Abstract

We present a general, undiscretized formulation of astronomical adaptive optics that encompasses arbitrary guide star sources and deformable mirror configurations. It is shown that wave-front measurements can be represented as samples of an integral transform of the turbulence perturbation and also that the desired information for adaptive correction is a subset of this transformed space. Some properties of this space are explored, and their implications for adaptive optics are discussed.

© 2000 Optical Society of America

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References

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  1. R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
    [CrossRef]
  2. F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, 1999), Chap. 2.
    [CrossRef]
  3. D. C. Johnston and B. M. Walsh, J. Opt. Soc. Am. A 11, 394 (1994).
    [CrossRef]
  4. S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).
  5. R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).
  6. T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
    [CrossRef]
  7. B. L. Ellerbroek and F. J. Rigaut, in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007 (to be published).

2000 (1)

R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
[CrossRef]

1999 (2)

R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

1994 (1)

Conan, J.-M.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Deans, S. R.

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).

Ellerbroek, B. L.

B. L. Ellerbroek and F. J. Rigaut, in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007 (to be published).

Fusco, T.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Johnston, D. C.

Marchetti, E.

R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
[CrossRef]

R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).

Michau, V.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Mugnier, L. M.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Raggazoni, R.

R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
[CrossRef]

R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).

Rigaut, F.

R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).

Rigaut, F. J.

B. L. Ellerbroek and F. J. Rigaut, in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007 (to be published).

Rousset, G.

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Valente, G.

R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
[CrossRef]

Walsh, B. M.

Astron. Astrophys. (1)

R. Raggazoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, L53 (1999).

J. Opt. Soc. Am. A (1)

Nature (1)

R. Raggazoni, E. Marchetti, and G. Valente, Nature 403, 54 (2000).
[CrossRef]

Proc. SPIE (1)

T. Fusco, J.-M. Conan, V. Michau, L. M. Mugnier, and G. Rousset, Proc. SPIE 3763, 125 (1999).
[CrossRef]

Other (3)

B. L. Ellerbroek and F. J. Rigaut, in Adaptive Optical Systems Technology, P. L. Wizinowich, ed., Proc. SPIE4007 (to be published).

F. Roddier, ed., Adaptive Optics in Astronomy (Cambridge U. Press, Cambridge, 1999), Chap. 2.
[CrossRef]

S. R. Deans, The Radon Transform and Some of Its Applications (Wiley, New York, 1983).

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Figures (3)

Fig. 1
Fig. 1

Straight ray of light integrates the phase perturbation along its path. This path can be parameterized by η and ξ, its intersections with the two horizontal planes shown.

Fig. 2
Fig. 2

When turbulence and light propagation are confined to a vertical plane the measurement space can be parameterized by scalar quantities η and ξ. Thicker lines show how this space is sampled by a laser guide star at ξ=ξ0, a natural guide star with (anticlockwise) zenith distance θ, and a natural star at zenith.

Fig. 3
Fig. 3

Gray-scale representation of a deformable mirror function in ηξ parameter space for the two-dimensional problem. The mirror function mx is mapped directly onto line ξ=η, and lines of equiphase have slope 1-H/h, where h is the conjugation height of the mirror (h/H=0.1 in the depicted case). The area inside the dashed lines indicates a region over which functions such as this must match Ψη,ξ to correct for a finite field view.

Tables (1)

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Table 1 Sampling Functions for Various Sources

Equations (6)

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Ψη,ξ=1+η-ξH21/2×ψrδ2x-η+η-ξHzdr,
ψr=jψjxδz-hj,
Ψη,ξ=jψjh˜jξ+1-h˜jη,
wη=Ψη,ξsη,
Mη,ξ=mh˜ξ+1-h˜η
σ2=kPdηΨη,ξkη+iMiη,ξkη2,

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