Abstract

Laser guide stars (LGSs) aim at increasing the sky coverage of adaptive optics (AO) as this is highly restricted when using only natural guide stars. With such three-dimensional extended objects, spot elongation may limit the measurement accuracy of wavefronts. We evaluate the effect of differential focal anisoplanatism, induced solely by the longitudinal extension of a side-launched LGS, on the slope measurements performed by a Shack–Hartmann for a 40m class telescope. We also take this effect into account in the wavefront reconstruction and derive estimations of the resulting wavefront error in a multi-LGS AO system. We find an error of 100nm in the worst case at the subaperture level and a small error of the order of 10nm for six LGSs after wavefront reconstruction.

© 2011 Optical Society of America

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References

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  1. D. L. Fried, J. Opt. Soc. Am. 72, 52 (1982).
    [CrossRef]
  2. F. Chassat, J. Opt. 20, 13 (1989).
    [CrossRef]
  3. C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, J. Opt. Soc. Am. A 23, 613 (2006).
    [CrossRef]
  4. N. Vedrenne, V. Michau, C. Robert, and J.-M. Conan, J. Opt. Soc. Am. A 24, 2980 (2007).
    [CrossRef]
  5. R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).
  6. C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
    [CrossRef]
  7. T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
    [CrossRef]
  8. S. Oberti, “E-ELT AO design inputs: relevant atmospheric parameters,” E-SPE-ESO-276-0206 issue 1 (2008).
  9. M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
    [CrossRef]

2010 (2)

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
[CrossRef]

2008 (1)

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

2007 (1)

2006 (1)

1989 (1)

F. Chassat, J. Opt. 20, 13 (1989).
[CrossRef]

1985 (1)

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

1982 (1)

Amans, J.-P.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Béchet, C.

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

Chassat, F.

F. Chassat, J. Opt. 20, 13 (1989).
[CrossRef]

Clenet, Y.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Cohen, M.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Conan, J.-M.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
[CrossRef]

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

N. Vedrenne, V. Michau, C. Robert, and J.-M. Conan, J. Opt. Soc. Am. A 24, 2980 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, J. Opt. Soc. Am. A 23, 613 (2006).
[CrossRef]

Foy, R.

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

Fried, D. L.

Fusco, T.

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
[CrossRef]

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, J. Opt. Soc. Am. A 23, 613 (2006).
[CrossRef]

Gendron, E.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Gratadour, D.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
[CrossRef]

Hubin, N.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Jagourel, P.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Labeyrie, A.

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

Meimon, S.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Michau, V.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

N. Vedrenne, V. Michau, C. Robert, and J.-M. Conan, J. Opt. Soc. Am. A 24, 2980 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, J. Opt. Soc. Am. A 23, 613 (2006).
[CrossRef]

Oberti, S.

S. Oberti, “E-ELT AO design inputs: relevant atmospheric parameters,” E-SPE-ESO-276-0206 issue 1 (2008).

Paufique, J.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Petit, C.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Robert, C.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

C. Robert, J.-M. Conan, D. Gratadour, L. Schreiber, and T. Fusco, J. Opt. Soc. Am. A 27, A201 (2010).
[CrossRef]

N. Vedrenne, V. Michau, C. Robert, and J.-M. Conan, J. Opt. Soc. Am. A 24, 2980 (2007).
[CrossRef]

C. Robert, J.-M. Conan, V. Michau, T. Fusco, and N. Vedrenne, J. Opt. Soc. Am. A 23, 613 (2006).
[CrossRef]

Rousset, G.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Schnetler, H.

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Schreiber, L.

Tallon, M.

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

Tallon-Bosc, I.

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

Thiébaut, E.

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

Vedrenne, N.

Astron. Astrophys. (1)

R. Foy and A. Labeyrie, Astron. Astrophys. 152, L29 (1985).

J. Opt. (1)

F. Chassat, J. Opt. 20, 13 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Proc. SPIE (2)

M. Tallon, I. Tallon-Bosc, C. Béchet, and E. Thiébaut, Proc. SPIE 7015, 70151N (2008).
[CrossRef]

T. Fusco, S. Meimon, Y. Clenet, M. Cohen, H. Schnetler, J. Paufique, V. Michau, J.-P. Amans, D. Gratadour, C. Petit, C. Robert, P. Jagourel, E. Gendron, G. Rousset, J.-M. Conan, and N. Hubin, Proc. SPIE 7736, 77360D (2010).
[CrossRef]

Other (1)

S. Oberti, “E-ELT AO design inputs: relevant atmospheric parameters,” E-SPE-ESO-276-0206 issue 1 (2008).

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Figures (3)

Fig. 1
Fig. 1

X slope measurement error ( rad 2 ) versus the angular size of the spot (arcseconds) along X.

Fig. 2
Fig. 2

WFE ( rad 2 ) decomposed onto KL coefficients [see Eq. (1)]. LS and WLS reconstruction errors are shown as solid and dotted curves, respectively. (Top) 1000 modes are used for one LGS, while (bottom) 350 modes are used for six LGSs. The associated fits are shown as dashed curves.

Fig. 3
Fig. 3

WFE ( rad 2 ) decomposed onto KL coefficients (350 modes): WLS reconstructor for six side-launched LGSs, considering either C ε th or C ε d . Errors obtained with C ε th or C ε d are shown by dotted and solid curves, respectively. The associated fits are shown by dashed curves.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

WFE β = T r ( φ ε · φ ε T ) = i κ ε i 2 ,
WFE β = T r ( M β W C ε W T M β T + M β ( W Δ I ) C Φ ( W Δ I ) T M β T + M β [ W ε Φ T ( W Δ I ) T + ( W Δ I ) Φ ε T W T ] M β T ) ,
W WLS = ( Δ T C ε 1 Δ ) 1 · Δ T C ε 1 .
WFE β = T r ( M β W C ε W T M β T ) .

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