Abstract

Temperature structure in the atmosphere, transported by the wind across a laser beam, produces time variations in the optical path length. Using a He-Ne laser (0.6328 μm) on a 70-m propagation path, we measured the optical phase variations at four different spacings, ρ≤30 cm. Simultaneously, a midpath measurement of wind velocity and temperature structure parameter, CT2, provided the necessary meteorological measurements to compare the observed phase structure function with Tatarski’s theoretical curve. We obtained excellent agreement between theory and experiment. Direct measurements of the outer scale of turbulence, taken continuously over a 24-h period at a height of 1.6 m, indicated an average outer scale of 1.3 m with diurnal variations of ±20%. The frequency spectrum of the received phase difference at each of the four spacings is plotted and its implications for the data-sampling rate are examined. The curves obtained exhibit excellent agreement with the predicted spherical-wave phase-difference frequency spectrum.

© 1971 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. A. Consortini and L. Ronchi, Nuovo Cimento 2, 683 (1969).
  3. A. Ishimaru, Radio Sci. 4, 295 (1969).
    [Crossref]
  4. D. L. Fried, J. Opt. Soc. Am. 57, 175 (1967).
    [Crossref]
  5. M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette, Appl. Opt. 7, 2246 (1968).
    [Crossref] [PubMed]
  6. P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).
  7. G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).
    [Crossref]
  8. R. G. Buser and G. K. Born, J. Opt. Soc. Am. 60, 1079 (1970).
    [Crossref]
  9. M. Bertolotti, M. Carnevale, B. Crosignani, and P. D. Porto, Appl. Opt. 8, 1111 (1969).
    [Crossref] [PubMed]
  10. G. M. B. Bouricius and S. F. Clifford, Rev. Sci. Instr. 41, 1800 (1970).
    [Crossref]
  11. G. R. Ochs, ESSA Tech. Rept. IER 47-ITSA 46, U. S. Govt. Printing Office, Washington, D. C. (1967).
  12. G. R. Ochs, ESSA Tech. Rept. ERL 63-WPL 2, U. S. Govt. Printing Office, Washington, D. C. (1968).
  13. V. I. Tatarski, Wave Propagation in a Turbulent Atmosphere (in Russian) (Nauka, Moscow, 1967).
  14. D. L. Fried, Proc. IEEE 55, 57 (1967).
    [Crossref]
  15. M. Bertolotti, M. Carnevale, L. Muzii, and D. Sette, Appl. Opt. 9, 510 (1970).
    [Crossref]
  16. S. F. Clifford, J. Opt. Soc. Am. 61, 1285 (1971).
    [Crossref]

1971 (1)

1970 (4)

1969 (3)

M. Bertolotti, M. Carnevale, B. Crosignani, and P. D. Porto, Appl. Opt. 8, 1111 (1969).
[Crossref] [PubMed]

A. Consortini and L. Ronchi, Nuovo Cimento 2, 683 (1969).

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

1968 (1)

1967 (2)

Bertolotti, M.

Born, G. K.

Bouricius, G. M. B.

G. M. B. Bouricius and S. F. Clifford, Rev. Sci. Instr. 41, 1800 (1970).
[Crossref]

G. M. B. Bouricius and S. F. Clifford, J. Opt. Soc. Am. 60, 1484 (1970).
[Crossref]

Burlamacchi, P.

P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).

Buser, R. G.

Carnevale, M.

Clifford, S. F.

Consortini, A.

A. Consortini and L. Ronchi, Nuovo Cimento 2, 683 (1969).

P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).

Crosignani, B.

Fried, D. L.

Ishimaru, A.

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

Muzii, L.

Ochs, G. R.

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

G. R. Ochs, ESSA Tech. Rept. ERL 63-WPL 2, U. S. Govt. Printing Office, Washington, D. C. (1968).

Porto, P. D.

Ronchi, L.

A. Consortini and L. Ronchi, Nuovo Cimento 2, 683 (1969).

P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).

Sette, D.

Tatarski, V. I.

