Abstract

We recently introduced matched filtering in the context of astronomical Shack–Hartmann wavefront sensing with elongated sodium laser beacons [Appl. Opt. 45, 6568 (2006) ]. Detailed wave optics Monte Carlo simulations implementing this technique for the Thirty Meter Telescope dual conjugate adaptive optics system have, however, revealed frequent bursts of degraded closed loop residual wavefront error [Proc. SPIE 6272, 627236 (2006) ]. The origin of this problem is shown to be related to laser guide star jitter on the sky that kicks the filter out of its linear dynamic range, which leads to bursts of nonlinearities that are reconstructed into higher-order wavefront aberrations, particularly coma and trifoil for radially elongated subaperture spots. An elegant reformulation of the algorithm is proposed to extend its dynamic range using a set of linear constraints while preserving its improved noise rejection and Monte Carlo performance results are reported that confirm the benefits of the method.

© 2008 Optical Society of America

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References

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  1. L. Gilles and B. L. Ellerbroek, Appl. Opt. 45, 6568 (2006).
    [CrossRef] [PubMed]
  2. G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).
  3. L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
    [CrossRef]
  4. L. Gilles, Appl. Opt. 44, 993 (2005).
    [CrossRef] [PubMed]
  5. S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
    [CrossRef]

2006 (3)

L. Gilles and B. L. Ellerbroek, Appl. Opt. 45, 6568 (2006).
[CrossRef] [PubMed]

L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
[CrossRef]

S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
[CrossRef]

2005 (1)

Adkins, S. M.

S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
[CrossRef]

Andersen, D.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Azucena, O.

S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
[CrossRef]

Conan, R.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Ellerbroek, B.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Ellerbroek, B. L.

L. Gilles and B. L. Ellerbroek, Appl. Opt. 45, 6568 (2006).
[CrossRef] [PubMed]

L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
[CrossRef]

Gilles, L.

L. Gilles and B. L. Ellerbroek, Appl. Opt. 45, 6568 (2006).
[CrossRef] [PubMed]

L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
[CrossRef]

L. Gilles, Appl. Opt. 44, 993 (2005).
[CrossRef] [PubMed]

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Herriot, G.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Hickson, P.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Jackson, K.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Lardière, O.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Nelson, J. E.

S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
[CrossRef]

Véran, J. P.

L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
[CrossRef]

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Wang, L.

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

Appl. Opt. (2)

Proc. SPIE (2)

S. M. Adkins, O. Azucena, and J. E. Nelson, Proc. SPIE 6272, 62721E (2006).
[CrossRef]

L. Gilles, B. L. Ellerbroek, and J. P. Véran, Proc. SPIE 6272, 627236 (2006).
[CrossRef]

Other (1)

G. Herriot, R. Conan, O. Lardière, D. Andersen, B. Ellerbroek, L. Gilles, P. Hickson, K. Jackson, J. P. Véran, and L. Wang, “Compensation of TMT laser wavefront sensors for variations of sodium layer,” Proc. SPIE (to be published).

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Figures (3)

Fig. 1
Fig. 1

Sample performance results on noise-free data for a scenario with an elongated beacon and the polar coordinate CCD array with 16 × 4 500 mas pixels per subaperture. The dots on the LGS trajectories correspond to the three first bursts of degraded closed loop residual wavefront error.

Fig. 2
Fig. 2

Upper panels display the incremental wavefront error (in quadrature) in the coma and trifoil Zernike modes from the constrained filter results shown in Fig. 1.

Fig. 3
Fig. 3

Wavefront error owing to measurement noise for the same atmospheric phase screen used in Fig. 1 and for a signal level of 900 pde per subaperture per integration time and 3 electrons readout noise per pixel.

Equations (9)

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

I ( θ ) = I 0 + G θ + η ,
θ ̂ = arg min θ I I ( θ ) 2 = R ( I I 0 ) ,
R = ( G T C η 1 G ) 1 G T C η 1 .
C θ = R C η R T = ( G T C η 1 G ) 1 .
θ ̂ = R I .
R = M ( G e T C η 1 G e ) 1 G e T C η 1 ,
M = [ 1 0 0 0 1 0 ] , G e = [ G I 0 ] ,
M = [ 1 0 0 1 1 0 0 0 1 0 0 0 1 1 ] ,
G e = [ G I 0 I 1 I 2 I 3 I 4 ] ,

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