Abstract

The control of two deformable mirrors for compensation of time-varying fluctuations in the complex field that results from wave propagation through a turbulent medium is considered. Iterative vector space projection methods are utilized to determine the control commands to be applied to the two deformable mirrors. Convergence of the iterative algorithm is accelerated when the algorithm is initialized, at each measurement period, with the values for the phase commands obtained from the previous measurement period. Furthermore, it is found that, if the sample frequency is sufficiently greater than the Greenwood frequency, then only a single iterative step at each measurement period is required to obtain good compensation of both amplitude and phase fluctuations.

© 2002 Optical Society of America

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References

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  1. M. C. Roggemann, D. J. Lee, “Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere,” Appl. Opt. 37, 4577–4585 (1998).
    [CrossRef]
  2. M. C. Roggemann, S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bisonnette, eds., Proc. SPIE3763, 29–40 (1999).
    [CrossRef]
  3. R. A. Gonsalves, “Compensation of scintillation with a phase-only adaptive optic,” Opt. Lett. 22, 588–590 (1997).
    [CrossRef] [PubMed]
  4. J. D. Barchers, B. L. Ellerbroek, “Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments,” J. Opt. Soc. Am. A 18, 399–411 (2001).
    [CrossRef]
  5. J. D. Barchers, “Evaluation of the impact of finite-resolution effects on scintillation compensation using two deformable mirrors,” J. Opt. Soc. Am. A 18, 3098–3109 (2001).
    [CrossRef]
  6. J. D. Barchers, “Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation,” J. Opt. Soc. Am. A 19, 54–63 (2002).
    [CrossRef]
  7. J. D. Barchers, B. L. Ellerbroek, “Increase in the compensated field of view in strong scintillation by use of two deformable mirrors,” in Beyond Conventional Adaptive Optics, R. Ragazzonni, ed. (European Southern Observatory, Garching, Germany, available online at http://www.adaopt.it/venice2001/proceedings/pdf/barchers_pap.pdf .).
  8. R. A. Gonsalves, “Adaptive optics by sequential diversity imaging,” in Beyond Conventional Adaptive Optics, R. Ragazzonni, ed., (European Southern Observatory, Garching, Germany, available online at http://www.adaopt.it/venice2001/proceedings/pdf/gonsalves_pap.pdf .).
  9. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

2002 (1)

2001 (2)

1998 (1)

1997 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Barchers, J. D.

Deng, S.

M. C. Roggemann, S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bisonnette, eds., Proc. SPIE3763, 29–40 (1999).
[CrossRef]

Ellerbroek, B. L.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Gonsalves, R. A.

Lee, D. J.

Roggemann, M. C.

M. C. Roggemann, D. J. Lee, “Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere,” Appl. Opt. 37, 4577–4585 (1998).
[CrossRef]

M. C. Roggemann, S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bisonnette, eds., Proc. SPIE3763, 29–40 (1999).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Appl. Opt. (1)

J. Opt. Soc. Am. A (3)

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane images,” Optik (Stuttgart) 35, 225–246 (1972).

Other (3)

M. C. Roggemann, S. Deng, “Scintillation compensation for laser beam projection using segmented deformable mirrors,” in Propagation and Imaging through the Atmosphere III, M. C. Roggemann, L. R. Bisonnette, eds., Proc. SPIE3763, 29–40 (1999).
[CrossRef]

J. D. Barchers, B. L. Ellerbroek, “Increase in the compensated field of view in strong scintillation by use of two deformable mirrors,” in Beyond Conventional Adaptive Optics, R. Ragazzonni, ed. (European Southern Observatory, Garching, Germany, available online at http://www.adaopt.it/venice2001/proceedings/pdf/barchers_pap.pdf .).

R. A. Gonsalves, “Adaptive optics by sequential diversity imaging,” in Beyond Conventional Adaptive Optics, R. Ragazzonni, ed., (European Southern Observatory, Garching, Germany, available online at http://www.adaopt.it/venice2001/proceedings/pdf/gonsalves_pap.pdf .).

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Figures (2)

Fig. 1
Fig. 1

Algorithm performance for (a) and (b) f S /f G = 100 and (c) and (d) f S /f G = 10. The recursive implementation of the WSGPA requires fewer iterations than the WSGPA for both cases. The one-step recursive algorithm has equivalent performance to the other two algorithms when the sample frequency is much higher than the Greenwood frequency.

Fig. 2
Fig. 2

Algorithm performance as a function of f S /f G . (a) The average Strehl ratio for each algorithm and (b) the average number of iterations for each algorithm. The one-step recursive algorithm exhibits good performance for values of f S /f G greater than 20.

Equations (9)

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Tz·=-1·expiπλzκ¯2,
S=| dr¯1Ubr¯1expiϕ1r¯1TzUr*r¯2exp-iϕ2r¯2|2| dr¯1Ubr¯1Ub*r¯1|| dr¯2Urr¯2Ur*r¯2|,
S  Ub expiϕ1, TzUl expiϕ2.
Tz,α·=-1·expiπλzκ¯2-signα×πα22κ¯2.
Sˆα  Ub expiϕ1, Tz,αUl expiϕ2.
ϕ1=arg Ub*T-z,αUr expiϕ2.
ϕ2=arg Ur*Tz,αUb expiϕ1.
ϕ2k=arg Ur*kTz,αUbkexpiϕ1k-1,
ϕ1k=arg Ub*kT-z,αUrkexpiϕ2k.

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