Abstract

Up to now only a few numerical or experimental simulations of atmospheric turbulent layers have been performed in the laboratory. These are devoted mainly to show the validity of Kolmogorov behavior but are not suitable to implement in an optical bench to test light propagation. Here we present a small size experimental simulation of an optical turbulent layer. With optical and in situ measurements, we managed to determine its characteristics: the mean variance of the refractive-index fluctuations integrated over the thickness of the turbulent flow and longitudinal and transverse structure functions of angles of arrival. From these measurements we found that the power spectrum of the refractive index is well fitted by a Von Karman function with an outer scale of 91 mm and an inner scale of 4.7 mm. Moreover, the temporal stationarity of these parameters indicates the reproducibility of this simulated turbulent flow.

© 1996 Optical Society of America

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References

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  1. R. Betchov, “On the fine structure of turbulent flows,” J. Fluid Mech. 3, 205–216 (1957).
    [CrossRef]
  2. D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
    [CrossRef]
  3. M. Billard, G. Fertin, J. C. Fontanella, “Atmospheric turbulence simulation cell for optical propagation experiment,” presented at Fourth International Symposium on Gas Flow and Chemical Lasers, Stresa, Italy (13–14 Sept. 1982).
  4. R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).
  5. L. J. Sanchez, R. G. Petrov, “About the optimization of partially correcting adaptive optics,” Atmos. Oceanic Opt. 8, 177–181 (1995).
  6. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 7, p. 147.
  7. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 312–376.
    [CrossRef]
  8. A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz. 13, 58–63 (1949).
  9. J. Vernin, C. Muñoz-Tuñón, “Optical seeing at La Plama Observatory. 1: General guidelines and preliminary results at the Nordic Optical Telescope,” Astron. Astrophys. 257, 811–816 (1992).
  10. M. Sarazin, F. Roddier, “The E.S.O. differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).
  11. J. Vernin, C. Muñoz-Tuñón, “Measuring astronomical seeing: the DA/IAC DIMM,” Publ. Astron. Soc. Pac. 107, 265–272 (1995).
    [CrossRef]
  12. V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).
  13. A. Consortini, L. Ronchi, L. Stefanutti, “Investigation of atmospheric turbulence by narrow laser beams,” Appl. Opt. 9, 2543–2547 (1970).
    [CrossRef] [PubMed]
  14. J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
    [CrossRef]

1995 (2)

L. J. Sanchez, R. G. Petrov, “About the optimization of partially correcting adaptive optics,” Atmos. Oceanic Opt. 8, 177–181 (1995).

J. Vernin, C. Muñoz-Tuñón, “Measuring astronomical seeing: the DA/IAC DIMM,” Publ. Astron. Soc. Pac. 107, 265–272 (1995).
[CrossRef]

1994 (1)

D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
[CrossRef]

1992 (3)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).

J. Vernin, C. Muñoz-Tuñón, “Optical seeing at La Plama Observatory. 1: General guidelines and preliminary results at the Nordic Optical Telescope,” Astron. Astrophys. 257, 811–816 (1992).

J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
[CrossRef]

1990 (1)

M. Sarazin, F. Roddier, “The E.S.O. differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

1970 (1)

1957 (1)

R. Betchov, “On the fine structure of turbulent flows,” J. Fluid Mech. 3, 205–216 (1957).
[CrossRef]

1949 (1)

A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz. 13, 58–63 (1949).

Banakh, V. A.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).

Betchov, R.

R. Betchov, “On the fine structure of turbulent flows,” J. Fluid Mech. 3, 205–216 (1957).
[CrossRef]

Billard, M.

M. Billard, G. Fertin, J. C. Fontanella, “Atmospheric turbulence simulation cell for optical propagation experiment,” presented at Fourth International Symposium on Gas Flow and Chemical Lasers, Stresa, Italy (13–14 Sept. 1982).

Borgnino, J.

J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
[CrossRef]

Consortini, A.

Dainty, J. C.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).

Fertin, G.

