Abstract

Phase fluctuations of a laser beam propagating through a turbulent atmosphere are studied as a function of the distance in a cross section of the beam. An interferometer is described that allows simultaneous measurements of phase fluctuations for pairs of rays that travel in the beam at different distances between each other. Experiments with this method have been performed in an urban center at a distance of 3.5 km and 0.5 km from the source (a helium–neon laser). The results of these measurements are described, and the behavior of the mean square fluctuation of the phase difference is studied. The values of the structure constant Cn are calculated.

© 1968 Optical Society of America

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References

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  1. K. E. Erickson, J. Opt. Soc. Amer. 52, 777 (1962).
    [CrossRef]
  2. A. L. Buck, Appl. Opt. 6, 703 (1967).
    [CrossRef] [PubMed]
  3. R. B. Herrick, J. R. Meyer-Arendt, Appl. Opt. 5, 981 (1966).
    [CrossRef] [PubMed]
  4. D. N. B. Hall, Appl. Opt. 6, 1992 (1967).
    [CrossRef] [PubMed]
  5. P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967).
    [CrossRef] [PubMed]
  6. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).
  7. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Company, Inc., London, 1960).
  8. P. Beckmann, Radio Sci. J. Res. 69D, 629 (1965).
  9. J. I. Davis, Appl. Opt. 5, 139 (1966).
    [CrossRef] [PubMed]
  10. M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 112 (1968).
    [CrossRef]
  11. M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

1968 (1)

M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 112 (1968).
[CrossRef]

1967 (3)

1966 (2)

1965 (1)

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

1962 (1)

K. E. Erickson, J. Opt. Soc. Amer. 52, 777 (1962).
[CrossRef]

Beckmann, P.

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

Bertolotti, M.

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

Buck, A. L.

Burlamacchi, P.

Carnevale, M.

M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 112 (1968).
[CrossRef]

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Company, Inc., London, 1960).

Consortini, A.

Crosignani, B.

M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 112 (1968).
[CrossRef]

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

Davis, J. I.

Di Porto, P.

M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 112 (1968).
[CrossRef]

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

Erickson, K. E.

K. E. Erickson, J. Opt. Soc. Amer. 52, 777 (1962).
[CrossRef]

Hall, D. N. B.

Herrick, R. B.

Meyer-Arendt, J. R.

Muzii, L.

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

Ronchi, L.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).

Appl. Opt. (6)

J. Opt. Soc. Amer. (1)

K. E. Erickson, J. Opt. Soc. Amer. 52, 777 (1962).
[CrossRef]

Radio Sci. J. Res. (1)

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

Other (3)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Company, Inc., London, 1960).

M. Bertolotti, M. Carnevale, B. Crosignani, P. Di Porto, L. Muzii, in the Proceedings of the LII Meeting of the Società Italiana di Fisica (Suppl. Nuovo Cimento1967).

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Figures (10)

Fig. 1
Fig. 1

Geometry of the experimental setup.

Fig. 2
Fig. 2

The interferometric apparatus.

Fig. 3
Fig. 3

Experimental set up for recording fringe displacements by means of photodiode.

Fig. 4
Fig. 4

Fringe patterns recorded by a continuously moving camera.

Fig. 5
Fig. 5

Statistical distribution of the phase differences. ν is the relative number of events.

Fig. 6
Fig. 6

Mean square values of the phase fluctuations as a function of the distance of the beams.

Fig. 7
Fig. 7

Mean square values of the phase fluctuations as a function of the distance of the beams.

Fig. 8
Fig. 8

Mean square values of the phase fluctuations as a function of the distance of the beams.

Fig. 9
Fig. 9

Mean square values of the phase fluctuations as a function of the distance of the beams.

Fig. 10
Fig. 10

Showing the correspondence in the displacements of fringes from each mirror in run C when suitable time delays are introduced.

Tables (2)

Tables Icon

Table I Values of Mi2 and Cn

Equations (13)

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V ( x , t ) = A ( x , t ) e i ϕ ( x , t ) ,
I = V ( x o i , t ) V * ( x o i , t ) + V ( x i , t ) V * ( x i , t ) + 2 R e { V ( x o i , t ) V * ( x i , t + τ ) } ,
R e { V ( x o i , t ) V * ( x i , t + τ ) } = A ( x o i , t ) A ( x i , t + τ ) cos [ ϕ ( x o i , t ) - ϕ ( x i , t + τ ) ] .
sin [ ϕ ( x o i , t ) - ϕ ( x i , t + τ ) ] .
δ o i = ϕ ( x o i ) - ϕ ( x i ) .
Δ x i ( x o i - x i ) α / ( 1 - α ) ,
δ o i j = ϕ j ( x o i ) - ϕ j ( x i )
M i 2 = j = 1 N [ ϕ j ( x o i ) - ϕ j ( x i ) ] 2 N = j = 1 N { ϕ j ( x o i ) } 2 N + j = 1 N { ϕ j ( x i ) } 2 N - 2 j = 1 N ϕ j ( x o i ) ϕ j ( x i ) N 2 { j = 1 N { ϕ j ( x o i ) } 2 N - j = 1 N ϕ j ( x o i ) ϕ j ( x i ) N } = 2 [ ϕ 2 ( x o i ) - ϕ ( x o i ) ϕ ( x i ) ] .
ϕ ( x o i ) ϕ ( x i ) = ϕ 2 ( x o i ) - ( M i 2 / 2 )
ϕ ( x o i ) ϕ ( x ) = 0 ,
2 ϕ 2 ( x o i ) = M 2 .
ϕ ( x o i ) ϕ ( x i ) = ( 1 / 2 ) ( M 2 - M i 2 ) .
M i 2 = 2.91 R K 2 C n 2 x 5 3 ,

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