Abstract

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness.

© 2000 Optical Society of America

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References

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, New York, 1991).
  2. W. Jiang, H. Li, “Hartmann–Shack wavefront sensing and wavefront control algorithm,” in Adaptive Optics and Optical Structures, J. J. Schulte-in-den-Baeumen, R. K. Tyson, eds., Proc. SPIE1271, 82–93 (1990).
    [CrossRef]
  3. C. Boyer, V. Michon, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the COME-ON project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–423 (1990).
    [CrossRef]
  4. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  5. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
    [CrossRef]
  6. J. M. Martin, S. M. Flatte, “Intensity images and statistics from numerical simulation of wave propagation in 3-D random media,” Appl. Opt. 27, 2111–2126 (1988).
    [CrossRef] [PubMed]
  7. B. M. Welsh, C. S. Gardner, “Effects of turbulence-induced anisoplanatism on the imaging performance of adaptive-astronomical telescopes using laser guide stars,” J. Opt. Soc. Am. A 8, 69–80 (1991).
    [CrossRef]
  8. R. R. Parenti, R. J. Sasiela, “Laser-guide-star systems for astronomical applications,” J. Opt. Soc. Am. A 11, 288–309 (1994).
    [CrossRef]
  9. P. B. Ulrich, L. E. Wilson, eds., Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, Proc. SPIE1221, (1990); P. B. Ulrich, L. E. Wilson eds., Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, Proc. SPIE1408, (1991).
  10. R. V. Digumarthi, N. G. Metha, R. M. Blankinship, “Effects of a realistic adaptive optics system on the atmospheric propagation of a high energy laser beam,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 157–165 (1990).
    [CrossRef]
  11. C. A. Primmerman, T. R. Price, R. A. Humphreys, B. G. Zollars, H. T. Barclay, J. Herrman, “Atmospheric-compensation experiments in strong-scintillation conditions,” Appl. Opt. 34, 2081–2088 (1995).
    [CrossRef] [PubMed]

1995 (1)

1994 (1)

1991 (1)

1988 (1)

1976 (2)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of 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]

Barclay, H. T.

Blankinship, R. M.

R. V. Digumarthi, N. G. Metha, R. M. Blankinship, “Effects of a realistic adaptive optics system on the atmospheric propagation of a high energy laser beam,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 157–165 (1990).
[CrossRef]

Boyer, C.

C. Boyer, V. Michon, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the COME-ON project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–423 (1990).
[CrossRef]

Digumarthi, R. V.

R. V. Digumarthi, N. G. Metha, R. M. Blankinship, “Effects of a realistic adaptive optics system on the atmospheric propagation of a high energy laser beam,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 157–165 (1990).
[CrossRef]

Feit, M. D.

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

Flatte, S. M.

Fleck, J. A.

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

Gardner, C. S.

Herrman, J.

Humphreys, R. A.

Jiang, W.

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

Martin, J. M.

Metha, N. G.

R. V. Digumarthi, N. G. Metha, R. M. Blankinship, “Effects of a realistic adaptive optics system on the atmospheric propagation of a high energy laser beam,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 157–165 (1990).
[CrossRef]

Michon, V.

C. Boyer, V. Michon, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the COME-ON project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–423 (1990).
[CrossRef]

Morris, J. R.

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

Noll, R. J.

Parenti, R. R.

Price, T. R.

Primmerman, C. A.

Rousset, G.

C. Boyer, V. Michon, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the COME-ON project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–423 (1990).
[CrossRef]

Sasiela, R. J.

Tyson, R. K.

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

Welsh, B. M.

Zollars, B. G.

Appl. Opt. (2)

Appl. Phys. (1)

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

J. Opt. Soc. Am. (1)

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

Other (5)

P. B. Ulrich, L. E. Wilson, eds., Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, Proc. SPIE1221, (1990); P. B. Ulrich, L. E. Wilson eds., Propagation of High-Energy Laser Beams through the Earth’s Atmosphere II, Proc. SPIE1408, (1991).

R. V. Digumarthi, N. G. Metha, R. M. Blankinship, “Effects of a realistic adaptive optics system on the atmospheric propagation of a high energy laser beam,” in Propagation of High-Energy Laser Beams through the Earth’s Atmosphere, P. B. Ulrich, L. E. Wilson, eds., Proc. SPIE1221, 157–165 (1990).
[CrossRef]

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

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

C. Boyer, V. Michon, G. Rousset, “Adaptive optics: interaction matrix measurements and real time control algorithms for the COME-ON project,” in Amplitude and Intensity Spatial Interferometry, J. B. Breckinridge, ed., Proc. SPIE1237, 406–423 (1990).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Combination of numerical simulation of laser propagation in the atmosphere with that of an AO system.

