Abstract

We report the results of 1,049 measurements of the vertical profile of optical turbulence as recorded by a scintillometer above a site at White Sands Missile Range. The distributional law for these measurements is shown to be approximately log normal and examples of monthly to hourly variations in profile structure are presented. An estimate is formed for the isoplanatic angle for wave propagation through each profile by calculating its five-third moment. The ensemble of these calculations is found to be log normally distributed with a mean of 7.2 μrad at a wavelength of 0.5 μm. A strong temporal correction is observed between the size of the isoplanatic angle and the intensity of scintillations. We develop a theory based upon aperture averaging to account for this phenomenon and propose the use of scintillometry to make direct measurements of isoplanatism.

© 1979 Optical Society of America

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References

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  1. G. R. Ochs, T. Wang, R. S. Lawrence, Appl. Opt. 15, 2504 (1976).
    [CrossRef] [PubMed]
  2. M. G. Miller, P. L. Zieske, Prof. SPIE 75, 30 (1976).
    [CrossRef]
  3. Barletti et al., J. Opt. Soc. Am. 66, 1380 (1976).
    [CrossRef]
  4. J. H. Shapiro, J. Opt. Soc. Am. 65, 65 (1975).
    [CrossRef]
  5. D. L. Fried, “Isoplanatism Dependence of a Ground to Space Laser Transmitter with Adaptive Optics,” Optical Sciences Company Report No. TR-249 (1977).
  6. D. L. Fried, Proc. IEEE 55, 57 (1967).
    [CrossRef]
  7. D. L. Fried, J. Opt. Soc. Am. 57, 169 (1967).
    [CrossRef]
  8. R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 59, 1247 (1969).
    [CrossRef]
  9. P. H. Taft, M. Hoidale, “White Sands Missile Range Climatology No. 5 Stallion Site, WSMR,” Atmospheric Sciences Laboratory Report DR-399 (1969), p 8.
  10. E. W. Rork, MIT Lincoln Laboratory personal communication. This table is extracted from a log of cloud conditions maintained at the Project GEODDS field site.

1976 (3)

1975 (1)

1969 (1)

1967 (2)

Barletti,

Fried, D. L.

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

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

D. L. Fried, “Isoplanatism Dependence of a Ground to Space Laser Transmitter with Adaptive Optics,” Optical Sciences Company Report No. TR-249 (1977).

Hoidale, M.

P. H. Taft, M. Hoidale, “White Sands Missile Range Climatology No. 5 Stallion Site, WSMR,” Atmospheric Sciences Laboratory Report DR-399 (1969), p 8.

Lawrence, R. S.

Lutomirski, R. F.

Miller, M. G.

M. G. Miller, P. L. Zieske, Prof. SPIE 75, 30 (1976).
[CrossRef]

Ochs, G. R.

Rork, E. W.

E. W. Rork, MIT Lincoln Laboratory personal communication. This table is extracted from a log of cloud conditions maintained at the Project GEODDS field site.

Shapiro, J. H.

Taft, P. H.

P. H. Taft, M. Hoidale, “White Sands Missile Range Climatology No. 5 Stallion Site, WSMR,” Atmospheric Sciences Laboratory Report DR-399 (1969), p 8.

Wang, T.

Yura, H. T.

Zieske, P. L.

M. G. Miller, P. L. Zieske, Prof. SPIE 75, 30 (1976).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (4)

Proc. IEEE (1)

D. L. Fried, Proc. IEEE 55, 57 (1967).
[CrossRef]

Prof. SPIE (1)

M. G. Miller, P. L. Zieske, Prof. SPIE 75, 30 (1976).
[CrossRef]

Other (3)

D. L. Fried, “Isoplanatism Dependence of a Ground to Space Laser Transmitter with Adaptive Optics,” Optical Sciences Company Report No. TR-249 (1977).

P. H. Taft, M. Hoidale, “White Sands Missile Range Climatology No. 5 Stallion Site, WSMR,” Atmospheric Sciences Laboratory Report DR-399 (1969), p 8.

E. W. Rork, MIT Lincoln Laboratory personal communication. This table is extracted from a log of cloud conditions maintained at the Project GEODDS field site.

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Figures (17)

Fig. 1
Fig. 1

Stellar scintillometer. Inset depicts method of operation.

Fig. 2
Fig. 2

Composite path-weighting functions for the stellar scintillometer.

Fig. 3
Fig. 3

Cumulative probability of C n 2 at 2.2 km.

Fig. 4
Fig. 4

Cumulative probability of C n 2 at 3.4 km.

Fig. 5
Fig. 5

Cumulative probability of C n 2 at 5.2 km.

Fig. 6
Fig. 6

Cumulative probability of C n 2 at 7.3 km.

Fig. 7
Fig. 7

Cumulative probability of C n 2 at 9.4 km.

Fig. 8
Fig. 8

Cumulative probability of C n 2 at 14 km.

