Abstract

Scintillation measurements are described for a very-large integrated-path turbulence. Measurements were made with simultaneous, coincident beams at 10.6 μm and 4880 Å over a 6-km uniform path. The experimental results include (i) the (log amplitude) variance at 10.6 μm showed saturation at a level comparable to that for shorter wavelengths; (ii) the variance beyond saturation at 4880 Å decreased for increasing turbulence (Cn2), with an exponent of (−0.48) and no apparent asymptote; (iii) the covariance functions, Cl(r), exhibited the emergence of two scale sizes, as manifested by a rapid initial drop vs (r), and a residual correlation out to large separations; (iv) a corresponding effect was revealed by the spectra of scintillations; (v) receiver-aperture smoothing at 4880 Å was very poor, owing to the large residual correlation sizes; and (vi) the amplitude statistics at both wavelengths approximated log-normal distributions.

© 1973 Optical Society of America

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References

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  1. R. S. Lawrence and J. W. Strohbehn, Proc. IEEE 58, 1523 (1970).
    [Crossref]
  2. J. Richard Kerr, J. Opt. Soc. Am. 62, 1040 (1972).
    [Crossref]
  3. W. P. Brown, J. Opt. Soc. Am. 62, 966 (1972).
    [Crossref]
  4. D. A. de Wolf, J. Opt. Soc. Am. 63, 171 (1973).
    [Crossref]
  5. Note that Eq. (T13) of Ref. 1 has an incorrect coefficient. The correct value is 2.24.
  6. J. C. Wyngaard, Y. Izumi, and S. A. Collins, J. Opt. Soc. Am. 61, 1646 (1971).
    [Crossref]
  7. R. H. Kleen and G. R. Ochs, J. Opt. Soc. Am. 60, 1695 (1970).
    [Crossref]
  8. H. T. Yura, Aerospace Corp., Los Angeles, Calif. (private communication).
  9. H. R. Carlon, Appl. Opt. 4, 1089 (1965).
    [Crossref]
  10. D. A. de Wolf, J. Opt. Soc. Am. 59, 1455 (1969).
    [Crossref]

1973 (1)

1972 (2)

1971 (1)

1970 (2)

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

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

1969 (1)

1965 (1)

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Figures (14)

Fig. 1
Fig. 1

Experimental log-amplitude variance vs time of day. (×): 4880 Å on 14 September 1972; (○): 10.6 pm on 14 September 1972; (●): 4880 Å on 29 August 1972. The weather was clear except for a trace of ground fog from 0600 to 0700 on 14 September. During the neutral period, typically 0700–0800, the turbulence was poorly developed.

Fig. 2
Fig. 2

Log-amplitude variance at 10.6 μm vs strength of turbulence at 1.8-m height. The data points include several clear days of operation.

Fig. 3
Fig. 3

Same as Fig. 2, for 4880 Å.

Fig. 4
Fig. 4

Experimental vs theoretical (Rytov) log-amplitude variance for 10.6 μm. The abscissa is corrected for beam refraction and earth-curvature effects. The line indicates the (σE2 = σT2) condition.

Fig. 5
Fig. 5

Same as Fig. 4, for 4880 Å. The equation of the linear regression line is log10σB2 = (−0.22)−(0.48) log10σT2, with a correlation coefficient of 0.78.

Fig. 6
Fig. 6

Experimental variances at 4880 Å vs those at 10.6 μm. The line represents a k7/6 dependence.

Fig. 7
Fig. 7

Transverse log-amplitude covariance length vs strength of turbulence. The experimental and theoretical (Rytov) values are for 4880 Å (×, ——) and 10.6 μm (○, - - - -).

Fig. 8
Fig. 8

Normalized covariance curves for 10.6 μm. The normalizing quantity Cl(0) is identical to σE2 and the 1/e points are indicated. The broken line represents the theoretical (Rytov) function.

CurveCn2σT2
A4.2 × 10−152.6 × 10−3
B3.6 × 10−133.0 × 10−1
C5.9 × 10−135.9 × 10−1
D3.2 × 10−123.9
Fig. 9
Fig. 9

Same as Fig. 8, for 4880 Å.

CurveCn2σT2
A4.5 × 10−151.0 × 10−1
B3.8 × 10−131.2 × 101
C6.3 × 10−132.3 × 101
D3.4 × 10−121.5 × 102
Fig. 10
Fig. 10

RMS scintillation spectra at 10.6 μm for the Cn2 values of Fig. 8. The 1/e frequencies are indicated.

Fig. 11
Fig. 11

RMS scintillation spectra at 4880 Å for the Cn2 values of Fig. 9.

Fig. 12
Fig. 12

Linear (left) and log (right) irradiance scintillations at 4880 Å. The pictures from top to bottom represent Cn2 values A–D, respectively, of Fig. 9. The abscissa is 0.2 s/cm; the ordinate for the log signal is one decade of irradiance per cm. The linear baseline is 1 cm up from the bottom of each frame; the log baseline is indefinite and not pertinent.

Fig. 13
Fig. 13

Same as Fig. 12, for 10.6 μm. The turbulence levels are those of Fig. 8.

Fig. 14
Fig. 14

Cumulative probability distributions for log irradiance

CurveWavelengthCn2σT2
A4880 Å4.5 × 10−151.0 × 10−1
B4880 Å3.4 × 10−121.5 × 102
C10.6 μm4.2 × 10−152.6 × 10−3
D10.6 μm3.2 × 10−123.9

Tables (4)

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Table I Experimental measurements.

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Table II Experimental parameters.

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Table III Beam height (in meters) vs temperature gradient and distance.

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Table IV Typical receiver-aperture smoothing results at 4880 Å. The receiver-smoothing factor Ω is the log-amplitude variance for a 32-cm receiver, normalized by that for a small (6-mm) receiver.

Equations (4)

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σ T 2 = 0.56 k 7 / 6 0 L C n 2 ( x ) ( x L ) 5 / 6 ( L x ) 5 / 6 d x ,
σ T 2 = 0.56 k 7 / 6 z 0 4 / 3 C n 2 ( z 0 ) L 5 / 6 × 0 L z ( x ) 4 / 3 x 5 / 6 ( L x ) 5 / 6 d x ,
d n ( z ) d z ~ β .
0.60 < 0.48 < 0.36 .