Abstract

Phase correction of a plane wave and a spatiolimited beam propagating through a turbulent layer of atmosphere were considered. The required adaptive corrector element size and the system bandwidth were found by numerical simulation. These requirements were determined to be the same as for a weak-intensity scintillation approximation. The size of the required segmented mirror element was found to be equal to Fried length r 0, whereas the tolerable time lag was r 0/V, where V is the wind velocity. However, the local slope sensors then became impractical, as did tip-tilt correction over the corrector subapertures.

© 2002 Optical Society of America

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References

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  1. V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, USSR, 1967).
  2. N. B. Baranova, B. Ya. Zeldovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).
  3. D. L. Fried, J. L. Vaught, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef] [PubMed]
  4. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrmann, Appl. Opt. 34, 2081–2089 (1995).
    [CrossRef] [PubMed]
  5. V. P. Lukin, B. V. Fortes, “Adaptive phase correction of turbulent distortions under strong intensity fluctuations,” in Proceedings of the III International Symposium on Atmospheric and Oceanic OpticsV. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, USSR, 1996), pp. 28–29.
  6. V. P. Lukin, Atmospheric Adaptive Optics (Nauka, Novosibirsk, USSR, 1986).
  7. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
    [CrossRef]
  8. P. A. Konyaev, “Numerical solution of stochastical quasi-optical problems by splitting method,” in Proceedings of the VII All-Union Symposium on Laser Radiation Propagation in the Atmosphere, V. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, Russia, 1983), pp. 104–106.
  9. V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).
  10. B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Visual Data Interpretation, J. R. Alexander, ed., Proc. SPIE1668, 477–488 (1992).
  11. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  12. D. L. Fried, “Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977).
    [CrossRef]
  13. R. H. Hudgin, “Wavefront reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
    [CrossRef]
  14. B. R. Hunt, “Matrix formulation of the reconstruction of phase value from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979).
    [CrossRef]
  15. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980).
    [CrossRef]
  16. T. Hiroaki, T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988).
    [CrossRef]
  17. H. Takajo, T. Takahashi, “Noniterative mothod for obtaining the exact solution for the normal equation in least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 1818–1827 (1988).
    [CrossRef]
  18. L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
    [CrossRef]
  19. V. P. Lukin, B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 61–72 (1999).
    [CrossRef]
  20. B. V. Fortes, “Phase compensation of image turbulent distortions at strong intensity scintillation,” Atmos. Ocean. Opt. 12, 422–427 (1999).
  21. V. P. Lukin, B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1999).

1999

B. V. Fortes, “Phase compensation of image turbulent distortions at strong intensity scintillation,” Atmos. Ocean. Opt. 12, 422–427 (1999).

1995

1992

1991

V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).

1988

1981

N. B. Baranova, B. Ya. Zeldovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).

1980

1979

1977

1976

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zeldovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).

Barclay, H. T.

Becker, J.

L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
[CrossRef]

Eisenhardt, P.

L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
[CrossRef]

Feit, M. D.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Fortes, B. V.

B. V. Fortes, “Phase compensation of image turbulent distortions at strong intensity scintillation,” Atmos. Ocean. Opt. 12, 422–427 (1999).

V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).

V. P. Lukin, B. V. Fortes, “Adaptive phase correction of turbulent distortions under strong intensity fluctuations,” in Proceedings of the III International Symposium on Atmospheric and Oceanic OpticsV. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, USSR, 1996), pp. 28–29.

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Visual Data Interpretation, J. R. Alexander, ed., Proc. SPIE1668, 477–488 (1992).

V. P. Lukin, B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1999).

V. P. Lukin, B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 61–72 (1999).
[CrossRef]

Fried, D. L.

Goad, L.

L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
[CrossRef]

Herrmann, J.

Hiroaki, T.

Hudgin, R. H.

Humphreys, R. A.

Hunt, B. R.

Konyaev, P. A.

P. A. Konyaev, “Numerical solution of stochastical quasi-optical problems by splitting method,” in Proceedings of the VII All-Union Symposium on Laser Radiation Propagation in the Atmosphere, V. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, Russia, 1983), pp. 104–106.

Lukin, V. P.

V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).

V. P. Lukin, Atmospheric Adaptive Optics (Nauka, Novosibirsk, USSR, 1986).

V. P. Lukin, B. V. Fortes, “Adaptive phase correction of turbulent distortions under strong intensity fluctuations,” in Proceedings of the III International Symposium on Atmospheric and Oceanic OpticsV. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, USSR, 1996), pp. 28–29.

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Visual Data Interpretation, J. R. Alexander, ed., Proc. SPIE1668, 477–488 (1992).

V. P. Lukin, B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1999).

V. P. Lukin, B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 61–72 (1999).
[CrossRef]

Mayer, N. N.

V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Noll, R. J.

Price, T. R.

Primmerman, C. A.

Roddier, F.

L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
[CrossRef]

Takahashi, T.

Takajo, H.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, USSR, 1967).

Vaught, J. L.

Zeldovich, B. Ya.

