Abstract

The achievable Strehl ratio when a finite-bit correction to an aberrated wave front is implemented is examined. The phase-conjugate engine used to measure the aberrated wave front consists of a quadrature interferometric wave-front sensor, a liquid-crystal spatial light modulator, and computer hardware–software to calculate and apply the correction. A finite-bit approximation to the conjugate phase is calculated and applied to the spatial light modulator to remove the aberrations from the optical beam. The experimentally determined Strehl ratio of the corrected beam is compared with analytical expressions for the expected Strehl ratio and shown to be in good agreement with those predictions.

© 2004 Optical Society of America

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References

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  1. G. D. Love, N. Andrews, P. Burch, D. Buscher, P. Doel, C. Dunlop, J. Major, R. Myers, A. Purvis, R. Sharples, A. Vick, A. Zadrozny, S. R. Restaino, and A. Glindemann, Appl. Opt. 34, 6058 (1995).
    [CrossRef] [PubMed]
  2. E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).
  3. K. L. Baker, E. A. Stappaerts, S. C. Wilks, P. E. Young, D. Gavel, J. Tucker, D. A. Silva, and S. S. Olivier, Opt. Lett. 29, 47 (2004).
    [CrossRef] [PubMed]
  4. C. J. Buchenauer and A. R. Jacobson, Rev. Sci. Instrum. 48, 769 (1977).
    [CrossRef]
  5. J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, 1998).
  6. D. L. Fried, J. Opt. Soc. Am. A 15, 2759 (1998).
    [CrossRef]
  7. K. Itoh, Appl. Opt. 21, 2470 (1982).
    [CrossRef]

2004 (1)

1998 (1)

1995 (1)

1982 (1)

1977 (1)

C. J. Buchenauer and A. R. Jacobson, Rev. Sci. Instrum. 48, 769 (1977).
[CrossRef]

Andrews, N.

Baker, K.

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Baker, K. L.

Brase, J.

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Buchenauer, C. J.

C. J. Buchenauer and A. R. Jacobson, Rev. Sci. Instrum. 48, 769 (1977).
[CrossRef]

Burch, P.

Buscher, D.

Doel, P.

Dunlop, C.

Fried, D. L.

Gavel, D.

K. L. Baker, E. A. Stappaerts, S. C. Wilks, P. E. Young, D. Gavel, J. Tucker, D. A. Silva, and S. S. Olivier, Opt. Lett. 29, 47 (2004).
[CrossRef] [PubMed]

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Glindemann, A.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, 1998).

Itoh, K.

Jacobson, A. R.

C. J. Buchenauer and A. R. Jacobson, Rev. Sci. Instrum. 48, 769 (1977).
[CrossRef]

Love, G. D.

Major, J.

Myers, R.

Olivier, S.

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Olivier, S. S.

Purvis, A.

Restaino, S. R.

Sharples, R.

Silva, D. A.

Stappaerts, E.

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Stappaerts, E. A.

Tucker, J.

Vick, A.

Wilks, S.

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

Wilks, S. C.

Young, P. E.

Zadrozny, A.

Appl. Opt. (2)

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

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

C. J. Buchenauer and A. R. Jacobson, Rev. Sci. Instrum. 48, 769 (1977).
[CrossRef]

Other (2)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, Oxford, 1998).

E. Stappaerts, K. Baker, D. Gavel, S. Wilks, S. Olivier, and J. Brase, in 2004 IEEE Aerospace Conference (Institute of Electrical and Electronic Engineers, Piscataway, N.J., 2004).

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Figures (5)

Fig. 1
Fig. 1

Closed-loop adaptive-optics layout: BS, beam splitters; M, mirrors; L, lenses; I, iris; IF, interference filter; λ/2, λ/4, half- and quarter-wave plates, respectively; WFS, wave-front sensor.

Fig. 2
Fig. 2

Algorithm flow chart used to determine the finite-bit phase from the sine and cosine interferograms.

Fig. 3
Fig. 3

(a) Near-field image and (b) uncorrected far-field image. (c) Wrapped phase from the interferometric wave-front sensor, (d) locations of the branch points in the wrapped phase.

Fig. 4
Fig. 4

Finite-bit corrected point-spread functions. The 1-, 2-, 3-, and 6-bit corrected far-field images are displayed.

Fig. 5
Fig. 5

Strehl ratio values as a function of bit corrections. The analytical Strehl ratio values are represented by the black circles and the solid gray curve, with the percentage error between the two expressions displayed as a dashed gray curve. The measured Strehl ratio values obtained using the data displayed in Fig. 4 are displayed as solid gray squares representing the 1-, 2-, 3-, and 6-bit corrections.

Equations (2)

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σ2=1mi=0m-1ϕi-ϕavg2,
σ21ϕ00ϕ0ϕ-ϕ0/22dϕ=π23122n.

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