Abstract

The new generation of extremely large telescopes will have adaptive optics. Due to the complexity and cost of such systems, it is important to simulate their performance before construction. Most systems planned will have Shack-Hartmann wavefront sensors. Different mathematical models are available for simulation of such wavefront sensors. The choice of wavefront sensor model strongly influences computation time and simulation accuracy. We have studied the influence of three wavefront sensor models on performance calculations for a generic, adaptive optics (AO) system designed for K-band operation of a 42 m telescope. The performance of this AO system has been investigated both for reduced wavelengths and for reduced r0 in the K band. The telescope AO system was designed for K-band operation, that is both the subaperture size and the actuator pitch were matched to a fixed value of r0 in the K-band. We find that under certain conditions, such as investigating limiting guide star magnitude for large Strehl-ratios, a full model based on Fraunhofer propagation to the subimages is significantly more accurate. It does however require long computation times. The shortcomings of simpler models based on either direct use of average wavefront tilt over the subapertures for actuator control, or use of the average tilt to move a precalculated point spread function in the subimages are most pronounced for studies of system limitations to operating parameter variations. In the long run, efficient parallelization techniques may be developed to overcome the problem.

© 2009 OSA

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References

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  1. G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems Engineering for the Preliminary Design of the Thirty Meter Telescope,”Proc. SPIE 7017, 701704–1-11(2008).
  2. M. W. Johns, “The Giant Magellan Telescope (GMT), in Ground-based and Airborne Telescope,” Proc. SPIE 6267, 762–776 (2006).
  3. A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).
  4. N. Hubin, B. L. Ellerbroedk, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J. P. Veran, and C. Verinaud, “Adaptive optics for Extremely Large Telescope, ” in Proceedings of the 232nd Symposium of the International Astronomical Union, P.A.Whitelock, M. Dennefeld and B. Leibundgut, ed. (Cambridge University Press, Cambridge, 2006), pp.60–85.
  5. D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
    [Crossref]
  6. M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
    [Crossref]
  7. B. L. Ellerbroek, “Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors,” Proc. SPIE 6272, 62724K (2006).
    [Crossref]
  8. T. Andersen, A. Enmark, P. Linde, M. Owner-Petersen, A. Sjöström, F. Koch, M. L. Muller, L. Noethe, and B. Sedghi, “An Intergrated Model of the European Extremely Large Telescope,”Proc. SPIE 7017, 70170S1–12 (2008).
  9. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  10. MATLAB is a registered trademark of MathWorks Inc.
  11. J. W. Hardy, Adaptive Optics for Astronomical Telescope, (Oxford University Press, 1998).
  12. B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).
  13. P. Martinez, and A. Klotz, A Practical Guide to CCD Astronomy, (Cambridge University Press, Cambridge, 1997).
  14. M. Owner-Petersen, and N. Devaney, Private communication.
  15. B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
    [Crossref]
  16. M. Kutner, Astronomy, A physical perspective, (Cambridge University Press, Cambridge, 2003).
  17. M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
    [Crossref]

2006 (6)

M. W. Johns, “The Giant Magellan Telescope (GMT), in Ground-based and Airborne Telescope,” Proc. SPIE 6267, 762–776 (2006).

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

B. L. Ellerbroek, “Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors,” Proc. SPIE 6272, 62724K (2006).
[Crossref]

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

2005 (1)

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

1976 (2)

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
[Crossref]

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

Andersen, T.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

Anderson, D.

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

Ardeberg, A.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

Bauman, B.

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

Beckers, J.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

Britton, M.

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

Browne, M.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

Dekany, R.

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

Ellerbroek, B. L.

B. L. Ellerbroek, “Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors,” Proc. SPIE 6272, 62724K (2006).
[Crossref]

Enmark, A.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

Fuensalida, J. J.

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

García-Lorenzo, B.

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

Gavel, D.

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

Hubin, N.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

Johns, M. W.

M. W. Johns, “The Giant Magellan Telescope (GMT), in Ground-based and Airborne Telescope,” Proc. SPIE 6267, 762–776 (2006).

Knutsson, P.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

Korkiakoski, V.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

Le Louarn, M.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

Marchetti, E.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

McGlamery, B. L.

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

Mendizabal, E.

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

Munoz-Tunón, C.

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

Noll, R. J.

Owner-Petersen, M.

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

Shearer, A.

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

Vérinaud, C.