M. Billard, G. Fertin, J. C. Fontanella, “Atmospheric turbulence simulation cell for optical propagation experiment,” presented at Fourth International Symposium on Gas Flow and Chemical Lasers, Stresa, Italy (13–14 Sept. 1982).

Fontanella, J. C.

M. Billard, G. Fertin, J. C. Fontanella, “Atmospheric turbulence simulation cell for optical propagation experiment,” presented at Fourth International Symposium on Gas Flow and Chemical Lasers, Stresa, Italy (13–14 Sept. 1982).

Glindemann, A.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).

Kopeika, N. S.

D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
[CrossRef]

Lane, R. G.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).

Martin, F.

J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
[CrossRef]

Mironov, V. L.

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).

Muñoz-Tuñón, C.

J. Vernin, C. Muñoz-Tuñón, “Measuring astronomical seeing: the DA/IAC DIMM,” Publ. Astron. Soc. Pac. 107, 265–272 (1995).
[CrossRef]

J. Vernin, C. Muñoz-Tuñón, “Optical seeing at La Plama Observatory. 1: General guidelines and preliminary results at the Nordic Optical Telescope,” Astron. Astrophys. 257, 811–816 (1992).

Obukhov, A. M.

A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz. 13, 58–63 (1949).

Petrov, R. G.

L. J. Sanchez, R. G. Petrov, “About the optimization of partially correcting adaptive optics,” Atmos. Oceanic Opt. 8, 177–181 (1995).

Roddier, F.

M. Sarazin, F. Roddier, “The E.S.O. differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 312–376.
[CrossRef]

Ronchi, L.

Sadot, D.

D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
[CrossRef]

Sanchez, L. J.

L. J. Sanchez, R. G. Petrov, “About the optimization of partially correcting adaptive optics,” Atmos. Oceanic Opt. 8, 177–181 (1995).

Sarazin, M.

M. Sarazin, F. Roddier, “The E.S.O. differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

Shemtov, D.

D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
[CrossRef]

Stefanutti, L.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 7, p. 147.

Vernin, J.

J. Vernin, C. Muñoz-Tuñón, “Measuring astronomical seeing: the DA/IAC DIMM,” Publ. Astron. Soc. Pac. 107, 265–272 (1995).
[CrossRef]

J. Vernin, C. Muñoz-Tuñón, “Optical seeing at La Plama Observatory. 1: General guidelines and preliminary results at the Nordic Optical Telescope,” Astron. Astrophys. 257, 811–816 (1992).

Ziad, A.

J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (2)

J. Vernin, C. Muñoz-Tuñón, “Optical seeing at La Plama Observatory. 1: General guidelines and preliminary results at the Nordic Optical Telescope,” Astron. Astrophys. 257, 811–816 (1992).

M. Sarazin, F. Roddier, “The E.S.O. differential image motion monitor,” Astron. Astrophys. 227, 294–300 (1990).

Atmos. Oceanic Opt. (2)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Atmos. Oceanic Opt. 4, 209–224 (1992).

L. J. Sanchez, R. G. Petrov, “About the optimization of partially correcting adaptive optics,” Atmos. Oceanic Opt. 8, 177–181 (1995).

Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz. (1)

A. M. Obukhov, “Structure of the temperature field in a turbulent flow,” Izv. Akad. Nauk SSSR, Ser. Geograf. Geofiz. 13, 58–63 (1949).

J. Fluid Mech. (1)

R. Betchov, “On the fine structure of turbulent flows,” J. Fluid Mech. 3, 205–216 (1957).
[CrossRef]

Opt. Commun. (1)

J. Borgnino, F. Martin, A. Ziad, “Effect of a finite spatial-coherence outer scale on the covariances of angle-of-arrival fluctuations,” Opt. Commun. 91, 267–279 (1992).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

J. Vernin, C. Muñoz-Tuñón, “Measuring astronomical seeing: the DA/IAC DIMM,” Publ. Astron. Soc. Pac. 107, 265–272 (1995).
[CrossRef]

Waves Random Media (1)

D. Sadot, D. Shemtov, N. S. Kopeika, “Theoretical and experimental investigation of image quality through an inho-mogeneous turbulent medium,” Waves Random Media 4, 177–189 (1994).
[CrossRef]

Other (4)

M. Billard, G. Fertin, J. C. Fontanella, “Atmospheric turbulence simulation cell for optical propagation experiment,” presented at Fourth International Symposium on Gas Flow and Chemical Lasers, Stresa, Italy (13–14 Sept. 1982).

