Abstract

Wave fronts distorted by the atmosphere preserve high-spatial-frequency information. This information can be retrieved by use of adaptive optics systems to correct the incoming wave front. This correction should be as nearly complete as possible. In experiments performed in the visible, only partial compensation is attainable. We provide a theoretical model to predict the intensity statistics of the light in the image center as a function of the number of Zernike polynomials corrected.

© 1998 Optical Society of America

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References

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  1. J. Y. Wang and J. K. Markey, J. Opt. Soc. Am. 68, 78 (1978).
    [CrossRef]
  2. F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).
  3. M. C. Roggemann, Appl. Opt. 30, 4227 (1991).
    [CrossRef] [PubMed]
  4. M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).
  5. A. Labeyrie, Astron. Astrophys. 298, 544 (1995).
  6. J. R. P. Angel, Nature (London) 368, 203 (1994).
    [CrossRef]
  7. S. M. Stahl and D. G. Sandler, Astrophys. J. 454, L153 (1995).
  8. J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 12–19.
  9. R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976).
    [CrossRef]
  10. J. Conan, “Etude de la correction partielle en optique adaptative,” Ph.D. dissertation (Office National d’Études et de Recherches Aérospatiales, Chatillon, France, 1995).
  11. J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985).
  12. N. Roddier, Opt. Eng. 29, 1174 (1990).
    [CrossRef]

1995 (2)

A. Labeyrie, Astron. Astrophys. 298, 544 (1995).

S. M. Stahl and D. G. Sandler, Astrophys. J. 454, L153 (1995).

1994 (1)

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

1991 (2)

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

M. C. Roggemann, Appl. Opt. 30, 4227 (1991).
[CrossRef] [PubMed]

1990 (1)

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

1978 (1)

1976 (1)

Angel, J. R. P.

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

Conan, J.

J. Conan, “Etude de la correction partielle en optique adaptative,” Ph.D. dissertation (Office National d’Études et de Recherches Aérospatiales, Chatillon, France, 1995).

Fontanella, J. C.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Gaffard, J. P.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985).

J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 12–19.

Labeyrie, A.

A. Labeyrie, Astron. Astrophys. 298, 544 (1995).

Lena, P.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Markey, J. K.

Merkle, F.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Noll, R. J.

Rigaut, F.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Roddier, N.

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

Roggemann, M. C.

M. C. Roggemann, Appl. Opt. 30, 4227 (1991).
[CrossRef] [PubMed]

M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

Rousset, G.

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

Sandler, D. G.

S. M. Stahl and D. G. Sandler, Astrophys. J. 454, L153 (1995).

Stahl, S. M.

S. M. Stahl and D. G. Sandler, Astrophys. J. 454, L153 (1995).

Wang, J. Y.

Welsh, B.

M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

Appl. Opt. (1)

Astron. Astrophys. (2)

F. Rigaut, G. Rousset, J. C. Fontanella, J. P. Gaffard, F. Merkle, and P. Lena, Astron. Astrophys. 250, 280 (1991).

A. Labeyrie, Astron. Astrophys. 298, 544 (1995).

Astrophys. J. (1)

S. M. Stahl and D. G. Sandler, Astrophys. J. 454, L153 (1995).

J. Opt. Soc. Am. (2)

Nature (London) (1)

J. R. P. Angel, Nature (London) 368, 203 (1994).
[CrossRef]

Opt. Eng. (1)

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

Other (4)

J. Conan, “Etude de la correction partielle en optique adaptative,” Ph.D. dissertation (Office National d’Études et de Recherches Aérospatiales, Chatillon, France, 1995).

J. W. Goodman, Statistical Optics (Wiley-Interscience, New York, 1985).

J. W. Goodman, Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 12–19.

M. C. Roggemann and B. Welsh, Imaging through Turbulence (CRC, Boca Raton, Fla., 1996).

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Figures (2)

Fig. 1
Fig. 1

Value of D/ρ0 in the telescope pupil predicted by Eqs.  (9) and (10) (solid curve) and values obtained from the simulation (filled circles) as a function of the number of corrected polynomials for D/r0=38.4.

Fig. 2
Fig. 2

From top to bottom and left to right, light-intensity probability distribution for 1, 41, 71, and 101 corrected polynomials. Solid curves, theoretical values; filled circles, simulated values. Intensity values have been normalized to the central value of the Airy pattern with full correction.

Equations (10)

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Φr,θ=i=1aiZir,θ,
Δj=i=j+1ai2,
Ar=1Nk=1Nαkcos ϕk,Ai=1Nk=1Nαksin ϕk,
PAr,Ai=12πσr2exp-Ar-Ar2/2σr2×12πσi2exp-Ai2/2σi2,
PI,θ=1212πσr2exp-I cos θ-Ar22σr2×12πσi2exp-I sin θ22σi2,
PI=-ππPI,θdθ.
Pϕ=12πΔj1/2exp-ϕ2/2Δj.
Ar=Nα¯Mϕ1=Nα¯-cosϕPϕdϕ,σr2=α2¯/21+Mϕ2-α¯2Mϕ21, σi2=α2¯/21-Mϕ2.
ΔjD/r0=coefjD/r05/3,
Δ3D/ρ0=0.134D/ρ05/3.

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