Abstract

A method to generate the turbulence measurements of a Shack–Hartmann wavefront sensor is presented. Numerical simulations demonstrate that the spatial and temporal statistic properties of the slopes are respected, allowing us to generate the turbulence wavefront gradient corresponding to both natural and laser guide stars, as well as time series in accordance with the frozen flow model.

© 2014 Optical Society of America

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References

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  1. R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
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  2. C. Harding, R. Johnston, and R. Lane, Appl. Opt. 38, 2161 (1999).
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  4. G. Dai, Proc. SPIE 2302, 62 (1994).
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  5. C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, J. Opt. Soc. Am. A 26, 1307 (2009).
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  6. M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
    [CrossRef]
  7. L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
    [CrossRef]
  8. D. Fried, J. Opt. Soc. Am. 55, 1427 (1965).
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  9. W. P. Burckel and R. N. Gray, Appl. Opt. 52, 4672 (2013).
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  11. V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).
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    [CrossRef]
  13. D. L. Fried, J. Opt. Soc. Am. 67, 370 (1977).
    [CrossRef]
  14. F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
    [CrossRef]
  15. R. Conan, Importance de l'echelle externe pour la Haute Resolution en Astronomie (EUE, 2011).
  16. F. Roddier, in Progress in Optics, E. Wolf, ed. (North-Holland, 1981), Vol. 19, pp. 281–376.

2013

2009

2006

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

2004

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

1999

1998

F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
[CrossRef]

1994

G. Dai, Proc. SPIE 2302, 62 (1994).
[CrossRef]

1992

R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
[CrossRef]

1990

1977

1966

1965

Borgnino, J.

Bradley, C.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Burckel, W. P.

Conan, J.-M.

Conan, R.

R. Conan, Importance de l'echelle externe pour la Haute Resolution en Astronomie (EUE, 2011).

Dai, G.

G. Dai, Proc. SPIE 2302, 62 (1994).
[CrossRef]

Dainty, J.

R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
[CrossRef]

Fried, D.

Fried, D. L.

Glindemann, A.

R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
[CrossRef]

Gray, R. N.

Harding, C.

Hilton, A.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Hubin, N.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

Johnston, R.

Jolissaint, L.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Keskin, O.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Korkiakoski, V.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

Kulcsár, C.

Lai, O.

F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
[CrossRef]

Lane, R.

C. Harding, R. Johnston, and R. Lane, Appl. Opt. 38, 2161 (1999).
[CrossRef]

R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
[CrossRef]

Le Louarn, M.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

Marchetti, E.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

Petit, C.

Raynaud, H.-F.

Rigaut, F.

F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
[CrossRef]

Roddier, F.

F. Roddier, in Progress in Optics, E. Wolf, ed. (North-Holland, 1981), Vol. 19, pp. 281–376.

Roddier, N.

N. Roddier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Tatarskii, V.

V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

Véran, J.-P.

F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
[CrossRef]

Vérinaud, C.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

Wallace, B.

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

N. Roddier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Proc SPIE

L. Jolissaint, O. Keskin, C. Bradley, B. Wallace, and A. Hilton, Proc SPIE 5572, 256 (2004).
[CrossRef]

Proc. SPIE

G. Dai, Proc. SPIE 2302, 62 (1994).
[CrossRef]

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, Proc. SPIE 6272, 627234 (2006).
[CrossRef]

F. Rigaut, J.-P. Véran, and O. Lai, Proc. SPIE 3353, 1038 (1998).
[CrossRef]

Waves Random Media

R. Lane, A. Glindemann, and J. Dainty, Waves Random Media 2, 209 (1992).
[CrossRef]

Other

R. Conan, Importance de l'echelle externe pour la Haute Resolution en Astronomie (EUE, 2011).

F. Roddier, in Progress in Optics, E. Wolf, ed. (North-Holland, 1981), Vol. 19, pp. 281–376.

V. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, 1971).

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Figures (5)

Fig. 1.
Fig. 1.

Normalized covariance matrices for D=8m and a 40×40 lenslet array. The top graph shows, from left to right, the sx and sy covariance and the cross-covariance between sx and sy. The top and bottom rows correspond to the theoretical and numerical covariances, respectively. The bottom graph shows the difference between the theoretical and numerical covariances.

Fig. 2.
Fig. 2.

X axis cut of the sx structure function. The dashed lines and the black dots correspond to the theoretical and the numerical structure functions, respectively.

Fig. 3.
Fig. 3.

Y axis cut of the sx structure function. The dashed lines and the black dots correspond to the theoretical and the numerical structure functions, respectively.

Fig. 4.
Fig. 4.

Slope variance for a source at infinity and at z=20km as a function of the lenslet size d. The dashed lines correspond to the theoretical variance and the round unfilled markers correspond to the numerical variance.

Fig. 5.
Fig. 5.

Spatiotemporal sx (top) and sy (bottom) covariance matrices for D=8m and a 40×40 lenslet array.

Tables (2)

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Table 1. Seven-Layer Turbulence Model

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Table 2. Three-Layer Turbulence Profile

Equations (23)

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φ(x,y)=1.4r056i=1Nκj=1NφΓ(κ¯i)l=1NLξ0l12,×{ζ1l(i,j)cos[η1l(i,j),+κ¯i(xlcosϕj+ylsinϕj)],+ζ2l(i,j)cos[η2l(i,j),κ¯i(xlsinϕjylcosϕj)]},xl=γl(xvx,lt)+hlθx,yl=γl(yvy,lt)+hlθy,γl=1hlz,
Γ(κ¯i)=[Λ(κ¯i)κ¯iΔκiΔφ]12.
Λ(κ¯i)=(κ¯i2+κ02)116
f=κmaxκmin,
δ=Δκiκ¯i.
κ¯i=κmin2fiNκ(1+f1Nκ).
Δκi=κminfiNκ(1f1Nκ).
φj=(j12)Δφ
Nκ=lnfln(2+δ2δ)
Nφ=π4(f1Nκ+1f1Nκ1).
f=(4Nφ+π4Nφπ)Nκ
δ=π2Nφ.
ζ=(lnβ1)12
η=2πβ2,
sx,y=λ2π1d2d/2d/2d/2d/2dr⃗φ(xxL,yyL)x,y,
sx=λ2π1d2d/2d/2dy[φ(xL+d2,y+yL)φ(xLd2,y+yL)],
sy=λ2π1d2d/2d/2dx[φ(x+xL,yL+d2)φ(x+xL,yLd2)].
sx=λ2π1.4r056i=1Nκj=1NφΓ(κ¯i)×l=1NLξ0l12sinc(γlκ¯x,ijd2)sinc(γlκ¯y,ijd2)×(ξ1lκ¯x,ijξ2lκ¯y,ij),
sy=λ2π1.4r056i=1Nκj=1NφΓ(κ¯i)×l=1NLξ0l12sinc(γlκ¯x,ijd2)sinc(γlκ¯y,ijd2)×(ξ1lκ¯y,ij+ξ2lκ¯x,ij),
ξ1l=ζ1l(i,j)sin[η1l(i,j)+κ¯x,ijxL,l+κ¯y,ijyL,l]
ξ2l=ζ2l(i,j)sin[η2l(i,j)κ¯y,ijxL,l+κ¯x,ijyL,l],
xL,l=γl(xLvx,lt)+hlθx,yL,l=γl(yLvy,lt)+hlθy,κ¯x,ij=κ¯icosϕj,
κ¯y,ij=κ¯isinϕj.

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