Abstract

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.

© 1998 Optical Society of America

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References

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1996

1995

W. A. Coles, J. P. Filice, R. G. Frehlich, M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Appl. Opt. 34, 2089–2101 (1995).
[CrossRef] [PubMed]

G. D. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News 6, 16–21 (1995).
[CrossRef]

1994

1993

1992

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” J. Opt. Soc. Am. A 9, 1525–1535 (1992).

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstruction,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

1991

M. P. Dames, R. J. Dowling, P. McKee, D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 30, 2685–2691 (1991).
[CrossRef] [PubMed]

F. Yu. Kanev and V. P. Lukin, “Amplitude phase beam control with the help of a two-mirror adaptive system,” Atmos. Opt. 4, 878–881 (1991).

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 4, 856–863 (1991).

1989

1980

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

1973

1969

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Boeke, B. R.

Cederquist, J. N.

Cleis, R. A.

Cochran, G.

G. Cochran, “Phase screen generation,” Tech. Rep. TR-663 (The Optical Sciences Company, Placentia, Calif., 1985).

Cohn, R. W.

Coles, W. A.

Dames, M. P.

Dowling, R. J.

Eismann, M. T.

Ellerbroek, B. L.

Enguehard, S.

S. Enguehard, B. Hatfield, “Compensated atmospheric optics,” Prog. Quantum Electron.19, 239–301 (1995).

Fender, J. S.

G. D. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News 6, 16–21 (1995).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

Filice, J. P.

Fortes, B. V.

Frehlich, R. G.

Fugate, R. Q.

Gallagher, N. C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8.

Harp, J. C.

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Hatfield, B.

S. Enguehard, B. Hatfield, “Compensated atmospheric optics,” Prog. Quantum Electron.19, 239–301 (1995).

Higgins, C. H.

Jelonek, M. P.

Kanev, F. Yu.

Kanev and V. P. Lukin, F. Yu.

F. Yu. Kanev and V. P. Lukin, “Amplitude phase beam control with the help of a two-mirror adaptive system,” Atmos. Opt. 4, 878–881 (1991).

Konyaev, P. A.

Lange, W. J.

Lee, R. W.

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Liang, M.

Liu, B.

Love, G. D.

G. D. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News 6, 16–21 (1995).
[CrossRef]

Lukin, V. P.

Matson, C. L.

McKee, P.

Meinhardt, J. A.

Moroney, J. F.

Oliker, M. D.

Restaino, S. R.

G. D. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News 6, 16–21 (1995).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann, J. A. Meinhardt, “Image reconstruction by means of wave-front sensor measurements in closed-loop adaptive-optics systems,” J. Opt. Soc. Am. A 10, 1996–2007 (1993).
[CrossRef]

M. C. Roggemann, C. L. Matson, “Power spectrum and Fourier phase spectrum estimation by using fully and partially compensating adaptive optics and bispectrum postprocessing,” J. Opt. Soc. Am. A 9, 1525–1535 (1992).

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstruction,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

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

Ruane, R. E.

Sindle, D. W.

Slavin, A. C.

Spinhirne, J. M.

Tai, A. M.

Tatarskii, V. I.

V. I. Tatarskii, “The effects of the turbulence atmosphere on wave propagation,” U.S. Department of Commerce TT68-50464 (National Technical Information Service, Springfield, Va., 1971).

Welsh, B. M.

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

Wild, W. J.

Winker, D. M.

Wood, D.

Wynia, J. M.

Yadlowsky, M.

Appl. Opt.

Atmos. Opt.

F. Yu. Kanev and V. P. Lukin, “Amplitude phase beam control with the help of a two-mirror adaptive system,” Atmos. Opt. 4, 878–881 (1991).

F. Yu. Kanev, V. P. Lukin, “Algorithms of compensation for thermal blooming,” Atmos. Opt. 4, 856–863 (1991).

Comput. Electr. Eng.

