, 1151 (1965).

Lawrence, R. S.

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).Familiarity with this review of scintillation phenomena is assumed in this paper.
[Crossref]

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[Crossref]

Lee, R. W.

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

Livingston, P. M.

Lumley, J. L.

J. L. Lumley, Phys. Fluids 8, 1056 (1965).
[Crossref]

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

Lutomirski, R. F.

Mano, K.

K. Mano, Proc. IEEE (Corresp.) 58, 1168 (1970).
[Crossref]

K. Mano, Proc. IEEE (Corresp.) 58, 1405 (1970).
[Crossref]

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Mevers, G. E.

Modesitt, G. E.

Ochs, G. R.

S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, and M. H. Ackley, J. Opt. Soc. Am. 61, 1279 (1971).
[Crossref]

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[Crossref]

R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
[Crossref]

G. R. Ochs, Measurements of 0.63 μm Laser-Beam Scintillation in Strong Atmospheric Turbulence, ESSA Technical Report No. ERL 154-WPL 10 (U. S. Government Printing Office, Washington, D. C., 1969).

Panofsky, H. A.

H. A. Panofsky, Radio Sci. 4, 1143 (1969).
[Crossref]

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

Pond, S.

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

Portman, D. J.

D. J. Portman, E. Ryznar, and A. A. Waqif, Laser Scintillation Caused by Turbulence Near the Ground, University of Michigan Research Report No. 225 (available as AD 666 798,Clearinghouse, Springfield, Va., 1968).

Pries, T. H.

T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmospheric Temperature Fluctuations, ECOM-5387 (available as AD 729 791, Clearinghouse, Springfield, Va., 1971).

Ryznar, E.

D. J. Portman, E. Ryznar, and A. A. Waqif, Laser Scintillation Caused by Turbulence Near the Ground, University of Michigan Research Report No. 225 (available as AD 666 798,Clearinghouse, Springfield, Va., 1968).

Saffman, P. G.

P. G. Saffman, in Topics in Nonlinear Physics, edited by N. J. Zabusky, (Springer, New York, 1968), p. 485.
[Crossref]

Sancer, M. I.

Smith, S. D.

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

Stewart, R. W.

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

Strohbehn, J. W.

R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).Familiarity with this review of scintillation phenomena is assumed in this paper.
[Crossref]

Tarazano, D. O.

W. H. Dungey, D. O. Tarazano, and J. C. Wyngaard, J. Opt. Soc. Am. 61, 1552A (1971).

Tatarski, V. I.

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

V. I. Tatarski, Propagation of Waves in a Turbulent Atmosphere (Nauka, Moscow, 1967).

Taylor, L. S.

Torrieri, D. J.

Varvatsis, A. D.

Waqif, A. A.

D. J. Portman, E. Ryznar, and A. A. Waqif, Laser Scintillation Caused by Turbulence Near the Ground, University of Michigan Research Report No. 225 (available as AD 666 798,Clearinghouse, Springfield, Va., 1968).

Waterman, A. T.

The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated.Pertinent references areD. A. Gray and A. T. Waterman, J. Geophys. Res. 75, 1077 (1970)and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
[Crossref]

Wilson, J. R.

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

Wyngaard, J. C.

W. H. Dungey, D. O. Tarazano, and J. C. Wyngaard, J. Opt. Soc. Am. 61, 1552A (1971).

Young, A. T.

Yura, H. T.

Zwang, L. R.

V. M. Koprov and L. R. Zwang, Izv. Atmos. Oceanic Phys. 2, 1142 (1966).

L. R. Zwang, Izv. Geophys. Series 8, 1252 (1960).

L. R. Zwang, Izv. Geophys. Series 8, 1674 (1960).

Appl. Opt. (3)

Astron. J. (1)

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

IEEE Trans (1)

E. Brookner, IEEE Trans COM-18, 396 (1970).
[Crossref]

Izv. Atmos. Oceanic Phys. (2)

V. M. Koprov and L. R. Zwang, Izv. Atmos. Oceanic Phys. 2, 1142 (1966).

V. M. Koprov, Izv. Atmos. Oceanic Phys. 1, 1151 (1965).

Izv. Geophys. Series (2)

L. R. Zwang, Izv. Geophys. Series 8, 1252 (1960).

L. R. Zwang, Izv. Geophys. Series 8, 1674 (1960).

J. Appl. Mech. (1)

G. Heskestad, J. Appl. Mech. 32, 735 (1965).
[Crossref]

J. Atmos. Sci. (1)

S. Pond, S. D. Smith, P. F. Hamblin, and R. W. Burling, J. Atmos. Sci. 23, 376 (1966).
[Crossref]

J. Fluid Mech. (2)

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
[Crossref]

