Abstract

Many adaptive optics applications require wavefront corrections with a high stroke, and at a high bandwidth. Often, these two requirements cannot be met by a single wavefront corrector, and, instead, the combination of a low-bandwidth, high-stroke woofer and a high-bandwidth low-stroke tweeter is used in a so-called woofer–tweeter architecture. The optimal (minimum residual phase variance) way to split the correction between the woofer and the tweeter in the context of a linear–quadratic–Gaussian (LQG) controller has been addressed previously. However, the necessity to fold the temporal characteristics of the woofer and tweeter into the LQG controller significantly increases its complexity. In this Letter, this optimal strategy is compared to a simpler, ad hoc approach, which consists in optimizing the LQG controller as if it were controlling a high-bandwidth, high-stroke corrector and splitting the correction using first-order high- and low-pass temporal filters. In the case of tilt correction for NFIRAOS on the Thirty Meter Telescope, it is found that the ad hoc approach, which is already used or planned for several systems, holds the same overall correction performance compared to the optimal strategy.

© 2012 Optical Society of America

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References

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  1. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford, 1998).
  2. L. A. Poyneer and J.-P. Véran, J. Opt. Soc. Am. A 27, A223 (2010).
    [CrossRef]
  3. G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
    [CrossRef]
  4. C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, J. Opt. Soc. Am. A 27, A133 (2010).
    [CrossRef]
  5. R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, Appl. Opt. 45, 8964 (2006).
    [CrossRef]
  6. C. Correia, J.-P. Véran, and L. Poyneer, Adaptive Optics: Methods, Analysis and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMB2.

2010 (3)

L. A. Poyneer and J.-P. Véran, J. Opt. Soc. Am. A 27, A223 (2010).
[CrossRef]

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, J. Opt. Soc. Am. A 27, A133 (2010).
[CrossRef]

2006 (1)

Andersen, D.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Atwood, J.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Beauvillier, A.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Boyer, C.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Byrnes, P.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Clare, R. M.

Conan, J.-M.

Conan, R.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Correia, C.

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, J. Opt. Soc. Am. A 27, A133 (2010).
[CrossRef]

C. Correia, J.-P. Véran, and L. Poyneer, Adaptive Optics: Methods, Analysis and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMB2.

Ellerbroek, B.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Ellerbroek, B. L.

Fitzsimmons, J.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Gilles, L.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford, 1998).

Herriot, G.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, Appl. Opt. 45, 8964 (2006).
[CrossRef]

Hickson, P.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Hill, A.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Jackson, K.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Kulcsár, C.

Lardière, O.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Pazder, J.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Pfrommer, T.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Poyneer, L.

C. Correia, J.-P. Véran, and L. Poyneer, Adaptive Optics: Methods, Analysis and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMB2.

Poyneer, L. A.

Raynaud, H.-F.

Reshetov, V.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Roberts, S.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Véran, J.-P.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

L. A. Poyneer and J.-P. Véran, J. Opt. Soc. Am. A 27, A223 (2010).
[CrossRef]

R. M. Clare, B. L. Ellerbroek, G. Herriot, and J.-P. Véran, Appl. Opt. 45, 8964 (2006).
[CrossRef]

C. Correia, J.-P. Véran, and L. Poyneer, Adaptive Optics: Methods, Analysis and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMB2.

Wang, L.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Wevers, I.

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. A (2)

Proc. SPIE (1)

G. Herriot, D. Andersen, J. Atwood, C. Boyer, A. Beauvillier, P. Byrnes, R. Conan, B. Ellerbroek, J. Fitzsimmons, L. Gilles, P. Hickson, A. Hill, K. Jackson, O. Lardière, J. Pazder, T. Pfrommer, V. Reshetov, S. Roberts, J.-P. Véran, L. Wang, and I. Wevers, Proc. SPIE 7736, 77360B (2010).
[CrossRef]

Other (2)

C. Correia, J.-P. Véran, and L. Poyneer, Adaptive Optics: Methods, Analysis and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper AMB2.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford, 1998).

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Figures (2)

Fig. 1.
Fig. 1.

Block diagram of a hybrid continuous–discrete model with continuous uncorrected disturbances and phase correction (solid lines) and discrete measurements and commands (dashed lines). The bottom-left panel depicts the MV controller, and the bottom-right panel shows the suboptimal ad hoc solution using first-order single-pole low-pass/high-pass split correction.

Fig. 2.
Fig. 2.

Top panel, (a) Overall performance in mas rms (b) Optimal frame rates. Solid lines show the MV solution with a single DM+LP/HP filter and dashed lines show the MV solution addressing the woofer and tweeter jointly. The minima and the frame rates with which they were obtained are also indicated in red and green, respectively. Bottom panel, (c) photon+read noise added to the measurements. (d) Effort in mas rms of the correction demanded from the TTS and the DM.

Tables (1)

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Table 1. Parameters Used in the End-to-End Monte Carlo Numerical Simulations

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