Abstract

We propose a maximum a posteriori–based estimation of the turbulent phase in a large field of view (FOV) to overcome the anisoplanatism limitation in adaptive optics. We show that, whatever the true atmospheric profile, a small number of equivalent layers (two or three) is required for accurate restoration of the phase in the whole FOV. The implications for multiconjugate adaptive optics are discussed in terms of the number and conjugated heights of the deformable mirrors. The number of guide stars required for wave-front measurements in the field is also discussed: three (or even two) guide stars are sufficient to produce good performance.

© 1999 Optical Society of America

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References

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  1. M. Tallon and R. Foy, Astron. Astrophys. 235, 549 (1990).
  2. R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).
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    [CrossRef]
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    [CrossRef]
  8. N. Roddier, Opt. Eng. 29, 1174 (1990).
    [CrossRef]
  9. F. Rigaut and E. Gendron, Astron. Astrophys. 261, 677 (1992).
  10. G. Rousset, NATO ASI Ser. C 115 (1993).
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    [CrossRef]
  13. R. G. Paxman, B. J. Thelen, and J. H. Seldin, Opt. Lett. 19, 123 (1994).
    [CrossRef]

1999 (1)

R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).

1998 (1)

A. Fuchs, M. Tallon, and J. Vernin, Publ. Astron. Soc. Pac. 110, 86 (1998).
[CrossRef]

1995 (1)

R. Racine and B. L. Ellerbroek, Proc. SPIE 2534, 248 (1995).
[CrossRef]

1994 (3)

1993 (1)

G. Rousset, NATO ASI Ser. C 115 (1993).

1992 (1)

F. Rigaut and E. Gendron, Astron. Astrophys. 261, 677 (1992).

1990 (3)

M. Tallon and R. Foy, Astron. Astrophys. 235, 549 (1990).

N. Roddier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

J. Primot, G. Rousset, and J.-C. Fontanella, J. Opt. Soc. Am. A 7, 1598 (1990).
[CrossRef]

1976 (1)

Beckers, J. M.

J. M. Beckers, in Proceedings of the Conference on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1989), p. 693.

Ellerbroek, B. L.

R. Racine and B. L. Ellerbroek, Proc. SPIE 2534, 248 (1995).
[CrossRef]

B. L. Ellerbroek, J. Opt. Soc. Am. A 11, 783 (1994).
[CrossRef]

Fontanella, J.-C.

Foy, R.

M. Tallon and R. Foy, Astron. Astrophys. 235, 549 (1990).

Fuchs, A.

A. Fuchs, M. Tallon, and J. Vernin, Publ. Astron. Soc. Pac. 110, 86 (1998).
[CrossRef]

Gendron, E.

F. Rigaut and E. Gendron, Astron. Astrophys. 261, 677 (1992).

Johnston, D. C.

Marchetti, E.

R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).

Noll, R. J.

Paxman, R. G.

Primot, J.

Racine, R.

R. Racine and B. L. Ellerbroek, Proc. SPIE 2534, 248 (1995).
[CrossRef]

Ragazzoni, R.

R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).

Rigaut, F.

R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).

F. Rigaut and E. Gendron, Astron. Astrophys. 261, 677 (1992).

Roddier, N.

N. Roddier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Rousset, G.

Seldin, J. H.

Tallon, M.

A. Fuchs, M. Tallon, and J. Vernin, Publ. Astron. Soc. Pac. 110, 86 (1998).
[CrossRef]

M. Tallon and R. Foy, Astron. Astrophys. 235, 549 (1990).

Thelen, B. J.

Vernin, J.

A. Fuchs, M. Tallon, and J. Vernin, Publ. Astron. Soc. Pac. 110, 86 (1998).
[CrossRef]

Welsh, B. M.

Astron. Astrophys. (3)

M. Tallon and R. Foy, Astron. Astrophys. 235, 549 (1990).

R. Ragazzoni, E. Marchetti, and F. Rigaut, Astron. Astrophys. 342, 53 (1999).

F. Rigaut and E. Gendron, Astron. Astrophys. 261, 677 (1992).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

NATO ASI Ser. C (1)

G. Rousset, NATO ASI Ser. C 115 (1993).

Opt. Eng. (1)

N. Roddier, Opt. Eng. 29, 1174 (1990).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

R. Racine and B. L. Ellerbroek, Proc. SPIE 2534, 248 (1995).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

A. Fuchs, M. Tallon, and J. Vernin, Publ. Astron. Soc. Pac. 110, 86 (1998).
[CrossRef]

Other (1)

J. M. Beckers, in Proceedings of the Conference on Very Large Telescopes and Their Instrumentation, M.-H. Ulrich, ed. (European Southern Observatory, Garching, Germany, 1989), p. 693.

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Figures (3)

Fig. 1
Fig. 1

Cn2 true profile used in the simulation; Cn2=0 above 15 km. Telescope altitude, 0 km.

Fig. 2
Fig. 2

Influence of the number of EL’s on SR α (in percent). Dashed curve, conventional on-axis single GS and one EL on the telescope pupil. With 5 GS’s: + one EL at 6.5 km; * two EL’s (0 and 8.5 km); three EL’s (0, 5.4, and 11.7 km); four EL’s (0, 4.2, 8.4, and 12.5 km); five EL’s (0, 3, 6.8, 10.7, and 13.7 km).

Fig. 3
Fig. 3

SR (in percent) versus number of GS’s: the maximum (solid curve) and the minimum (dashed curve) values in the FOV. Three EL’s are considered here.

Equations (6)

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Φαr=j=1Ntrueφjr+hjα,
Pφjρjj|ΦαimriPΦαimrj|φjρjjPφjρjj.
PΦαimri|φjrji=1NGSexp-½ΨαirTCi-1Ψαir,
Pφjρjj=j=1NELexp-½φjTρjCKol,j-1φjρj,
Jφjρjj=i=1NGSΨαirTCi-1Ψαir+j=1NELφjρjTCKol,j-1φjρj
σerr2α=1SSΦr,α-j=1NELφˆjr+hjα2dr,

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