J. Geophys. Res. (1)

The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated.Pertinent references areD. A. Gray and A. T. Waterman, J. Geophys. Res. 75, 1077 (1970)and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
[Crossref]

J. Opt. Soc. Am. (24)

R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
[Crossref]

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

P. M. Livingston, P. H. Deitz, and E. C. Alcaraz, J. Opt. Soc. Am. 60, 925 (1970).
[Crossref]

J. R. Kerr and R. Eiss, J. Opt. Soc. Am. 62, 682 (1972).
[Crossref]

D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
[Crossref]

S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
[Crossref]

D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
[Crossref]

D. L. Fried, G. E. Mevers, and M. P. Keister, J. Opt. Soc. Am. 57, 787 (1967).Note that independently scintillating patches equal to the diffraction scale of a finite transmitter aperture would result in improved aperture averaging, since this scale is smaller than (λL)12. Hence, it appears that transmitter-aperture effects cannot explain observations of poor receiver smoothing.
[Crossref]

M. W. Fitzmaurice and J. L. Bufton, J. Opt. Soc. Am. 59, 462 (1969).
[Crossref]

G. E. Modesitt, J. Opt. Soc. Am. 61, 797 (1971).
[Crossref]

H. T. Yura, J. Opt. Soc. Am. 59, 111 (1969).
[Crossref]

A. T. Young, J. Opt. Soc. Am. 60, 248 (1970).
[Crossref]

A. T. Young, J. Opt. Soc. Am. 60, 1495 (1970).
[Crossref]

C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
[Crossref]

W. H. Dungey, D. O. Tarazano, and J. C. Wyngaard, J. Opt. Soc. Am. 61, 1552A (1971).

M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 60, 654 (1970).
[Crossref]

W. P. Brown, J. Opt. Soc. Am. 61, 981 (1971).
[Crossref]

M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 61, 982 (1971).
[Crossref]

L. S. Taylor and D. J. Torrieri, J. Opt. Soc. Am. 62, 145 (1972).
[Crossref]

W. P. Brown, J. Opt. Soc. Am. 62, 45 (1972).
[Crossref]

D. A. deWolf, J. Opt. Soc. Am. 62, 730A (1972).

R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[Crossref]

S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, and M. H. Ackley, J. Opt. Soc. Am. 61, 1279 (1971).
[Crossref]

G. E. Mevers, M. P. Keister, and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).

Phys. Fluids (1)

J. L. Lumley, Phys. Fluids 8, 1056 (1965).
[Crossref]

Proc. IEEE (2)

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).Familiarity with this review of scintillation phenomena is assumed in this paper.
[Crossref]

Proc. IEEE (Corresp.) (2)

K. Mano, Proc. IEEE (Corresp.) 58, 1168 (1970).
[Crossref]

K. Mano, Proc. IEEE (Corresp.) 58, 1405 (1970).
[Crossref]

Radio Sci. (2)

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

H. A. Panofsky, Radio Sci. 4, 1143 (1969).
[Crossref]

Other (12)

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill, New York, 1960).

T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmospheric Temperature Fluctuations, ECOM-5387 (available as AD 729 791, Clearinghouse, Springfield, Va., 1971).

P. G. Saffman, in Topics in Nonlinear Physics, edited by N. J. Zabusky, (Springer, New York, 1968), p. 485.
[Crossref]

D. J. Portman, E. Ryznar, and A. A. Waqif, Laser Scintillation Caused by Turbulence Near the Ground, University of Michigan Research Report No. 225 (available as AD 666 798,Clearinghouse, Springfield, Va., 1968).

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

The measured scintillation variance may be reduced up to 20% (Sec. II E) owing to the nonzero receiver aperture. However, because of the (3/7) dependence in obtaining l0, the maximum effect on these points is to reduce the ordinate by 9%.

G. R. Ochs, Measurements of 0.63 μm Laser-Beam Scintillation in Strong Atmospheric Turbulence, ESSA Technical Report No. ERL 154-WPL 10 (U. S. Government Printing Office, Washington, D. C., 1969).

V. I. Tatarski, Propagation of Waves in a Turbulent Atmosphere (Nauka, Moscow, 1967).

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Receiver-aperture smoothing was apparently a significant factor in the results of Ref. 8. The scaling of finite receiver sizes by λ12 is not well justified under saturated conditions, in which covariances depart from those predicted by first-order theory.

