Abstract

Wave-front reconstruction with use of the Fourier transform has been validated through theory and simulation. This method provides a dramatic reduction in computational costs for large adaptive (AO) systems. Because such a reconstructor can be expressed as a matrix, it can be used as an alternative in a matrix-based AO control system. This was done with the Palomar Observatory AO system on the 200-in. Hale telescope. Results of these tests indicate that Fourier-transform wave-front reconstruction works in a real system. For both bright and dim stars, a Hudgin-geometry Fourier-transform method produced performance comparable to that of the Palomar Adaptive Optics least squares. The Fried-geometry method had a noticeable Strehl ratio performance degradation of 0.043 in the K band (165-nm rms wave-front error added in quadrature) on a dim star.

© 2003 Optical Society of America

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References

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  1. F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
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  5. M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
    [CrossRef]
  6. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).
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    [CrossRef]

2003 (2)

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

L. A. Poyneer, Proc. SPIE 4839, 1023 (2003).
[CrossRef]

2002 (2)

2000 (1)

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Bloemhof, E.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Brack, G.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Brack, G. L.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

Brandl, B.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Brase, J. M.

Burruss, R. S.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

Dekany, R.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Dekany, R. G.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

Dekens, F.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Ellerbroek, B.

Gavel, D. T.

Gilles, L.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

Hayward, T.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

MacMartin, D. G.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

Oppenheimer, B.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Poyneer, L. A.

Shi, F.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Trinh, T.

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Troy, M.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Vogel, C.

Weerahandi, S.

S. Weerahandi, Exact Statistical Methods for Data Analysis (Springer-Verlag, New York, 1995).
[CrossRef]

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

Proc. SPIE (3)

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, and R. G. Dekany, Proc. SPIE 4839, 1035 (2003).
[CrossRef]

L. A. Poyneer, Proc. SPIE 4839, 1023 (2003).
[CrossRef]

M. Troy, R. Dekany, G. Brack, B. Oppenheimer, E. Bloemhof, T. Trinh, F. Dekens, F. Shi, T. Hayward, and B. Brandl, Proc. SPIE 4007, 31 (2000).
[CrossRef]

Other (2)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

S. Weerahandi, Exact Statistical Methods for Data Analysis (Springer-Verlag, New York, 1995).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Strehl ratios for the four stars tested versus average subaperture flux (as obtained from telemetry). Averages with σ error bars for PALAO LS only are plotted for clarity for the brighter stars, which have a narrow range of flux. The theoretical performance curve for an AO system under varying flux is best-fitted to the data.

Fig. 2
Fig. 2

Strehl ratios through time for bright star SAO 53755 mv=6.6. FT-Hud-fil achieved the same average Strehl ratio as LS (0.61) FT-Fri-lw came in slightly below, at 0.59.

Fig. 3
Fig. 3

Average subaperture flux versus time for observation of dim star BD+25 51 mv=10.5. A reasonable explanation for this drop-off across the observation period is that high cirrus clouds were gradually reducing available guide-star light.

Fig. 4
Fig. 4

Differences in method performance are visible for dim star BD+25 51 mv=10.5. The statistical correlations between Strehl and flux are very high: 0.88 for LS, 0.94 for FT-Hud-fil, and 0.96 got FT-Fri-lw. Based on best-fit curves of Eq. (1), FT-Fri-lw has clearly lower Strehl ratio performance (by 0.045) as a function of flux than the other two methods.

Equations (1)

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SNp=exp-0.5-k1Np+165.72Np2,

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