M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstruction,” Comput. Electr. Eng. 18, 451–466 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[CrossRef]

Opt. Photon. News

G. D. Love, J. S. Fender, S. R. Restaino, “Adaptive wavefront shaping with liquid crystals,” Opt. Photon. News 6, 16–21 (1995).
[CrossRef]

Proc. IEEE

R. W. Lee, J. C. Harp, “Weak scattering in random media, with applications to remote probing,” Proc. IEEE 57, 375–406 (1969).
[CrossRef]

Other

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 8.

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

V. I. Tatarskii, “The effects of the turbulence atmosphere on wave propagation,” U.S. Department of Commerce TT68-50464 (National Technical Information Service, Springfield, Va., 1971).

S. Enguehard, B. Hatfield, “Compensated atmospheric optics,” Prog. Quantum Electron.19, 239–301 (1995).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 3.

G. Cochran, “Phase screen generation,” Tech. Rep. TR-663 (The Optical Sciences Company, Placentia, Calif., 1985).

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Figures (4)

Fig. 1
Fig. 1

Block diagram of the scintillation-correction system.

Fig. 2
Fig. 2

Block diagram of the phase-retrieval technique for controlling the amplitude of the field falling on DM2.

Fig. 3
Fig. 3

Example of a single realization of the scintillation-correction simulation for r 0 = 10 cm: (a) amplitude of the incident scintillated field at the receiving aperture, (b) amplitude of the field falling on DM2 for the outgoing beam, (c) amplitude of the scintillation-corrected field propagated to the phase-screen plane, (d) amplitude of the phase-only corrected field propagated to the phase-screen plane, (e) x-axis slices of the phase of the two-deformable-mirror corrected field and the phase-only corrected field after propagation from the aperture back through the phase screen and the phase of the original random phase screen, (f) x-axis slice of the amplitude of both the scintillation-corrected field (solid curve) and the phase-only corrected field (dash–dot curve) in the far field of the phase-screen plane.

Fig. 4
Fig. 4

x-axis slices of the average far-field amplitude patterns for three values of r 0: (a) 10 cm, (b) 20 cm, (c) 30 cm. The solid curves indicate the results obtained for the two-deformable-mirror scintillation-control technique and the dash–dot curves indicate the results obtained for phase-only correction.

Tables (2)

Tables Icon

Table 1 Comparison of Theoretical σχ 2 and σ̂χ 2 Obtained from the Simulation for Various Values of r0

Tables Icon

Table 2 Ratio of Peak On-Axis Amplitudes R and Mean Number of Phase-Retrieval Iterations NI Required for Convergence for Various Values of r0

Equations (26)

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

Ũ b x f = A b x f exp j ψ b x f ,
Ũ t x f = B x f exp j ψ t x f ,
B x f     A b x f ,
ψ t x f = - ψ b x f ,
Ũ 1 x = A   exp j ψ 1 x .
Ũ 2 x f = FT Ũ 1 x = B x f exp j ϕ x f ,
B x f norm = A b x f norm .
σ 2 =   | A b x f norm | - | B x f norm | 2 d x f .
| σ k - σ k - 1 | σ k - 1 10 - 4
Ũ out x s = Ũ in x s exp j ϕ s x x ,
ρ 0 = 3.44 - 3 / 5 r 0 ,
H f = exp j   2 π z λ 1 - λ f 2 1 / 2 ,
d H f d f 2 λ zf
d H f d f max 2 λ z   1 2 Δ x .
P = d H f d f max - 1 = Δ x λ z .
P Δ f 3 ,
N 3 λ z Δ x 2 .
σ χ 2 = 0.563 k 7 / 6 0 L d z C n 2 z L - z 5 / 6 ,
C n 2 z = C n 2 z = 0 z = 0 0 z > 0 ,
σ χ 2 = 0.563 k 7 / 6 C ˜ n 2 L 5 / 6 ,
C ˜ n 2 = 0 L d z C n 2 z .
r 0 = 0.185 4 π k 2 C ˜ n 2 3 / 5 .
σ χ 2 = 7.075 k - 5 / 6 r 0 0.185 - 5 / 3 L 5 / 6 .
σ χ 2 = 1 4 ln σ I 2 + 1 ,
σ I 2 = E I 2 - E I 2 E I 2 .
R = on-axis far-field amplitude for two-deformable-mirror correction case on-axis far-field amplitude for phase-only correction case

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