Abstract

An experiment is performed the aim of which is to investigate the phase fluctuations of a laser beam artificially generated thermal turbulence. This is achieved by observing the displacements of a fringe pattern obtained by means of a Mach-Zehnder interferometer. The temporal decay of the mean square refractive index fluctuation is studied. An interpretation of the results is given on the basis of the theory of an isotropic turbulent scalar field.

© 1968 Optical Society of America

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References

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  1. L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1961).
  2. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Co., Inc., New York, 1961).
  3. See for example, H. Bremmer, in Proceedings of the Symposium on Quasi-Optics (Polytechnic Press, Brooklyn, New York, 1964); F. Beckman, Radio Sci. 69 D, 629 (1965); D. A. DeWolf, J. Opt. Soc. Amer. 55, 812 (1965); J. I. Davis, Appl. Opt. 5, 139 (1966); H. Hodara, Proc. IEEE 54, 368 (1966); D. L. Fried, J. Opt. Soc. Amer. 57, 169, 175 (1967).
    [Crossref] [PubMed]
  4. See for example, R. B. Herrick, J. R. Meyer, Appl. Opt. 5, 981 (1966); D. H. Höhn, Appl. Opt. 5, 1427 (1966); P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967); M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, in Proceedings of the LIII Meeting of the Società Italiana di Fisica (Società Italiana di Fisica, Bologna1967).
    [Crossref] [PubMed]
  5. J. O. Hinze, Turbulence (McGraw-Hill Book Co., Inc., New York, 1959) and bibliography therein.

1966 (1)

Bremmer, H.

See for example, H. Bremmer, in Proceedings of the Symposium on Quasi-Optics (Polytechnic Press, Brooklyn, New York, 1964); F. Beckman, Radio Sci. 69 D, 629 (1965); D. A. DeWolf, J. Opt. Soc. Amer. 55, 812 (1965); J. I. Davis, Appl. Opt. 5, 139 (1966); H. Hodara, Proc. IEEE 54, 368 (1966); D. L. Fried, J. Opt. Soc. Amer. 57, 169, 175 (1967).
[Crossref] [PubMed]

Chernov, L. A.

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1961).

Herrick, R. B.

Hinze, J. O.

J. O. Hinze, Turbulence (McGraw-Hill Book Co., Inc., New York, 1959) and bibliography therein.

Meyer, J. R.

Tatarski, V. I.

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

Appl. Opt. (1)

Other (4)

J. O. Hinze, Turbulence (McGraw-Hill Book Co., Inc., New York, 1959) and bibliography therein.

L. A. Chernov, Wave Propagation in a Random Medium (McGraw-Hill Book Co., Inc., New York, 1961).

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

See for example, H. Bremmer, in Proceedings of the Symposium on Quasi-Optics (Polytechnic Press, Brooklyn, New York, 1964); F. Beckman, Radio Sci. 69 D, 629 (1965); D. A. DeWolf, J. Opt. Soc. Amer. 55, 812 (1965); J. I. Davis, Appl. Opt. 5, 139 (1966); H. Hodara, Proc. IEEE 54, 368 (1966); D. L. Fried, J. Opt. Soc. Amer. 57, 169, 175 (1967).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the problem.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Schematic plot of the oscilloscope pattern.

Fig. 4
Fig. 4

Mean square value of the phase fluctuations as a function of time.

Equations (10)

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[ Q γ γ ( r , t ) ] A , B = γ A γ B .
t Q γ γ ( r , t ) = 2 χ 1 r 2 r [ r 2 r Q γ γ ( r , t ) ] .
Δ n = - [ ( n ¯ - 1 ) / T ¯ ] Δ T ,
Q γ γ ( r , t ) = ( C / t / 2 3 ) exp - r 2 / 8 χ t ) .
( Δ ϕ ) 2 = { k 0 0 L [ Δ n ( 1 ) - Δ n ( 2 ) ] d z } 2 = k 0 2 0 L d z 0 L d z [ Δ n ( x , 0 , z ) Δ n ( x , 0 , z ) + Δ n ( x , 0 , z ) Δ n ( x , 0 , z ) - 2 Δ n ( x , 0 , z ) Δ n ( x , 0 , z ) ] .
( Δ ϕ ) 2 = 4 C k 0 2 ( n ¯ - 1 ) 2 C p 2 T ¯ 2 1 t ¯ ³ / 0 L d z 0 z d s exp ( - s 2 / 8 χ t ¯ ) { 1 - exp [ - ( x - x ) 2 / 8 χ t ¯ ] } = D 1 t ¯ { 1 - exp [ - ( x - x ) 2 / 8 χ t ¯ ] } 0 L d z E r f [ z / ( 8 χ t ¯ ) 1 2 ,
Erf ( z ) = 2 ( π ) 1 2 0 z exp ( - x 2 ) d x
( Δ ϕ ) 2 = D t ¯ ( 8 χ t ¯ ) 1 2 0 L / ( 8 χ t ¯ ) 1 2 Erf ( ξ ) d ξ = D t ¯ ( 8 χ t ¯ ) 1 2 [ L ( 8 χ t ¯ ) 1 2 Erf ( L ( 8 χ t ¯ ) 1 2 ) + 1 ( π ) 1 2 exp ( - L 2 / 8 χ t ¯ ) - 1 ( π ) 1 2 ] ,
( Δ ϕ ) 2 = D L / t ¯ .
( Δ ϕ ) 2 = ( D L / x ) v .

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