Abstract

An experimental study on phase compensation for turbulent effects with a 37-element adaptive optics system is performed in both a simulated turbulence cell and in a real atmosphere. The experimental results demonstrate that the compensated Strehl ratio S 0, which is influenced mainly by the deformable-mirror fitting error, has a functional form S 0 =exp[-κ(d/ r 0)5/3], where r 0 is Fried’s coherence length and d is the average interval of the actuators on the deformable mirror. The fitting parameter κ is 0.45. Numerical simulations are also performed with the experimental parameters. The numerical results are in agreement with data obtained in the experiment, which shows that the direct-tilt phase-reconstruction method used in our four-dimensional simulation code is reasonable.

© 1998 Optical Society of America

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References

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  1. R. Hudgin, “Wave-front compensation error due to finite corrector-element size,” J. Opt. Soc. Am. 67, 393–395 (1977).
    [CrossRef]
  2. R. K. Tyson, D. P. Crawford, R. J. Morgan, “Adaptive optics system considerations for ground-to-space propagation,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 146–156 (1990).
    [CrossRef]
  3. J. F. Belsher, D. L. Fried, “Adaptive optics mirror fitting error,” Optical Sciences Rep. TR-521 (Optical Sciences, Placentia, Calif., 1983).
  4. R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).
  5. Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).
  6. Zh. Gong, Y. Y. Wu, “Finite temporal measurements of the statistical characteristics of the atmospheric coherence length,” Appl. Opt. 37, 4541–4543 (1998).
    [CrossRef]
  7. M. T. Tavis, H. T. Yura, “Scintillation effects on centroid anisoplanatism,” J. Opt. Soc. Am. A 4, 57–59 (1987).
    [CrossRef]
  8. Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).
  9. Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).
  10. W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” in Adaptive Optics and Optical Structures, J. Schulte, R. K. Tyson, eds., Proc. SPIE1271, 82–93 (1990).
    [CrossRef]
  11. Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).
  12. Y. Wang, “Research on the problems of laser propagation in the atmosphere and phase compensation,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Science, Hefei, China, 1996).

1998 (1)

1995 (2)

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).

1994 (2)

Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).

Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).

1987 (1)

1977 (1)

Belsher, J. F.

J. F. Belsher, D. L. Fried, “Adaptive optics mirror fitting error,” Optical Sciences Rep. TR-521 (Optical Sciences, Placentia, Calif., 1983).

Crawford, D. P.

R. K. Tyson, D. P. Crawford, R. J. Morgan, “Adaptive optics system considerations for ground-to-space propagation,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 146–156 (1990).
[CrossRef]

Fried, D. L.

J. F. Belsher, D. L. Fried, “Adaptive optics mirror fitting error,” Optical Sciences Rep. TR-521 (Optical Sciences, Placentia, Calif., 1983).

Gong, Zh.

Zh. Gong, Y. Y. Wu, “Finite temporal measurements of the statistical characteristics of the atmospheric coherence length,” Appl. Opt. 37, 4541–4543 (1998).
[CrossRef]

Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).

Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).

Hudgin, R.

Jiang, W.

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” in Adaptive Optics and Optical Structures, J. Schulte, R. K. Tyson, eds., Proc. SPIE1271, 82–93 (1990).
[CrossRef]

Li, H.

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” in Adaptive Optics and Optical Structures, J. Schulte, R. K. Tyson, eds., Proc. SPIE1271, 82–93 (1990).
[CrossRef]

Morgan, R. J.

R. K. Tyson, D. P. Crawford, R. J. Morgan, “Adaptive optics system considerations for ground-to-space propagation,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 146–156 (1990).
[CrossRef]

Tavis, M. T.

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

R. K. Tyson, D. P. Crawford, R. J. Morgan, “Adaptive optics system considerations for ground-to-space propagation,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 146–156 (1990).
[CrossRef]

Wang, Ch.

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

Wang, Y.

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).

Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).

Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).

Y. Wang, “Research on the problems of laser propagation in the atmosphere and phase compensation,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Science, Hefei, China, 1996).

Wu, X.

Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).

Wu, Y.

Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).

Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).

Wu, Y. Y.

Yura, H. T.

Acta Opt. Sin. (1)

Y. Wu, Y. Wang, Zh. Gong, “Analysis of the residual wavefront variance influenced by the nonlinear response of deformable mirror in wavefront correction,” Acta Opt. Sin. 15, 1028–1031 (1995).

Appl. Opt. (1)

High Power Laser and Particle Beams (3)

Y. Wang, Y. Wu, Zh. Gong, “Numerical model of adaptive optics system,” High Power Laser and Particle Beams 6, 59–64 (1994).

Y. Wu, Y. Wang, X. Wu, “Calibration of the optical quality of a large telescope system,” High Power Laser and Particle Beams 4, 510–514 (1994).

Y. Wu, Y. Wang, Ch. Wang, W. Jiang, “The effect of beacon intensity on the wavefront detection by Hartmann sensor,” High Power Laser and Particle Beams 7, 117–119 (1995).

J. Opt. Soc. Am. (1)

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

Other (5)

R. K. Tyson, D. P. Crawford, R. J. Morgan, “Adaptive optics system considerations for ground-to-space propagation,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 146–156 (1990).
[CrossRef]

J. F. Belsher, D. L. Fried, “Adaptive optics mirror fitting error,” Optical Sciences Rep. TR-521 (Optical Sciences, Placentia, Calif., 1983).

R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).

Y. Wang, “Research on the problems of laser propagation in the atmosphere and phase compensation,” Ph.D. dissertation (Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Science, Hefei, China, 1996).

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” in Adaptive Optics and Optical Structures, J. Schulte, R. K. Tyson, eds., Proc. SPIE1271, 82–93 (1990).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental schematic for the turbulence cell and the real atmosphere.

Fig. 2
Fig. 2

Probability density distributions of Strehl ratios measured in the turbulence cell.

Fig. 3
Fig. 3

Compensated Strehl ratio versus d/ r 0 measured in the turbulence cell and the real atmosphere.

Fig. 4
Fig. 4

Integral probability of the Strehl ratio in the turbulence cell.

Equations (8)

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r 1 = 0.364 0.6 D λ D 1.2 σ 1 2 - 0.6 ,
P r 1 = 5 3 r 1 N - 1 ! N r 0 / r 1 5 / 3 N exp - N r 0 / r 1 5 / 3 .
r 1 1 = Γ 2 / 5 r 0 , r 1 N = 1 - 8 / 5 N 1 - 1 / N 8 / 5   r 1 N - 1 ,     N 2 ,
N = σ 1 2 2 σ 1 2 2 - 1 - 1 .
P S 1 = 1 S 1 ln S 1 M - 1 ! M   ln S 1 ln S 0 M × exp - M   ln S 1 ln S 0 .
S 1 M = 1 - ln S 0 / M - M ,
S 1 2 M = 1 - 2   ln S 0 / M - M ,
σ 2 = σ χ 2 + σ fit 2 + σ sen 2 + σ tmp 2 + σ iso 2 + σ non 2 .

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