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

J. Opt. Soc. Am. (1)

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

B. García-Lorenzo, J. J. Fuensalida, C. Mũnoz-Tũnón, and E. Mendizabal, “Astronomical site ranking based on tropospheric wind statistics,” Mon. Not. R. Astron. Soc. 356(3), 849–858 (2005).
[Crossref]

Proc. SPIE (7)

B. L. McGlamery, “Computer simulation studies of compensation of turbulence degraded images,” Proc. SPIE 74, 225–233 (1976).

M. Browne, A. Enmark, T. Andersen, and A. Shearer, “Optimised external computation for the Euro50 MATLAB based integrated model,” Proc. SPIE 6271, 627103 (2006).
[Crossref]

M. W. Johns, “The Giant Magellan Telescope (GMT), in Ground-based and Airborne Telescope,” Proc. SPIE 6267, 762–776 (2006).

A. Ardeberg, T. Andersen, J. Beckers, M. Browne, A. Enmark, P. Knutsson, and M. Owner-Petersen, “From Euro50 toward a European ELT,” Proc. SPIE 6267, 62672501–62672510 (2006).

D. Gavel, B. Bauman, R. Dekany, M. Britton, and D. Anderson, “Adaptive Optics Designs for an Infrared Multi-Object Spectrograph on TMT,” Proc. SPIE 6272, 62720R (2006).
[Crossref]

M. Le Louarn, C. Vérinaud, V. Korkiakoski, N. Hubin, and E. Marchetti, “Adaptive optics simulations for the European Extremely Large Telescope,” Proc. SPIE 6272, 627234 (2006).
[Crossref]

B. L. Ellerbroek, “Spatial frequency domain model for adaptive optics compensation of segmented mirror misalignments and figure errors,” Proc. SPIE 6272, 62724K (2006).
[Crossref]

Other (8)

T. Andersen, A. Enmark, P. Linde, M. Owner-Petersen, A. Sjöström, F. Koch, M. L. Muller, L. Noethe, and B. Sedghi, “An Intergrated Model of the European Extremely Large Telescope,”Proc. SPIE 7017, 70170S1–12 (2008).

N. Hubin, B. L. Ellerbroedk, R. Arsenault, R. M. Clare, R. Dekany, L. Gilles, M. Kasper, G. Herriot, M. Le Louarn, E. Marchetti, S. Oberti, J. Stoesz, J. P. Veran, and C. Verinaud, “Adaptive optics for Extremely Large Telescope, ” in Proceedings of the 232nd Symposium of the International Astronomical Union, P.A.Whitelock, M. Dennefeld and B. Leibundgut, ed. (Cambridge University Press, Cambridge, 2006), pp.60–85.

MATLAB is a registered trademark of MathWorks Inc.

J. W. Hardy, Adaptive Optics for Astronomical Telescope, (Oxford University Press, 1998).

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems Engineering for the Preliminary Design of the Thirty Meter Telescope,”Proc. SPIE 7017, 701704–1-11(2008).

P. Martinez, and A. Klotz, A Practical Guide to CCD Astronomy, (Cambridge University Press, Cambridge, 1997).

M. Owner-Petersen, and N. Devaney, Private communication.

M. Kutner, Astronomy, A physical perspective, (Cambridge University Press, Cambridge, 2003).

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Figures (5)

Fig. 1
Fig. 1

Layout of a typical adaptive optics model.

Fig. 2
Fig. 2

Comparison of Strehl ratios as a function of observation wavelength using different wavefront sensor models. The AO system was operated at 2200 nm. No noise was assumed.

Fig. 3
Fig. 3

Comparison of Strehl ratios as a function of wavelength (measurement and observation) using different wavefront sensor models. No noise was assumed.

Fig. 4
Fig. 4

Comparison of the three models for different choice of Fried's parameter. No noise was assumed

Fig. 5
Fig. 5

Strehl ratio for the system using the intermediate and the full models for different guide star magnitudes. Poisson and readout noise was included.

Tables (4)

Tables Icon

Table 1 Adaptive optics system parameters.

Tables Icon

Table 2 FPA parameters.

Tables Icon

Table 3 Atmosphere screen parameters (seven layers) at ORM site [14] [15]

Tables Icon

Table 4 Approximate computation times for major WFS operations (multithreaded C on a 16x2.2GHz AMD Opteron machine) [17]

Equations (4)

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

θx=1Δj=1n(w(n,j)w(1,j))/n2
σ2=(λDs)2[1+0.134(Dsr0(λ))5/3]
W'(x,y)=(r0r0')5/6W(x,y)
F2F1=100.4(m2m1)

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