Fig. 2
Fig. 2

Surface drawing of deformed phase wave front including overall tilt before phase tailoring.

Fig. 3
Fig. 3

Topographic drawing of phase wave front of Fig. 2.

Fig. 4
Fig. 4

Surface drawing of AO-corrected phase wave front of Fig. 2.

Fig. 5
Fig. 5

Surface drawing of phase wave front of Fig. 2 after phase tailoring.

Fig. 6
Fig. 6

Surface drawing of residual phase wave front of Fig. 2 after phase tailoring.

Fig. 7
Fig. 7

Cross section of phase wave front of Fig. 2 at y grid point -4.

Fig. 8
Fig. 8

Cross section of phase wave front of Fig. 5 at y grid point -4.

Tables (9)

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Table 1 Six Strehl Ratios

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Table 2 STRCC in Different Turbulent Media

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Table 3 Effect of Grid Number of Propagation on Strehl Ratio

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Table 4 Test of Isotropism of Phase Screens (I)

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Table 5 Test of Isotropism of Phase Screens (II)

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Table 6 STRCC in the Different Turbulent Media

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Table 7 Strehl Ratio and Phase Variance σφ 2 without the Overall Tilt of an AO System

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Table 8 Comparison of Focusing Calculations with the FFT and the Integration Method

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Table 9 Effects of Lateral Wind Speed V on STRCC of AO Phase Compensation and the Complete Phase Conjugation

Equations (30)

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

2ik ϕz+2ϕx2+2ϕy2+k2n2-n02ϕ=0,
ϕx, y, z=Ex, y, zexp-ikz.
n2-n02=n0-n12-n022n1,
x¯=x/a1-z/l, y¯=y/a1-z/l, ζ=z/ka2,
2i ψζ+11-ka2ζ/l22ψx¯2+2ψy¯2+2k2a2n1ψ=0,
ψx¯, y¯, ζ=ca28πPT1/2×1-z/lϕx, y, zexpikx2+y22l1-z/l,
2i ψζ+2k2a2n1ψ=0.
ψx¯, y¯, ζ+Δζ=ψx¯, y¯, ζexpik2a2n1Δζ=ψx¯, y¯, ζexpikn1Δz,
ψx¯, y¯, ζ+=ψx¯, y¯, ζexpikn1Δz.
Γx, y=n1Δz=πΔzΔkxΔky1/2I=-Nx/2+1Nx/2J=-Ny/2+1Ny/2expiIΔkxx+iJΔkyyΦn1/2IΔkx, JΔkya1IΔkx, JΔky+ia2IΔkx, JΔky,
Φnkx, ky=0.033Cn2k02+kx2+ky2-11/6.
a1kx, ky=a1-kx, -ky, a2kx, ky=-a2-kx, -ky.
Δkx=2πNxΔx=2πNxΔx¯a1-ka2ζ/l, Δky=2πNyΔy=2πNyΔy¯a1-ka2ζ/l,
ΓmxΔx, myΔy=2πN0.033πΔzCn2ΔxΔy1/2×I=-N/2+1-N/2J=-N/2+1N/2exp2πIimxN+2πJimyN2πL02+2πINΔx2+2πJNΔy211/12×a1IΔkx, JΔky+ia2IΔkx, JΔky,
u2x, y=Σfiλr2expikru1x0, y0dx0dy0,
xc=T x|u2x, y|2dxdyT |u2x, y|2dxdy,
yc=T y|u2x, y|2dxdyT |u2x, y|2dxdy,
Gx=2π/fλxc,
Gy=2π/fλyc,
θx=1mi=1m Gxi,
θy=1mi=1m Gyi,
ψmx, y=j=1K VjRjx, y,
Rjx, y=2πλexplnbx-xj2+y-yj2/d2,
Gxi=j=1K GvxijVj,
Gyi=j=1K GvyijVj,
Gvxij=1si SiRjx, yxdxdy,
Gvyij=1si SiRjx, yydxdy.
G=GvV.
V=Gv+G,
ψc=ψtilt+ψm=θxx+θyy+j=1K VjRjx, y.

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