Abstract

In order to determine the characteristic parameters of the atmospheric turbulence, the mutual dancing of two parallel narrow laser beams propagating through a turbulent atmosphere has been investigated theoretically and experimentally. The experiments have been carried out with a He–Ne laser on a 130-m path, one meter from the ground. The method allowed the determination of the variance of the refractive index fluctuations, as well as the values of scale of the turbulence in the vertical and horizontal planes.

© 1970 Optical Society of America

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References

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  1. P. Beckmann, Radio Sciences J. Res. NBS/USNC-URSI 69D, 629 (1965).
  2. V. I. Tatarski, Wave Propagation in a Turbulent Atmosphere (Nauka Press, Moscow, 1967).
  3. A. Consortini, L. Ronchi, Lettere al Nuovo Cimento 2, 683 (1969).
    [Crossref]
  4. P. Burlamacchi, A. Consortini, Opt. Acta 14, 17 (1967).
    [Crossref]
  5. P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).
  6. M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).
  7. J. D. Gaskill, J. Opt. Soc. Amer. 59, 308 (1969).
    [Crossref]
  8. M. Bertolotti, communication presented at the 55th Congress of Socieà Italiana di Fisica, Bari, 28 October 1969.

1969 (2)

A. Consortini, L. Ronchi, Lettere al Nuovo Cimento 2, 683 (1969).
[Crossref]

J. D. Gaskill, J. Opt. Soc. Amer. 59, 308 (1969).
[Crossref]

1968 (1)

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

1967 (1)

P. Burlamacchi, A. Consortini, Opt. Acta 14, 17 (1967).
[Crossref]

1965 (1)

P. Beckmann, Radio Sciences J. Res. NBS/USNC-URSI 69D, 629 (1965).

Beckmann, P.

P. Beckmann, Radio Sciences J. Res. NBS/USNC-URSI 69D, 629 (1965).

Bertolotti, M.

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

M. Bertolotti, communication presented at the 55th Congress of Socieà Italiana di Fisica, Bari, 28 October 1969.

Burlamacchi, P.

P. Burlamacchi, A. Consortini, Opt. Acta 14, 17 (1967).
[Crossref]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).

Carnevale, M.

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

Consortini, A.

A. Consortini, L. Ronchi, Lettere al Nuovo Cimento 2, 683 (1969).
[Crossref]

P. Burlamacchi, A. Consortini, Opt. Acta 14, 17 (1967).
[Crossref]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).

Gaskill, J. D.

J. D. Gaskill, J. Opt. Soc. Amer. 59, 308 (1969).
[Crossref]

Muzii, L.

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

Ronchi, L.

A. Consortini, L. Ronchi, Lettere al Nuovo Cimento 2, 683 (1969).
[Crossref]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).

Sette, D.

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

Tatarski, V. I.

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

Toraldo di Francia, G.

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).

Appl. Opt. (1)

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2247 (1968).

J. Opt. Soc. Amer. (1)

J. D. Gaskill, J. Opt. Soc. Amer. 59, 308 (1969).
[Crossref]

Lettere al Nuovo Cimento (1)

A. Consortini, L. Ronchi, Lettere al Nuovo Cimento 2, 683 (1969).
[Crossref]

Opt. Acta (1)

P. Burlamacchi, A. Consortini, Opt. Acta 14, 17 (1967).
[Crossref]

Radio Sciences J. Res. NBS/USNC-URSI (1)

P. Beckmann, Radio Sciences J. Res. NBS/USNC-URSI 69D, 629 (1965).

Other (3)

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

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, “Phase Correlation Measurements of a Laser Beam Propagated through a Turbulent Atmosphere” in Proceedings of EPCIAGARD 13th Symposium on Phase and Frequency Instability in Electromagnetic Wave Propagation, (Ankara, Turkey, October1967, in press); see also, Alta Frequenza 38, May, 149 (1969).

M. Bertolotti, communication presented at the 55th Congress of Socieà Italiana di Fisica, Bari, 28 October 1969.

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Figures (8)

Fig. 1
Fig. 1

The plane yz orthogonal to the direction of propagation of the beams. P1 denotes the instantaneous position of the beam 1, P ¯ 1 being its unperturbed position.

