Abstract

A statistically repeatable, hot-air optical turbulence generator, based on the forced mixing of two air flows with different temperatures, is described. Characterization results show that it is possible to generate any turbulence strength up to CN2Δh6×1010m1/3, allowing a ratio of beam diameter to Fried's parameter as large as D/r025 for one crossing through the turbulator or D/r038 for two crossings. The outer scale (L0133±60  mm) is found to be compatible with the turbulator mixing chamber size (170  mm), and the inner scale (l07.6±3.8  mm) is compatible with the values in the literature for the free atmosphere. The temporal power spectrum analysis of the centroid of the focused image shows good agreement with Kolmogorov's theory. Therefore the device can be used with confidence to emulate realistic turbulence in a controlled manner. A calibrated CN2 profile, both in layer altitude and strength, is necessary for the testing of off-axis adaptive optics correction (multiconjugate adaptive optics). Testing was done to calibrate the CN2 profile using the slope detection and ranging technique. The first results, with only one layer, show the validity of the approach and indicate that a multiple-pass scheme is viable with a few modifications of the current setup.

© 2006 Optical Society of America

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References

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    [CrossRef]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, 1961).
  4. A. M. Obukhov, "Structure of the temperature field in a turbulent flow," Izv. Acad. Nauk. SSSR Ser. Geograf. Geofiz. 13, 58 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].
  5. A. M. Yaglom, "On the local structure of the temperature field in a turbulent flow," Doklady Acad. Nauk. SSSR Ser. Geograf. Geofiz. 69, 73 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].
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2004 (1)

A. Consortini and C. Innocenti, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the Von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[CrossRef]

2002 (1)

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

1997 (1)

1995 (1)

1994 (1)

1991 (1)

1982 (1)

1981 (1)

1978 (1)

V. P. Lukin and V. M. Sazanovich, "Investigations of turbulent characteristics in conditions of convection," Atmos. Ocean Phys. 14, 1212-1215 (1978).

1976 (2)

V. P. Lukin and V. L. Mironov, "Phase measurements of inner scale of atmospheric turbulence," Atmos. Ocean Phys. 12, 1317-1319 (1976).

R. J. Noll, "Zernike polynomials and atmospheric turbulence," J. Opt. Soc. Am. 66, 207-211 (1976).
[CrossRef]

1973 (1)

1972 (1)

1966 (1)

1948 (1)

T. Von Karman, "Progress in the statistical theory of turbulence," J. Mar. Res. 7, 252-264 (1948).

1941 (1)

A. N. Kolmogorov, "Local structure of turbulence in incompressible fluids with very high Reynold's number," Dokl. Akad. Nauk SSSR 30, 301-305 (1941).

Conan, J. M.

Consortini, A.

A. Consortini and C. Innocenti, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the Von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[CrossRef]

Fried, D. L.

Hamiter, M. A.

Innocenti, C.

A. Consortini and C. Innocenti, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the Von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[CrossRef]

Jolissaint, L.

L. Jolissaint, "Optique adaptative au foyer d'un telescope de la classe 1 metre," (Université de Genève, Geneva, Switzerland, 2000).

Kolmogorov, A. N.

A. N. Kolmogorov, "Local structure of turbulence in incompressible fluids with very high Reynold's number," Dokl. Akad. Nauk SSSR 30, 301-305 (1941).

Lukin, V. P.

V. P. Lukin and V. V. Pokasov, "Optical wave phase fluctuations," Appl. Opt. 20, 121-135 (1981).
[CrossRef] [PubMed]

V. P. Lukin and V. M. Sazanovich, "Investigations of turbulent characteristics in conditions of convection," Atmos. Ocean Phys. 14, 1212-1215 (1978).

V. P. Lukin and V. L. Mironov, "Phase measurements of inner scale of atmospheric turbulence," Atmos. Ocean Phys. 12, 1317-1319 (1976).

Madec, P. Y.

Masciadri, E.

Mironov, V. L.

V. P. Lukin and V. L. Mironov, "Phase measurements of inner scale of atmospheric turbulence," Atmos. Ocean Phys. 12, 1317-1319 (1976).

Noll, R. J.

Obukhov, A. M.

A. M. Obukhov, "Structure of the temperature field in a turbulent flow," Izv. Acad. Nauk. SSSR Ser. Geograf. Geofiz. 13, 58 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].

Pokasov, V. V.

Pries, T. H.

Roddier, F.

F. Roddier, "The effects of atmospheric turbulence in optical astronomy," in Progress in Optics, E. Wolf, ed. (North-Holland, 1981), Vol. 19.
[CrossRef]

Roussel, G.

Sazanovich, V. M.

V. P. Lukin and V. M. Sazanovich, "Investigations of turbulent characteristics in conditions of convection," Atmos. Ocean Phys. 14, 1212-1215 (1978).

Shipka, K. J.

Smith, J.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, 1961).

Tyler, G. A.

Vernin, J.

Von Karman, T.

T. Von Karman, "Progress in the statistical theory of turbulence," J. Mar. Res. 7, 252-264 (1948).

Wilson, R. W.

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

Winker, D. M.

Yaglom, A. M.

A. M. Yaglom, "On the local structure of the temperature field in a turbulent flow," Doklady Acad. Nauk. SSSR Ser. Geograf. Geofiz. 69, 73 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].

Appl. Opt. (2)

Atmos. Ocean Phys. (2)

V. P. Lukin and V. L. Mironov, "Phase measurements of inner scale of atmospheric turbulence," Atmos. Ocean Phys. 12, 1317-1319 (1976).

