Abstract

Optical vortices occur at light propagation in an inhomogeneous medium, disturbing the operation of adaptive optical systems and assuring a priori continuity of the phase fluctuation function. It is clear that the physical process of the light wave propagation has a threshold of complexity relative to the description and measurement of this process, after which the light wave contains points with zero intensity and there is no continuous wavefront. The appearance of zeros indicates the transition of phenomenon in a new condition. The results of numerous studies of phase fluctuations of optical waves in the atmosphere, first of all, provide a basis for estimating the efficiency of operation of adaptive optical systems, second, make it possible to determine the requirements on the wavefront sensors and adaptive mirrors, and, finally, make it possible to determine the structure and properties of phase-conjugated adaptive optical systems.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. I. Tatarskii, Wave Propagation in a Turbulent Medium(Dover, 1967).
  2. N. B. Baranova and B. Ya. Zel’dovich, “Dislocations of the wave-front surface and zeros of the amplitude,” Zh. Eksp. Teor. Fiz. 80, 1789–1797 (1981).
  3. D. L. Fried and J. L. Vaught, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef]
  4. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, and J. Herrmann, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2089 (1995).
    [CrossRef]
  5. V. P. Lukin and B. V. Fortes, “Adaptive phase correction of turbulent distortions under strong intensity fluctuations,” in Proceedings of the III International Symposium on Atmspheric and Oceanic Optics (Institute of Atmospheric Optics, Russian Academy of Sciences, 1996), pp. 28–29.
  6. V. P. Lukin, Atmospheric Adaptive Optics (Nauka, 1986).
  7. V. P. Lukin and B. V. Fortes, Adaptive Formation of Beams and Images in the Atmosphere (Siberian Branch of the Russian Academy of Sciences, 1999).
  8. V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broadening under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
    [CrossRef]
  9. B. V. Fortes, “Phase compensation of image turbulent distortions at strong intensity scintillation,” Atmos. Oceanic Opt. 12, 422–427 (1999).
  10. B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
    [CrossRef]
  11. V. P. Lukin, B. V. Fortes, and N. N. Mayer, “Numerical solution of a ground-based adaptive telescope,” Atmos. Opt. 4, 896–899 (1991).
  12. 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 (Institute of Atmospheric Optics, Russian Academy of Sciences, 1983), pp. 104–106.
  13. 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]
  14. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  15. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
    [CrossRef]
  16. B. R. Hunt, “Matrix formulation of the reconstruction of phase value from phase differences,” J. Opt. Soc. Am. 69, 393–399 (1979).
    [CrossRef]
  17. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980).
    [CrossRef]
  18. T. Hiroaki and T. Takahashi, “Least-squares phase estimation from the phase difference,” J. Opt. Soc. Am. A 5, 416–425 (1988).
    [CrossRef]
  19. H. Takajo and T. Takahashi, “Noniterative method 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]
  20. V. P. Lukin, “Two-color adaptive system and strong intensity fluctuations,” Proc. SPIE 4494 (2001).
  21. V. P. Lukin and B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under strong intensity fluctuations,” Appl. Opt. 41, 5616–5624 (2002).
    [CrossRef]

2002 (1)

2001 (1)

V. P. Lukin, “Two-color adaptive system and strong intensity fluctuations,” Proc. SPIE 4494 (2001).

1999 (2)

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broadening under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

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

1995 (1)

1992 (2)

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

D. L. Fried and J. L. Vaught, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef]

1991 (1)

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

1988 (2)

1981 (1)

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

1980 (1)

1979 (1)

1977 (2)

1976 (1)

Baranova, N. B.

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

Barclay, H. T.

Fortes, B. V.

V. P. Lukin and B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under strong intensity fluctuations,” Appl. Opt. 41, 5616–5624 (2002).
[CrossRef]

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broadening under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

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

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

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

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

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

Fried, D. L.

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 (Institute of Atmospheric Optics, Russian Academy of Sciences, 1983), pp. 104–106.

Lukin, V. P.

V. P. Lukin and B. V. Fortes, “Phase-correction of turbulent distortions of an optical wave propagating under strong intensity fluctuations,” Appl. Opt. 41, 5616–5624 (2002).
[CrossRef]

V. P. Lukin, “Two-color adaptive system and strong intensity fluctuations,” Proc. SPIE 4494 (2001).

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broadening under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

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

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

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

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

Mayer, N. N.

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

Noll, R. J.

Price, T. R.

Primmerman, C. A.

Takahashi, T.

Takajo, H.

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium(Dover, 1967).

Vaught, J. L.

Zel’dovich, B. Ya.

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

Zollars, B. G.

Appl. Opt. (3)

Atmos. Oceanic Opt. (1)

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

Atmos. Opt. (1)

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

J. Opt. Soc. Am. (5)

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

Proc. SPIE (3)

V. P. Lukin and B. V. Fortes, “Phase correction of an image turbulence broadening under condition of strong intensity fluctuations,” Proc. SPIE 3763, 61–72 (1999).
[CrossRef]

B. V. Fortes and V. P. Lukin, “Modeling of the image observed through the turbulent atmosphere,” Proc. SPIE 1668, 477–488 (1992).
[CrossRef]

V. P. Lukin, “Two-color adaptive system and strong intensity fluctuations,” Proc. SPIE 4494 (2001).

Zh. Eksp. Teor. Fiz. (1)

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

Other (5)

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 (Institute of Atmospheric Optics, Russian Academy of Sciences, 1983), pp. 104–106.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium(Dover, 1967).

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

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Schematics of a wave propagation.

Fig. 2.
Fig. 2.

Optical layout of the numerical experiment: (a) Scheme of compensation for phase distortions. (b) Scheme of phase conjugation.

Fig. 3.
Fig. 3.

Dependence of SR on the scintillation index β02 in the scheme of compensation for phase distortions.

Fig. 4.
Fig. 4.

Dependence of SR on the scintillation index β02 in the phase conjugation scheme.

Fig. 5.
Fig. 5.

Experimentally obtained dependence of SR on the variance of amplitude fluctuations β02 of a spherical wave and that calculated in the Rytov approximation.

Fig. 6.
Fig. 6.

Strehl ratio vs normalized path length L/L=dL/kr02 for an adaptive system with a segmented mirror. Circles correspond to control of pistons; rectangles correspond to control of pistons and tilts.

Fig. 7.
Fig. 7.

Dependence of parameter Strehl from normalized length of a path with correction “potential part” of phases. The wavefront sensor of complex amplitude uses algorithm based on the decision NE for d<<r0.

Fig. 8.
Fig. 8.

Dependence of the normalized intensity (parameter Strehl) from length of a wave of reference radiation. Meanings of normalized length of a path L/kr02 (normalized on length of a wave of corrected radiation): 10.25, 20.5, 30.75, 41.0.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

r0=(0.489k2Cn2L)3/5,
β02=1.24Cn2k7/6L11/6=1.241.46(Lkr02)5/6=2.54q5/6,
2ikUz=(2x2+2y2+2k2(n1))U,
φ+kSρ,
U(ρ)=A0(ρ)exp(argu(ρ)).
Δl=(λr/2π)(φr+2nπ),
φ=(λr/λ)(φr+2nπ).
φij=arg(U¯i,j);Δijx=φi+1jφi+1j;Δijy=φij+1φi+1j.

Metrics