Abstract

The aspect of atmospheric turbulence of interest to optical-propagation studies is the variation of refractive index. We demonstrate the application of high-speed temperature sensors to the direct measurement of this variation at optically important scale sizes, as small as a few millimeters. The thermometers, used in pairs with spacings ranging from 3 mm to 1 m, disclose that the turbulence near the ground frequently differs substantially from the Kolmogoroff model, and that the temperature difference does not follow the gaussian probability-distribution function. A model of the turbulent atmosphere containing sharply bounded regions with stronger than average turbulence agrees well with our observations. We also demonstrate the use of a single sensor mounted on an airplane to observe refractive-index variations at heights up to 3 km.

© 1970 Optical Society of America

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References

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  1. G. R. Ochs, ESSA Tech. Rept. IER 47-ITSA 46 (U. S. Govt. Printing Office, Washington, D. C., 1967).
  2. A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
    [Crossref]
  3. V. M. Koprov and L. R. Tsvang, Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. 2, 1142 (1966).
  4. J. W. Strohbehn, private communication (1969).
  5. C. E. Coulman, Solar Phys. 7, 122 (1969).
    [Crossref]
  6. R. E. Hufnagel, in Restoration of Atmospherically Degraded Images (Natl. Academy of Sciences, Washington, D. C., 1966), Vol. 2, p. 14.

1969 (1)

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

1967 (1)

A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
[Crossref]

1966 (1)

V. M. Koprov and L. R. Tsvang, Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. 2, 1142 (1966).

Coulman, C. E.

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

Deam, A. P.

A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
[Crossref]

Dodd, J. L.

A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
[Crossref]

Hufnagel, R. E.

R. E. Hufnagel, in Restoration of Atmospherically Degraded Images (Natl. Academy of Sciences, Washington, D. C., 1966), Vol. 2, p. 14.

Koprov, V. M.

V. M. Koprov and L. R. Tsvang, Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. 2, 1142 (1966).

Ochs, G. R.

G. R. Ochs, ESSA Tech. Rept. IER 47-ITSA 46 (U. S. Govt. Printing Office, Washington, D. C., 1967).

Straiton, A. W.

A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
[Crossref]

Strohbehn, J. W.

J. W. Strohbehn, private communication (1969).

Tsvang, L. R.

V. M. Koprov and L. R. Tsvang, Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. 2, 1142 (1966).

Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. (1)

V. M. Koprov and L. R. Tsvang, Bull. (Izv.) Acad. Sci. USSR, Atm. Oceanic Phys. 2, 1142 (1966).

J. Geophys. Res. (1)

A. W. Straiton, A. P. Deam, and J. L. Dodd, J. Geophys. Res. 72, 4051 (1967).
[Crossref]

Solar Phys. (1)

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

Other (3)

R. E. Hufnagel, in Restoration of Atmospherically Degraded Images (Natl. Academy of Sciences, Washington, D. C., 1966), Vol. 2, p. 14.

G. R. Ochs, ESSA Tech. Rept. IER 47-ITSA 46 (U. S. Govt. Printing Office, Washington, D. C., 1967).

J. W. Strohbehn, private communication (1969).

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Figures (12)

Fig. 1
Fig. 1

Samples of high-speed temperature measurements made 1.5 m above the ground on a calm, sunny day. Noon, 23 September 1969.

Fig. 2
Fig. 2

Samples of temperature-difference measurements made on a clear, sunny day with sensors 1.5 m above the ground, spaced 10 cm apart. Noon, 23 September 1969.

Fig. 3
Fig. 3

The distribution function of temperature-difference measurements made with sensors separated vertically by 3 cm, placed 2 m above the ground, compared with a model consisting of a gaussian distribution modulated by a rectangular wave. Noon, 14 January 1969.

Fig. 4
Fig. 4

The refractive-index structure parameter as measured with spaced temperature sensors having spacings of 1, 3, and 10 cm. 7 September 1968.

Fig. 5
Fig. 5

The refractive-index structure parameter as measured with spaced temperature sensors having two different spacings. 8 September 1968.

Fig. 6
Fig. 6

The log-amplitude variance of laser-beam scintillations observed simultaneously with the refractive-index variations shown in Fig. 5.

Fig. 7
Fig. 7

Typical daytime observations of the temperature structure function (1-h averages). 24 April 1969.

Fig. 8
Fig. 8

Typical nighttime observations of the temperature structure function (1-h averages). 24 April 1969.

Fig. 9
Fig. 9

Airborne temperature-fluctuation records, made on a sunny day in connection with a 5.5-km laser-beam propagation measurement. Average height above the ground is 200 ft. 3 July 1967.

Fig. 10
Fig. 10

Measurements, made in the forenoon of a sunny day with an airborne temperature sensor, of the variation of the refractive-index structure parameter in the first 3 km above the ground. Hufnagel’s models for normal conditions (smooth curve) and disturbed layers (dashed curve) are shown for comparison. 1100–1130 MST, 22 October 1968.

Fig. 11
Fig. 11

Measurements, made in the afternoon of a sunny day with an airborne temperature sensor, of the variation of the refractive-index structure parameter in the first 3 km above the ground. Hufnagel’s models for normal conditions (smooth curve) and disturbed layers (dashed curve) are shown for comparison. 1430–1500 MST, 26 November 1968.

Fig. 12
Fig. 12

Measurements, made on a clear evening with an airborne temperature sensor, of the variation of the refractive-index structure parameter in the first 3 km above the ground. Hufnagel’s models for normal conditions (smooth curve) and disturbed layers (dashed curve) are shown for comparison. 2030–2100 MST, 26 November 1968.

Equations (4)

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C T 2 = ( T 2 - T 1 ) 2 / r 2 3 av = D T / r 2 3 .
C n 2 = [ ( 79 p / T 2 ) 10 - 6 ] 2 C T 2 ,
C T 2 = 2.68 T 2 ( v / ω L ) 2 3 - ( v / ω H ) 2 3 ,
T 2 av = a ( Δ T av 2 - N ¯ 2 ) = a ( T - T ¯ av 2 - N ¯ 2 ) .