This qualitative rule is suggested by an unpublished analysis by D. L. Fried, in which he derives the relationship between equipment dynamic range and maximum measured (i.e., apparent) log-amplitude variances.

J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).

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Figures (22)

F. 1
F. 1

Examples of rms temporal spectra of microthermal fluctuations measured at a single probe with a 1-Hz resolution. For a given run, each experimental point was obtained from an average over the same 5-min time period. Runs A and B resulted in the expected inertial-subrange slope of −0.83, changing to −1.7 at high frequencies. The break points imply inner scales of 1.0 and 3.3 cm, respectively. Run C resulted in a slope of −0.57.

F. 2
F. 2

Turbulence spectral (rms) slope (×) and inner scale (○), obtained as shown in Fig. 1 vs strength of turbulence. The theoretical or inertial-subrange slope of 5 6 is shown.

F. 3
F. 3

Turbulence spectral slope (×) and inner scale (○) vs wind speed. The inertial-subrange slope of 5 6 is shown.

F. 4
F. 4

Experimental vs theoretical log-amplitude variance for 4880 Å. The circles indicate a relatively good inertial-subrange turbulence spectrum.

F. 5
F. 5

Experimental vs theoretical log-amplitude variance for 1.15 μm.

F. 6
F. 6

Experimental vs theoretical log-amplitude variance for 10.6 μm.

F. 7
F. 7

Experimental vs theoretical log-amplitude variance for 4880 Å, 1.15 μm, and 10.6 μm combined.

F. 8
F. 8

Experimental log-amplitude variances for 4880 Å vs 1.15 μm (●) and 10.6 μm (×).

F. 9
F. 9

Inner scales as determined from short-path scintillations measured at 6328 Å vs those from microthermal spectra.

F. 10
F. 10

Transverse log-amplitude correlation length ra at 4880 Å (×), 1.15 μm (●), and 10.6 μm (+) vs strength of turbulence. Theoretical values are indicated for each wavelength. The abscissa is given in terms of Cn2 and also corresponding theoretical log-amplitude variances for each wavelength.

F. 11
F. 11

Transverse log-amplitude correlation length ra for 4880 Å vs 1.15 μm. The theoretical value is indicated by (×).

F. 12
F. 12

Transverse log-amplitude correlation length ra for 4880 Å vs 10.6 μm. The theoretical value is indicated by (×).

F. 13
F. 13

Ratio of peak frequencies of scintillation spectra for 4880 Å and 10.6 μm vs strength of turbulence [Eq. (1)]. The theoretical value implied by Eq. (4) is indicated.

F. 14
F. 14

Ratio of peak frequencies of scintillation spectra for 1.15 and 10.6 μm vs strength of turbulence. The theoretical value is indicated.

F. 15
F. 15

Ratio of (peak frequency times transverse correlation length) for 4880 Å and 10.6 μm vs strength of turbulence.

F. 16
F. 16

Ratio of (peak frequency times transverse correlation length) for 1.15 and 10.6 μm vs strength of turbulence.

F. 17
F. 17

Ratio of log-amplitude variances at 4880 Å for large and small receivers, vs strength of turbulence.

F. 18
F. 18

Ratio of log-amplitude variances at 4880 Å for large and small receivers, vs transverse log-amplitude correlation length.

F. 19
F. 19

Ratio of log-amplitude variances at 4880 Å for large and small receivers, vs normalized covariance at r = 4 cm.

F. 20
F. 20

Log-amplitude variances at three wavelengths for 10-s averaging times, vs time.

F. 21
F. 21

Log-amplitude variances and turbulence strengths for 10-s averaging times, vs time.

F. 22
F. 22

Log-amplitude variances and turbulence strength for 10-s averaging times, vs time.

Tables (2)

Tables Icon

Table I Experimental measurements.

Tables Icon

Table II Experimental parameters.

Equations (9)

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σ T 2 = 0.124 C n 2 k 7 / 6 L 11 / 6 ,
σ 2 = 0.32 C n 2 L 3 l 0 7 / 3 .
C l ( r a ) C l ( 0 ) = 1 e ,
f m ( λ L ) 1 2 υ = ( constant ) ,
σ 2 = 0.14 k 7 / 6 0 L C n 2 ( z ) ( z / L ) 5 / 6 ( L z ) 5 / 6 d z .
dynamic range 100 σ 2 .
L cr = β λ m C n p ,
σ max 2 = 0.124 C n 2 k 7 / 6 L cr 11 / 6 = 1.05 β 11 / 6 λ ( 11 m 7 ) / 6 C n ( 12 11 p ) / 6 .
m + p / 3 = 1 .