Abstract

An iterative algorithm for constructing fully continuous phase screens for tailoring far-field intensity profiles is presented. The algorithm is robust, stable, and, if run properly, maintains the continuous nature of the phase throughout the iterative process. The iterative procedure is applied to generate continuous phase screens to produce a 12th-power super-Gaussian far-field intensity profile.

© 1996 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (2)

1992 (2)

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45(9), 32 (1992).
[CrossRef]

S. Weissbach, F. Wyrowski, O. Bryngdahl, Opt. Lett. 17, 235 (1992).
[CrossRef] [PubMed]

1991 (1)

R. Brauer, F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 8, 572 (1991).
[CrossRef]

1988 (1)

F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 5, 1058 (1988).
[CrossRef]

1986 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Armstrong, J. J.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. SPIE 1870, 95 (1993).
[CrossRef]

Bett, T. H.

Brauer, R.

R. Brauer, F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 8, 572 (1991).
[CrossRef]

Bryngdahl, O.

S. Weissbach, F. Wyrowski, O. Bryngdahl, Opt. Lett. 17, 235 (1992).
[CrossRef] [PubMed]

R. Brauer, F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 8, 572 (1991).
[CrossRef]

F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 5, 1058 (1988).
[CrossRef]

Campbell, E. M.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45(9), 32 (1992).
[CrossRef]

Chen, Z.

Danson, C. N.

Deng, X.

Dixit, S. N.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 8.3.

Henesian, M. A.

Kessler, T. J.

Y. Lin, T. J. Kessler, G. L. Lawrence, Opt. Lett. 20, 764 (1995).
[CrossRef] [PubMed]

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. SPIE 1870, 95 (1993).
[CrossRef]

Lawrence, G. L.

Lawson, J. K.

Liang, X.

Lin, Y.

Y. Lin, T. J. Kessler, G. L. Lawrence, Opt. Lett. 20, 764 (1995).
[CrossRef] [PubMed]

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. SPIE 1870, 95 (1993).
[CrossRef]

Lindl, J. D.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45(9), 32 (1992).
[CrossRef]

Ma, R.

Manes, K. R.

McCrory, R. L.

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45(9), 32 (1992).
[CrossRef]

Morgan, A. J.

Norman, M. J.

Nugent, K. A.

Pepler, D. A.

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Powell, H. T.

Ross, I. N.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Stevenson, R. M.

Thomas, I. M.

Velazquez, B.

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. SPIE 1870, 95 (1993).
[CrossRef]

Wegner, P. J.

Weissbach, S.

Woods, B. W.

Wyrowski, F.

S. Weissbach, F. Wyrowski, O. Bryngdahl, Opt. Lett. 17, 235 (1992).
[CrossRef] [PubMed]

R. Brauer, F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 8, 572 (1991).
[CrossRef]

F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 5, 1058 (1988).
[CrossRef]

Yu, W.

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 5, 1058 (1988).
[CrossRef]

R. Brauer, F. Wyrowski, O. Bryngdahl, J. Opt. Soc. Am. 8, 572 (1991).
[CrossRef]

Opt. Lett. (4)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Phys. Today (1)

J. D. Lindl, R. L. McCrory, E. M. Campbell, Phys. Today 45(9), 32 (1992).
[CrossRef]

Proc. SPIE (1)

T. J. Kessler, Y. Lin, J. J. Armstrong, B. Velazquez, Proc. SPIE 1870, 95 (1993).
[CrossRef]

Other (2)

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, in Principles of Phase Conjugation, Vol. 42 of Springer Series in Optical Sciences, T. Tamir, ed. (Springer-Verlag, Berlin, 1985), p. 79.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Sec. 8.3.

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Figures (3)

Fig. 1
Fig. 1

(a) Phase screen containing 2π-branch cuts. The color scale (same as that shown in Fig. 2, below) corresponds to a phase variation from 0 (black) to 2π (white). The black and white boundaries correspond to 2π phase jumps. (b) Contour map of the zeros of the real (green contour lines) and the imaginary (white contour lines) components of the electric field generated by the phase screen shown in Fig. 1(a).

Fig. 2
Fig. 2

(a) Continuous phase screen used to start the iteration process. The range of variation of the phase from 0 (black) to 23.6 rad (white). (b) Gaussian far-field intensity distribution produced by the phase screen of (a). (c) Iterated phase screen for producing a SG far field. The range of variation of the phase is from 0 (black) to 43.0 rad (white). (d) SG far-field intensity distribution produced by the phase screen of (c).

Fig. 3
Fig. 3

(a) Azimuthally averaged profiles corresponding to the images in Fig. 2(b) (dashed curves) and Fig. 2(d) (solid curves). Dashed–dotted curve, 12th-order super-Gaussian with r0 = 250 μm. (b) Fractional energy content in the far-field intensity profile. The curves are defined the same as in (a).

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