Fig. 9
Fig. 9

Cumulative probability of C n 2 at 18.5 km.

Fig. 10
Fig. 10

Logarithmic average of 1,049 C n 2 profiles with ±1σ points of the distribution at each level.

Fig. 11
Fig. 11

Comparison with other profile measurements.

Fig. 12
Fig. 12

Comparison with Hufnagel model.

Fig. 13
Fig. 13

Monthly average C n 2 profile measurements.

Fig. 14
Fig. 14

An example of the temporal variability of C n 2 profiles. θISO is the isoplanatic angle calculated for the average turbulence profile within each 20-min interval.

Fig. 15
Fig. 15

Cumulative probability of isoplanatic angle size.

Fig. 16
Fig. 16

Two examples illustrating the temporal correlation between isoplanatism and scintillation measurements.

Fig. 17
Fig. 17

Scintillations weighting function H (0.356m, η) for the stellar scintillometer compared to H(D,η) for a point aperture (η15/6) and H(D,η) required for an isoplanometer (η5/3).

Equations (28)

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G = 8 k 2 0 2 π d ϕ 0 D r d r τ D L ( r D ) exp [ - M ( r , ϕ , θ ) ] ,
τ D L ( r D ) = 2 π { cos - 1 ( r D ) - ( r D ) [ 1 - ( r D ) 2 ] 1 / 2 } ,
H 0 5 / 3 = 0 d h C n 2 ( h ) h 5 / 3 0 d h C n 2 ( h )
6.88 r 0 - 5 / 3 = 2.91 k 2 ( sec χ ) 0 C n 2 ( h ) d h ,
M ( r , ϕ , θ ) = 6.88 ( r r 0 ) 5 / 3 for r θ H 0 sec χ .
θ 0 - 5 / 3 = 6.88 r 0 - 5 / 3 ( cos χ ) - 5 / 3 H 0 5 / 3
θ 0 = 0.314 r 0 cos χ / H 0 ,
M ( r , ϕ , θ ) = ( θ θ 0 ) 5 / 3 for r θ H 0 sec χ .
G = D 2 k 2 4 π exp [ - ( θ / θ 0 ) 5 / 3 ] .
θ = θ 0 = 0.314 r 0 cos χ / H 0 ,
θ = θ 0 = 0.528 [ k 2 0 d h C n 2 ( h ) h 5 / 3 ] - 3 / 5 .
σ χ 2 = 0.56 k 2 0 L C n 2 ( z ) z 5 / 6 d z ,
σ ln I 2 = 4 σ χ 2 .
S ( t ) = d A I ( x ¯ , t ) .
θ ( D ) = σ s 2 ( D ) ( π D 2 4 ) 2 B I ( o ) ,
B I ( o ) = σ I 2 ,
θ ( D ) = 8 D 2 0 D ρ d ρ b I ( ρ ) M ( ρ , D ) ,
b I ( ρ ) = B I ( ρ ) σ I 2 .
M ( ρ , D ) = 2 / π { cos - 1 ( ρ D ) - ρ D [ 1 - ( ρ D ) 2 ] 1 / 2 } .
b I ( ρ ) = b χ ( ρ ) ,
θ ( D ) = 16 π D 2 0 D ρ d ρ b χ ( ρ ) { cos - 1 ( ρ D ) - ρ D [ 1 - ( ρ D ) 2 ] 1 / 2 } .
b χ ( ρ ) = 4 π 2 ( 0.033 ) σ χ 2 k 2 0 L d z C n 2 ( z ) × 0 K d K J 0 ( K ρ ) K - 11 / 3 sin 2 ( K 2 z 2 k ) .
θ ( D ) = 16 π D 2 4 π 2 ( 0.033 ) k 2 σ χ 2 0 L d z C n 2 ( z ) 0 K d K K - 11 / 3 sin 2 ( K 2 z 2 k ) × 0 D ρ d ρ J 0 ( K ρ ) { cos - 1 ( ρ D ) - ρ D [ 1 - ( ρ D ) 2 ] 1 / 2 } .
θ ( D ) = 64 π k 2 ( 0.033 ) σ χ 2 D 5 / 3 L 0 1 d η [ C n 2 ( η ) H ( D , η ) ] ,
H ( D , η ) = 0 ζ d ζ G ( ζ ) ζ - 11 / 3 sin 2 ( ζ 2 η 2 × L k D 2 ) ,
G ( ζ ) = 0 1 x d x J 0 ( ζ x ) [ cos - 1 ( x ) - x ( 1 - x 2 ) 1 / 2 ] = π ζ 2 J 1 2 ( ζ 2 ) .
d d D 0 1 [ H ( D , η ) - H ( D , 1 ) η 5 / 3 ] 2 d η d d D 0 1 H 2 ( D , η ) d η = 0 ,
0 1 [ H ( D , η ) - H ( D , 1 ) η 5 / 3 ] d η 0 1 H ( D , η ) d η = 0.

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