Abstract

We present the results of measurements of the optical phase variations on a short line-of-sight path through the turbulent atmosphere. A helium–neon laser (6328 Å) propagates along a folded 50-m path that is one arm of a Michelson interferometer, and its interference fringes are observed. A measured time-lagged structure function, found by using Taylor’s hypothesis, compares well with the theoretical predictions of Tatarski for a broad range of effective separations, in contrast with earlier observations. Simultaneous measurements of Cn2 are made to facilitate comparison with theory. Values of the outer scale, deduced from temperature measurements at a different time at the same location, indicate excellent agreement with the spacing corresponding to the knee of the observed phase structure function, a result predicted by Tatarski’s theory and not previously observed.

© 1970 Optical Society of America

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References

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  1. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1960).
  2. R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).
  3. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
    [CrossRef]
  4. P. Beckmann, Radio Sci. 69D, 629 (1965).
  5. A. S. Gurvich and M. A. Kallistratova, Radiofizika 11, 66 (1968).
  6. A. S. Gurvich and M. A. Kallistratova, N. S. Time 11, 1360 (1968).
  7. M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette, Appl. Opt. 7, 2246 (1968).
    [CrossRef] [PubMed]
  8. E. Djurle and A. Bäck, J. Opt. Soc. Am. 51, 1029 (1961).
    [CrossRef]
  9. C. E. Coulman, J. Opt. Soc. Am. 56, 1232 (1966).
    [CrossRef]
  10. J. D. Gaskill, J. Opt. Soc. Am. 59, 308 (1969).
    [CrossRef]
  11. V. I. Tatarski, Radofizika 5, 490 (1962).
  12. J. W. Strohbehn, Proc. IEEE 6G, 1301 (1968).
    [CrossRef]
  13. G. R. Ochs, ESSA Tech. Rep. IER47-ITSA46 (U. S. Govt. Printing Office, Washington, D. C., 1967).
  14. Handbook of Geophysics and Space Environments, edited by S. L. Valley (McGraw–Hill, New York, 1965).
  15. R. S. Lawrence, G. R. Ochs, and S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
    [CrossRef]
  16. V. I. Tatarski, Propagation of Waves in a Turbulent Atmosphere (Nauka, Moscow, 1967).

1970 (1)

1969 (1)

1968 (4)

A. S. Gurvich and M. A. Kallistratova, Radiofizika 11, 66 (1968).

A. S. Gurvich and M. A. Kallistratova, N. S. Time 11, 1360 (1968).

M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette, Appl. Opt. 7, 2246 (1968).
[CrossRef] [PubMed]

J. W. Strohbehn, Proc. IEEE 6G, 1301 (1968).
[CrossRef]

1967 (2)

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

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

1966 (1)

1965 (1)

P. Beckmann, Radio Sci. 69D, 629 (1965).

1962 (1)

V. I. Tatarski, Radofizika 5, 490 (1962).

1961 (1)

Bäck, A.

Beckmann, P.

P. Beckmann, Radio Sci. 69D, 629 (1965).

Bertolotti, M.

Carnevale, M.

Clifford, S. F.

Coulman, C. E.

Djurle, E.

Fried, D. L.

Gaskill, J. D.

Gurvich, A. S.

A. S. Gurvich and M. A. Kallistratova, Radiofizika 11, 66 (1968).

A. S. Gurvich and M. A. Kallistratova, N. S. Time 11, 1360 (1968).

Kallistratova, M. A.

A. S. Gurvich and M. A. Kallistratova, N. S. Time 11, 1360 (1968).

A. S. Gurvich and M. A. Kallistratova, Radiofizika 11, 66 (1968).

Lawrence, R. S.

Muzii, L.

Ochs, G. R.

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

G. R. Ochs, ESSA Tech. Rep. IER47-ITSA46 (U. S. Govt. Printing Office, Washington, D. C., 1967).

Schmeltzer, R. A.

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

Sette, D.

Strohbehn, J. W.

J. W. Strohbehn, Proc. IEEE 6G, 1301 (1968).
[CrossRef]

Tatarski, V. I.

V. I. Tatarski, Radofizika 5, 490 (1962).

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

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1960).

Appl. Opt. (1)

J. Opt. Soc. Am. (5)

N. S. Time (1)

A. S. Gurvich and M. A. Kallistratova, N. S. Time 11, 1360 (1968).

Proc. IEEE (1)

J. W. Strohbehn, Proc. IEEE 6G, 1301 (1968).
[CrossRef]

Quart. Appl. Math. (1)

R. A. Schmeltzer, Quart. Appl. Math. 24, 339 (1967).

Radio Sci. (1)

P. Beckmann, Radio Sci. 69D, 629 (1965).

Radiofizika (1)

A. S. Gurvich and M. A. Kallistratova, Radiofizika 11, 66 (1968).

Radofizika (1)

V. I. Tatarski, Radofizika 5, 490 (1962).

Other (4)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw–Hill, New York, 1960).

G. R. Ochs, ESSA Tech. Rep. IER47-ITSA46 (U. S. Govt. Printing Office, Washington, D. C., 1967).

Handbook of Geophysics and Space Environments, edited by S. L. Valley (McGraw–Hill, New York, 1965).

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

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Figures (4)

Fig. 1
Fig. 1

The optical-phase-measuring instrument, illustrating the relative position of half-wave plate, P, retardation plate, R, Wollaston prism, W, photodetectors, Di, and mirrors, M.

Fig. 2
Fig. 2

A typical run of phase as a function of time. The expanded section has been magnified 5× in the vertical direction and 20× in the horizontal direction.

Fig. 3
Fig. 3

The time-lagged phase structure function normalized to its value at 0.029 s for each of six runs. The labeled straight lines are theoretical curves. The run numbers and associated symbols are, 1—×, 2—△, 3—+, 4–○, 5—▽, 6—●.

Fig. 4
Fig. 4

The phase structure function, normalized by the coefficient of the theoretically predicted power law using the observed temperature structure parameter, is plotted vs separation. The dotted line is a theoretical curve that applies for all six runs.

Tables (1)

Tables Icon

Table I Transverse wind speed and intensity of turbulence for each run.

Equations (11)

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D ϕ ( ρ ) = 2.91 k 2 L C n 2 ρ 5 / 3 ;             ρ = ϱ 1 - ϱ 2 .
E x ( t ) = A F cos ϕ ,
E y ( t ) = B A F sin ϕ .
C T 2 = ( T 2 - T 1 ) 2 av ρ ν ,
n = 1 + ( 77.6 P / T ) ( 1 + 0.00753 / λ 2 ) × 10 - 6 .
C n 2 = [ ( 79 P / T 2 ) × 10 - 6 ] 2 C T 2 .
C n 2 = 2.48 [ 79 P T 2 × 10 - 6 ] 2 T 2 - T 1 2 av ρ 2 3
ϕ ( t ) = tan - 1 [ ( E y / B ) / E x ] ,
I ( t ) = [ E x 2 + ( E y / B ) 2 ] / A 2 = F 2 .
D ϕ ( n ) = 1 m i = 1 m [ ϕ i - ϕ i + n ] 2
D ϕ ( ρ ) = 6.66 × 10 12 C n 2 ρ 5 / 3 ,