N. B. Baranova, B. Ya. Zeldovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).

Zollars, B. G.

Appl. Opt.

Appl. Phys.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation in high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Atmos. Ocean. Opt.

B. V. Fortes, “Phase compensation of image turbulent distortions at strong intensity scintillation,” Atmos. Ocean. Opt. 12, 422–427 (1999).

Atmos. Opt.

V. P. Lukin, B. V. Fortes, N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Zh. Eksp. Teor. Fiz.

N. B. Baranova, B. Ya. Zeldovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).

Other

L. Goad, F. Roddier, J. Becker, P. Eisenhardt, “National Optical Astronomy Observatories (NOAO) IR adaptive optics program. III. Criteria for the wavefront sensor selection,” in Advanced Technology Optical Telescopes III, L. D. Barr, ed., Proc. SPIE628, 305–313 (1986).
[CrossRef]

V. P. Lukin, B. V. Fortes, “Phase correction of an image turbulence broading under condition of strong intensity fluctuations,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bissonnette, eds., Proc. SPIE3763, 61–72 (1999).
[CrossRef]

B. V. Fortes, V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” in Visual Data Interpretation, J. R. Alexander, ed., Proc. SPIE1668, 477–488 (1992).

V. I. Tatarskii, Wave Propagation in a Turbulent Atmosphere (Nauka, Moscow, USSR, 1967).

P. A. Konyaev, “Numerical solution of stochastical quasi-optical problems by splitting method,” in Proceedings of the VII All-Union Symposium on Laser Radiation Propagation in the Atmosphere, V. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, Russia, 1983), pp. 104–106.

V. P. Lukin, B. V. Fortes, “Adaptive phase correction of turbulent distortions under strong intensity fluctuations,” in Proceedings of the III International Symposium on Atmospheric and Oceanic OpticsV. E. Zuev, ed. (Institute of Atmospheric Optics, Russian Academy of Sciences, Tomsk, USSR, 1996), pp. 28–29.

V. P. Lukin, Atmospheric Adaptive Optics (Nauka, Novosibirsk, USSR, 1986).

V. P. Lukin, B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 1999).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the wave propagation.

Fig. 2
Fig. 2

Strehl ratio versus normalized time lag of the AOS.

Fig. 3
Fig. 3

Strehl ratio versus normalized path length L/(kr 0 2) for an adaptive system with a segmented mirror. Circles, control of pistons; rectangles, control of pistons and tilts.

Fig. 4
Fig. 4

Strehl ratio versus normalized path length L/(kr 0 2) for various sensors.

Fig. 5
Fig. 5

Dependence of the variance of phase-difference estimations through local tilts on normalized path length.

Fig. 6
Fig. 6

Results of correction for image aberrations. Strehl ratio (SR) versus normalized aperture diameter (D/ r 0) for several values of scintillation index.

Fig. 7
Fig. 7

Results of correction for spatiolimited beam aberrations. Strehl ratio (SR) versus normalized aperture diameter (D/ r 0) for several values of scintillation index. (a) indicates exact phase conjugation; in (b), phase dislocations have been filtered out.

Equations (26)

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r0=0.489k2Cn2L-3/5, ρ0=1.46k2Cn2L-3/5, r0/ρ0=1.46/0.4893/5 1.93,
β02=1.24Cn2k7/6L11/6=1.241.46Lkρ025/6=1.240.489Lkr025/6=2.54q5/6,
2ikUz=2x2+2y2+2k2n-1U.
Ux, y, z=0=1
φρ, t=argUρ, t-τ,
σ2DφτV=6.88τV/r05/3,
Sexp-σ2=exp-6.88τV/r05/3.
σ2=1.03d/r05/3.
σ2=0.134d/r05/3.
φ+kSρ,
φ=argŪ, Ū=1d2dd2ρUρ,
S=1kP d2ρIρφρ=1kP Re UIm U-Im URe Ud2ρ.
P=dd2ρIρ.
g=1Pd2ρIρφρ.
Δx=gxd, Δy=gyd.
gx=1PdRe U  Im Ux-Im U  Re Uxd2ρ,gy=1PdRe U  Im Uy-Im U  Re Uyd2ρ.
φl,j+gxx+gyy,
εi,j=arg Ūi+1,j-arg Ūi,j*-gxi,jd.
σx2=0.726L/kr025/6.
p1=k3Cn2, p2=k-1L.
r0-5/3=0.423p1p2, β02=1.23p1p211/6 plane wave,r0-5/3=0.159p1p2, β02=0.496p1p211/6 spherical wave.
4φi,j-φi+1,j-φi-1,j-φi,j+1-φi,j-1=Δi-1,jx+Δi,j-1y-Δi,jx-Δi,jy, i, j=1,  , N.
Δi,jx=argEi+1,jEi,j*, Δi,jy=argEi,j+1Ei,j*.
E0ρ=Aρexp-i arg Erρ.
β02=0.496k7/6Cn2L11/6.
E0ρ=Aρexp-iFˆErρ,

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