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

V. I. Tatarski, Wave Propagation in a Turbulent Atmosphere (in Russian) (Nauka, Moscow, 1967).

Toraldo di Francia, G.

P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).

Appl. Opt. (3)

J. Opt. Soc. Am. (4)

Nuovo Cimento (1)

A. Consortini and L. Ronchi, Nuovo Cimento 2, 683 (1969).

Proc. IEEE (1)

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

Radio Sci. (1)

A. Ishimaru, Radio Sci. 4, 295 (1969).
[Crossref]

Rev. Sci. Instr. (1)

G. M. B. Bouricius and S. F. Clifford, Rev. Sci. Instr. 41, 1800 (1970).
[Crossref]

Other (5)

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

G. R. Ochs, ESSA Tech. Rept. ERL 63-WPL 2, U. S. Govt. Printing Office, Washington, D. C. (1968).

V. I. Tatarski, Wave Propagation in a Turbulent Atmosphere (in Russian) (Nauka, Moscow, 1967).

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

P. Burlamacchi, A. Consortini, L. Ronchi, and G. Toraldo di Francia, Phase and Frequency Instabilities in Electromagnetic Wave Propagation (Technivision Services, Slough, England, 1970).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the optical-phase experiment, illustrating configuration of laser, retardation plate R, optical filters F1 and F2, and signal detectors D1 and D2.

Fig. 2
Fig. 2

Plot of temperature structure function vs separation measured on 2 June 1970.

Fig. 3
Fig. 3

Outer scale, measured at 1.6 m above the ground, vs time.

Fig. 4
Fig. 4

Phase difference vs time for July and August 1970, illustrating the variability of the data as a function of transverse wind v and average rectified temperature difference 〈|ΔT|〉2.

Fig. 5
Fig. 5

Typical data, phase difference vs time, taken at each of four spacings, ρ=0.3, 3, 15, 30 cm, illustrating predominance of lower frequencies and higher peak-to-peak variations as spacing increases.

Fig. 6
Fig. 6

Probability distribution of the received phase difference for each of four spacings, ρ=0.3, 3, 15, and 30 cm. σΔφ is the standard deviation of the phase difference at each point, σΔφ=√Dφ.

Fig. 7
Fig. 7

Phase structure function (degrees squared) vs spacing (cm). Data uncorrected for Cn2 variations and shown with a ρ5/3 curve for comparison.

Fig. 8
Fig. 8

Normalized phase structure function (degrees squared) vs spacing (cm). Each point represents the average value over the circled number of points. The solid line is the theoretical curve, Dφ(ρ)=1.09 k2LCn2ρ5/3.

Fig. 9
Fig. 9

Phase-difference temporal power spectrum Wδφ(f) plotted vs frequency for four different spacings, ρ. □—ρ=0.3 cm, ●—ρ=3 cm, △—ρ=15 cm, and ○—ρ =30 cm. The solid lines are the corresponding theoretical curves plotted from Eq. (8).

Equations (8)

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D φ = [ φ ( r + ϱ ) - φ ( r ) ] 2 .
D φ ( ρ ) = 2.91 k 2 L C n 2 ρ 5 / 3 ,             ( λ L ) ρ < L o
D φ ( ρ ) = 1.09 k 2 L C n 2 ρ 5 / 3 ,             ( λ L ) ρ < L o ,
C n 2 = [ ( 79 P / T 2 ) × 10 - 6 ] 2 C T 2 .
D T ( r ) = 2 T r 2 ( 1 - R r ) ,
D φ ( ρ ) = [ 1.09 × 10 - 13 k 2 L ρ 5 / 3 ] ( 57.3 ) 2 , ( degrees ) 2
D φ ( ρ ) = 2.5 × 10 6 ρ 5 / 3 , ( degrees ) 2 .
W δ φ ( f ) = 0.066 C n 2 k 2 L v 5 / 3 ( 1 - sin ( 2 π ρ f / v ) ( 2 π ρ f / v ) ) f - 8 / 3 .