V. P. Lukin and V. M. Sazanovich, "Investigations of turbulent characteristics in conditions of convection," Atmos. Ocean Phys. 14, 1212-1215 (1978).

Dokl. Akad. Nauk SSSR (1)

A. N. Kolmogorov, "Local structure of turbulence in incompressible fluids with very high Reynold's number," Dokl. Akad. Nauk SSSR 30, 301-305 (1941).

J. Mar. Res. (1)

T. Von Karman, "Progress in the statistical theory of turbulence," J. Mar. Res. 7, 252-264 (1948).

J. Mod. Opt. (1)

A. Consortini and C. Innocenti, "Estimate of characteristics scales of atmospheric turbulence by thin beams: comparison between the Von Karman and Hill-Andrews models," J. Mod. Opt. 51, 333-342 (2004).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (3)

Mon. Not. R. Astron. Soc. (1)

R. W. Wilson, "SLODAR: measuring optical turbulence altitude with a Shack-Hartmann wavefront sensor," Mon. Not. R. Astron. Soc. 337, 103-108 (2002).
[CrossRef]

Other (5)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (Dover, 1961).

A. M. Obukhov, "Structure of the temperature field in a turbulent flow," Izv. Acad. Nauk. SSSR Ser. Geograf. Geofiz. 13, 58 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].

A. M. Yaglom, "On the local structure of the temperature field in a turbulent flow," Doklady Acad. Nauk. SSSR Ser. Geograf. Geofiz. 69, 73 (1949) [German translation in Sammelband zur Statischen Theoric der Turbulenz (Akademie Verlag, 1958)].

F. Roddier, "The effects of atmospheric turbulence in optical astronomy," in Progress in Optics, E. Wolf, ed. (North-Holland, 1981), Vol. 19.
[CrossRef]

L. Jolissaint, "Optique adaptative au foyer d'un telescope de la classe 1 metre," (Université de Genève, Geneva, Switzerland, 2000).

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Figures (11)

Fig. 1
Fig. 1

Turbulence generator.

Fig. 2
Fig. 2

Optical setup for the Fried parameter characterization.

Fig. 3
Fig. 3

Left, PSF with turbulator off. Right, PSF with turbulator on at ΔT = 53 K.

Fig. 4
Fig. 4

Left, centroid displacement for ΔT = 33 K. Right, ΔT = 163 K. Pupil diameter is 6 mm and tracking time is 20 s.

Fig. 5
Fig. 5

Turbulator anisotropy.

Fig. 6
Fig. 6

Theoretical model fit to the variances for ΔT = 137 K.

Fig. 7
Fig. 7

Empirical relationship between ΔT and measured C N 2Δh average values. Squares, current experiment; diamonds, low-temperature Jolissaint's results.

Fig. 8
Fig. 8

Power spectrum of the centroid displacement (arbitrary units).

Fig. 9
Fig. 9

(Color online) Centroid movement for the two stars on a subimage lenslet.

Fig. 10
Fig. 10

Centroid temporal power spectrum for both stars (ΔT = 90 K).

Fig. 11
Fig. 11

Case at ΔT = 160 K. Left, raw cross-correlation matrix. Center, autocorrelation matrix. Right, deconvolved cross-correlation matrix.

Tables (1)

Tables Icon

Table 1 Experimentally Measured C N 2 and Associated r 0 Values

Equations (18)

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Re = kinetic   energy dissipated   energy = U L ν 1 ,
D T ( ρ ) = [ T ( r + ρ ) T ( r ) ] 2 r ,
D T ( ρ ) = D T ( | ρ | ) = C T 2 ρ 2 / 3 ,
D N ( ρ ) = C N 2 ρ 2 / 3 ,
C N 2 = ( α n P T 2 ) 2 C T 2 ,
C N 2 ( α n P T 2 ) 2 ( δ T ) 2 ,
r 0     5 / 3 = 0.4234 ( 2 π / λ ) 2 0 C N 2 ( h ) d h ,
ϕ ( f ) = 0.023 r 0 5 / 3 ( f 2 + 1 L 0 2 ) - 11 / 6 ,
η [ l 0 ] = exp ( l 0 2 f 2 ) .
η [ l 0 ] exp [ 0.137 ( n + 1 ) 2 ( l 0 / D 2 ) ] ,
f c = 0.3 ( n + 1 ) V D ,
θ iso = 0.314 r 0 h ,
h 5 / 3 = 0 C N 2 ( h ) h 5 / 3  d h 0 C N 2 ( h ) d h ,
FWHM ( FWHM telescope ) 2 + ( FWHM atmosphere ) 2 λ / D 1 + ( D / r 0 ) 2 .
α p = X C F L = P ( x , y ) W x ( x , y ) d x d y P ( x , y ) d x d y ,
σ AoA 2 [ x , y ] = ( 2 π ) 4 / 3 0.033 C N 2 δ h × R 2 f X , Y 2 ( f 2 + L 0 2 ) 11 / 6 exp ( l 0 2 f 2 ) × [ 2 J 1 ( π D f ) π D f ] 2 d f X d f Y .
σ A oA 2 [ x , y ] = 2.8375 C N 2 δ h D 1 / 3 = 0.1698 ( λ / D ) 2 ( D / r 0 ) 5 / 3 .
C N 2 F 1 { F [ C ( δ i , δ j ) ] F [ A ( δ i , δ j ) ] } ( δ i , 0 ) ,

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