V. A. Banakh, V. L. Mironov, Lidar in a Turbulent Atmosphere (Artech House, Boston, 1987).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, New York, 1961), Chap. 7, p. 147.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1981), Vol. 19, pp. 312–376.
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Laboratory optical turbulent channel. T and U represent temperature and velocity of air flows in opposite directions introduced into two pipes. W1 and W3 represent two glass windows that permit the light beam to cross the channel along the z axis. W2 represents an open window that permits the two flows to meet and produce a shear.

Fig. 2.
Fig. 2.

Measured rms of temperature fluctuations across the turbulent channel (along the light beam path) that was obtained by use of microthermal probes made of thin 3.2-μm-diameter platinum wire.

Fig. 3.
Fig. 3.

Normalized longitudinal D l (x) (dashes) and transverse D t (x)(dots) angle of arrival structure functions given by the DIMM across the entrance pupil. Attempts to fit our experimental data with theoretical longitudinal (full line) and transverse (dots) structure functions, derived from a Von Karman function (L = 91 mm and l = 47 mm) are satisfactory.

Fig. 4.
Fig. 4.

Temporal stationarity of the standard deviation of temperature fluctuations. For 15 min we allowed the two fans to work without heat. Then heat was injected into one pipe. The stationarity behavior of σ T was reached after 20 min and was maintained until the heat in the channel was turned off at t = 165 min when σ T dropped.

Equations (16)

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n ( λ , z ) = N ( λ , z ) 1 = α ( λ ) [ P ( z ) / T ( z ) ] ,
d n = ( α P / T 2 ) d T .
σ N 2 ( z ) = ( α P T 2 ) 2 σ T 2 ( z ) ,
σ N 2 δ z = 0 D σ N 2 ( z ) d z ,
Φ N ( K ) = 0.033 C N 2 ( K 2 + K 0 2 ) 11 / 6 exp ( K ² K m 2 ) ,
W N ( f ) = ( 2 π ) 3 Φ N ( 2 π f ) .
W α ( f x , f y ) = λ 2 f x 2 W φ ( f x , f y ) ,
W φ ( f x , f y ) = k 2 δ h W N ( f x , f y , 0 ) ,
C α ( x , y ) = λ 2 f x 2 W φ ( f x , f y )       × exp [ 2 i π ( x f x + y f y ) ] d f x d f y .
C l / t ( x ) = 1.196 C N 2 0 + f 3 ( f 2 + 1 L 2 ) 11 / 6      × exp ( f 2 l 2 ) [ J 0 ( 2 π x f ) J 2 ( 2 π x f ) ] d f .
D l / t ( x ) = 2 [ C l / t ( 0 ) C l / t ( x ) ] ,
D l / t ( x ) = 2.39 C N 2 δ h 0 + f 3 ( f 2 + 1 L 2 ) 11 / 6    ​  ​ × exp ( f 2 l 2 ) [ 1 J 0 ( 2 π x f ) ± J 2 ( 2 π x f ) ] d f ,
D sat = 2.39 C N 2 δ h 0 + f 3 ( f 2 + 1 L 2 ) 11 / 6 exp ( f 2 l 2 ) d f .
σ N 2 = Φ N ( K ) d K    .
σ N 2 δ h = 0.033 C N 2 δ h [ K 2 + ( 2 π L ) 2 ] 11 / 6      × exp [ K 2 ( l 2 π ) 2 ] d K    .
τ = l / Δ U ,

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