Fig. 2
Fig. 2

Relative structure functions Dy/Dysat and Dz/Dzsat plotted vs d/Roy.

Fig. 3
Fig. 3

Ray tracing scheme for an understanding of the curve Dy/Dysat of Fig. 2.

Fig. 4
Fig. 4

Sketch of the experimental setup.

Fig. 5
Fig. 5

Example of spots on the screen.

Fig. 6
Fig. 6

Various curves of Dy vs d for different values of Roy and <μ2>. Dots indicate experimental values; dashed line represents an example of curve best fitting the experimental values.

Fig. 7
Fig. 7

Experimental results for Dy and comparison with the theory.

Fig. 8
Fig. 8

Experimental results for Dz and comparison with the theory.

Tables (1)

Tables Icon

Table I Preliminary Results

Equations (13)

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y - y = η = 0 L α ( Q ) d x , z - z = ξ = 0 L β ( Q ) d x ,
α ( Q ) = 0 x y μ ( S ) d s , β ( Q ) = 0 x z μ ( S ) d s ,
D y ( P ¯ 1 , P ¯ 2 ) = ( η 1 - η 2 ) 2 = η 1 2 + η 2 2 - 2 0 L d x 1 0 L α ( Q 1 ) α ( Q 2 ) d x 2 .
D y ( P ¯ 1 , P ¯ 2 ) = 2 η 1 2 - 2 0 L d x 1 0 L α ( Q 1 ) α ( Q 2 ) d x 2 .
D z ( P ¯ 1 , P ¯ 2 ) = 2 ξ 1 2 - 2 0 L d x 1 0 L β ( Q 1 ) β ( Q 2 ) d x 2 .
α ( Q 1 ) α ( Q 2 ) = 0 x 1 y 1 μ ( S 1 ) d s 1 0 x 2 y 2 μ ( S 2 ) d s 2 = 0 x 1 d s 1 0 x 2 2 y 1 y 2 μ ( S 1 ) μ ( S 2 ) d s 2 = 0 x 1 d s 1 0 x 2 2 y 1 y 2 B μ ( S 1 , S 2 ) d s 2 .
D y ( P ¯ 1 , P ¯ 2 ) = 2 η 1 2 - 2 0 L d x 1 0 L d x 2 0 x 1 d s 1 0 x 2 2 y 1 y 2 B μ ( S 1 , S 2 ) d s 2 .
B μ ( S 1 , S 2 ) = μ 2 exp [ - ( R x 2 R 0 x 2 + R y 2 R 0 y 2 + R z 2 R 0 z 2 ) ] .
D y ( P ¯ 1 , P ¯ 2 ) = 4 π 1 2 3 μ 2 L 3 R 0 x R 0 y 2 [ 1 - ( 1 - 2 y 1 - y 2 2 R 0 y 2 ) × exp ( - y 1 - y 2 2 R 0 y 2 - z 1 - z 2 2 R 0 z 2 ) ] ,
D z ( P ¯ 1 , P ¯ 2 ) = 4 π 1 2 3 μ 2 L 3 R 0 x R 0 z 2 [ 1 - ( 1 - 2 z 1 - z 2 2 R 0 z 2 ) × exp ( - y 1 - y 2 2 R 0 y 2 - z 1 - z 2 2 R 0 z 2 ) ] ,
D y = 4 π 1 2 3 μ 2 L 3 R 0 x R 0 y 2 [ 1 - ( 1 - 2 d 2 R 0 y 2 ) exp ( - d 2 R 0 y 2 ) ] , D z = 4 π 1 2 3 μ 2 L 3 R 0 x R 0 z 2 [ 1 - exp ( - d 2 R 0 y 2 ) ] ,
D y     sat = ( 4 π 1 2 / 3 ) μ 2 L 3 R 0 x / R 0 y 2 , D z sat = ( 4 π 1 2 / 3 ) μ 2 L 3 R 0 x / R 0 z 2 ,
R 0 z 2 D z     sat = R 0 y 2 D y     sat .

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