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.

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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.
  2. J. R. Kerr and R. Eiss, J. Opt. Soc. Am. 62, 682 (1972).
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1961).
  4. A. Ishimaru, Radio Sci. 4, 295 (1969).
  5. F. P. Carlson, J. Opt. Soc. Am. 59, 1343 (1969).
  6. P. M. Livingston, P. H. Deitz, and E. C. Alcaraz, Jr., J. Opt. Soc. Am. 60, 925 (1970).
  7. The structure of turbulence for scale sizes smaller than the inner scale has not been widely investigated. Pertinent references are D. A. Gray and A. T. Waterman, Jr., J. Geophys. Res. 75, 1077 (1970) and Yih-Ho Pao, Phys. Fluids 8, 1063 (1963).
  8. R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
  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).
  11. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
  12. A. T. Young, Astron. J. 72, 747 (1967).
  13. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  14. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
  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, Jr., 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)½. Hence, it appears that transmitteraperture effects cannot explain observations of poor receiver smoothing.
  17. G. R. Ochs, Measurements of 0.63 µm Laser-Beam Scintillation in Strong Atmnospheric 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).
  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).
  21. Receiver-aperture smoothing was apparently a significant factor in the results of Ref. 8. The scaling of finite receiver sizes by λ½ 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, Jr., and D. L. Fried, J. Opt. Soc. Am. 59, 491 (1969).
  23. L. A. Chernov, Wave Propagation in a Randomn Medium (McGraw-Hill, New York, 1960).
  24. G. E. Modesitt, J. Opt. Soc. Am. 61, 797 (1971).
  25. H. T. Yura, J. Opt. Soc. Am. 59, 111 (1969).
  26. K. Mano, Proc. IEEE (Corresp.) 58, 1168 (1970).
  27. K. Mano, Proc. IEEE (Corresp.) 58, 1405 (1970).
  28. M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 60, 654 (1970).
  29. W. P. Brown, Jr., J. Opt. Soc. Am. 61, 981 (1971).
  30. M. I. Sancer and A. D. Varvatsis, J. Opt. Soc. Am. 61, 982 (1971).
  31. L. S. Taylor and D. J. Torrieri, J. Opt. Soc. Am. 62, 145 (1972).
  32. W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).
  33. D. A. deWolf, J. Opt. Soc. Am. 62, 730A (1972).
  34. R. F. Lutomnirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).
  35. A. T. Young, Appl. Opt. 8, 869 (1969).
  36. A. T. Young, J. Opt. Soc. Am. 60, 248 (1970).
  37. A. T. Young, J. Opt. Soc. Am. 60, 1495 (1970).
  38. C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
  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, Tue 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).
  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).
  47. S. F. Clifford, G. M. B. Bouricius, G. R. Ochs, and M. H. Ackley, J. Opt. Soc. Am. 61, 1279 (1971).
  48. R. W. Stewart, J. R. Wilson, and R. W. Burling, J. Fluid Mech. 41, 141 (1970).
  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, Clearing house, Springfield, Va., 1968).
  50. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
  51. T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmnospheric Temnperature 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.
  53. E. Brookner, IEEE Trans. COM-18, 396 (1970).
  54. J. L. Lumley, Phys. Fluids 8, 1056 (1965).
  55. G. Heskestad, J. Appl. Mech. 32, 735 (1965).
  56. H. R. Canon, Appl. Opt. 4, 1089 (1965).
  57. R. W. Lee and J. C. Harp, Proc. IEEE 57, 375 (1969).

Ackley, M. H.

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

Alcaraz, Jr., E. C.

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

Bouricius, G. M. B.

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

Brookner, E.

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

Brown, Jr., W. P.

W. P. Brown, Jr., J. Opt. Soc. Am. 61, 981 (1971).

W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).

Bufton, J. L.

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

Burling, R. W.

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

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

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

Campbell, G. S.

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

Canon, H. R.

H. R. Canon, Appl. Opt. 4, 1089 (1965).

Carlson, F. P.

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

Chernov, L. A.

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

Clifford, S. F.

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

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

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

Coulman, C. E.

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

Deitz, P. H.

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

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.

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

Fitzmaurice, M. W.

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

Fried, D. L.

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

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., 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)½. Hence, it appears that transmitteraperture effects cannot explain observations of poor receiver smoothing.

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

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

Gray, D. A.

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

Hamblin, P. F.

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

Harp, J. C.

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

Heskestad, G.

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

Ishimaru, A.

A. Ishimaru, Radio Sci. 4, 295 (1969).

Keister, Jr., M. P.

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., 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)½. Hence, it appears that transmitteraperture effects cannot explain observations of poor receiver smoothing.

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

Kerr, J. R.

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

Kleen, R. H.

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

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.

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

Lee, R. W.

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

Livingston, P. M.

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

Lumley, J. L.

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

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

Lutomnirski, R. F.

R. F. Lutomnirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

Mano, K.

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

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

Mertz, L.

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

Mevers, G. E.

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

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., 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)½. Hence, it appears that transmitteraperture effects cannot explain observations of poor receiver smoothing.

Modesitt, G. E.

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

Ochs, G. R.

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

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

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

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

Panofsky, H. A.

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

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

Pond, S.

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

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, Clearing house, Springfield, Va., 1968).

Pries, T. H.

T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmnospheric Temnperature 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, Clearing house, 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.

Sancer, M. I.

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

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

Smith, S. D.

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

Stewart, R. W.

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

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

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.

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.

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

Torrieri, D. J.

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

Varvatsis, A. D.

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

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

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, Clearing house, Springfield, Va., 1968).

Waterman, Jr., A. T.

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

Wilson, J. R.

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

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

Wyngaard, J. C.

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

Young, A. T.

A. T. Young, Appl. Opt. 8, 869 (1969).

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

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

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

Yura, H. T.

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

R. F. Lutomnirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

Zwang, L. R.

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

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

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

Other (57)

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

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

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

A. Ishimaru, Radio Sci. 4, 295 (1969).

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

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

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

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

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%.

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

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

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

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

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

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

D. L. Fried, G. E. Mevers, and M. P. Keister, Jr., 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)½. Hence, it appears that transmitteraperture effects cannot explain observations of poor receiver smoothing.

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

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

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.

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

Receiver-aperture smoothing was apparently a significant factor in the results of Ref. 8. The scaling of finite receiver sizes by λ½ is not well justified under saturated conditions, in which covariances depart from those predicted by first-order theory.

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

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

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

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

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

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

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

W. P. Brown, Jr., J. Opt. Soc. Am. 61, 981 (1971).

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

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

W. P. Brown, Jr., J. Opt. Soc. Am. 62, 45 (1972).

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

R. F. Lutomnirski and H. T. Yura, Appl. Opt. 10, 1652 (1971).

A. T. Young, Appl. Opt. 8, 869 (1969).

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

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

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

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

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

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

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

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

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

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

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

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

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

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, Clearing house, Springfield, Va., 1968).

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

T. H. Pries and G. S. Campbell, Spectral Analysis of High-Frequency Atmnospheric Temnperature 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.

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

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

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

H. R. Canon, Appl. Opt. 4, 1089 (1965).

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

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