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  1. R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971).
    [CrossRef] [PubMed]
  2. R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971).
    [CrossRef]
  3. C. E. Coulman, Solar Phys. 7, 122 (1969).
    [CrossRef]
  4. For example, ρo can be obtained by varying the slit separation in a Young’s interferometer and noting the separation where the fringe visibility is down by 1/e (as compared to its value for small slit separations).
  5. The spot size is defined here as twice the distance from the z axis where the mean irradiance distribution is down by 1/e.
  6. The mathematical expression used here to represent this aperture disturbance is given byUA(r)=Uo exp[-r2(wo-2+ikf-1)/2].
  7. We note that the detailed computer calculations of Lutomirski on the propagation of a truncated Gaussian wavefront in a turbulent atmosphere8 show that the results for the nontruncated Gaussian are valid when the truncation diameter exceeds 2wo. Conversely, when 2wo exceeds the truncation diameter, the results obtained in Ref. 1 for a plane wave in a circular aperture are applicable.
  8. R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).
  9. Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82).
    [CrossRef]
  10. S. Valley, ed., Handbook of Geophysics (Macmillan, New York, 1960), pp. 13–1, 13–2.
  11. R. S. Lawrence, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
    [CrossRef]

1971 (2)

1970 (2)

1969 (1)

C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]

Beran, M. J.

Clifford, S. F.

Coulman, C. E.

C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]

Lawrence, R. S.

Lutomirski, R. F.

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

R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971).
[CrossRef]

R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).

Ochs, G. R.

Whitman, A. M.

Yura, H. T.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Solar Phys. (1)

C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]

Other (6)

For example, ρo can be obtained by varying the slit separation in a Young’s interferometer and noting the separation where the fringe visibility is down by 1/e (as compared to its value for small slit separations).

The spot size is defined here as twice the distance from the z axis where the mean irradiance distribution is down by 1/e.

The mathematical expression used here to represent this aperture disturbance is given byUA(r)=Uo exp[-r2(wo-2+ikf-1)/2].

We note that the detailed computer calculations of Lutomirski on the propagation of a truncated Gaussian wavefront in a turbulent atmosphere8 show that the results for the nontruncated Gaussian are valid when the truncation diameter exceeds 2wo. Conversely, when 2wo exceeds the truncation diameter, the results obtained in Ref. 1 for a plane wave in a circular aperture are applicable.

R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).

S. Valley, ed., Handbook of Geophysics (Macmillan, New York, 1960), pp. 13–1, 13–2.

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Figures (1)

Fig. 1
Fig. 1

Angular beam spread, normalized to that of a 15-cm diffraction limited 0.53-μ laser beam as a function of the height of the laser transmitter above ground. The elevation of the transmitter site and zenith angle are taken as 3 km and 30°, respectively. The three curves correspond to the meteorological conditions referred to in Ref. 3. Curve (1) refers to average conditions during the midpart of clear summer days. Curve (2) refers to average conditions on clear summer days about 1 h before sunset. Curve (3) refers to conditions in the temperature-quiescent regions of air between convective plumes.

Tables (1)

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Table I Summary of Spherical Wave Lateral Coherence Lengths and Beam Spreads for an Initially Gaussian Wavefronta

Equations (8)

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ρ o [ 1.45 k 2 sec α z 1 z 2 C n 2 ( z ) ( z 2 - z z 2 - z 1 ) / d z ] - / ,
p o 2 z / k D , for ρ o D .
p T 2 z / k ρ o , for ρ o D .
S . S . ( λ / D ) f , for ρ o D [ λ / ρ o ( f ) ] f , for ρ o D .
p 1 2 p o 2 + [ 4 z 2 / k 2 ρ o 2 ( z ) ] ,
p o 2 = w o 2 [ 1 - ( z / f ) ] 2 + ( z 2 / k 2 w o 2 ) .
C n ( z ) 10 - 6 [ d ( z ) / d 0 ] [ 288.15 + 1.34 λ - 2 / T ( z ) ] C T ,
UA(r)=Uoexp[-r2(wo-2+ikf-1)/2].

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