Abstract

In fabricating a diffractive optical element the ratio of the etching depth between the (n - 1)th and the nth mask is usually 1/2. We found that the diffraction efficiency of a diffractive optical element can be improved by as much as 7.8% if the above ratio (1/2) is not kept constant. For achieving this improvement the difference between the desired and the actual diffraction pattern is also used as an objective function for phase quantization.

© 2001 Optical Society of America

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References

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  1. A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Sys. 22, 735–742 (1975).
    [CrossRef]
  2. G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge Press, Wellesley, Mass., 1986).
  3. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holograms,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]
  4. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
    [CrossRef]
  5. J. E. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  6. K. Ballüder, M. R. Taghizadeh, “Optimized phase quantization for diffractive elements by use of a bias phase,” Opt. Lett. 24, 1756–1758 (1999).
    [CrossRef]
  7. G. Zhou, Y. Chen, Z. Wang, H. Song, “Genetic local search algorithm for optimization design of diffractive optical elements,” Appl. Opt. 38, 4281–4290 (1999).
    [CrossRef]
  8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  9. R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).
  10. R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
    [CrossRef]

1999 (2)

1988 (1)

1982 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

1975 (1)

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Sys. 22, 735–742 (1975).
[CrossRef]

1974 (1)

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Ballüder, K.

Bryngdahl, O.

Chen, Y.

Fienup, J. R.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Goodman, J. E.

J. E. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Papouli, A.

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Sys. 22, 735–742 (1975).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Song, H.

Strang, G.

G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge Press, Wellesley, Mass., 1986).

Taghizadeh, M. R.

Wang, Z.

Wyrowski, F.

Zhou, G.

Appl. Opt. (2)

IEEE Trans. Circuits Sys. (1)

A. Papouli, “A new algorithm in spectral analysis and band-limited extrapolation,” IEEE Trans. Circuits Sys. 22, 735–742 (1975).
[CrossRef]

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

Opt. Acta (1)

R. W. Gerchberg, “Superresolution through error energy reduction,” Opt. Acta 21, 709–720 (1974).
[CrossRef]

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–306 (1980).
[CrossRef]

Opt. Lett. (1)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A particular algorithm for the determination of phase from image plane picture,” Optik (Stuttgart) 35, 237–246 (1972).

Other (2)

J. E. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge Press, Wellesley, Mass., 1986).

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Figures (1)

Fig. 1
Fig. 1

Diffraction pattern of the designed DOE by use of the two-layer mask as obtained by (a) the conventional technique and (b) the proposed technique.

Tables (1)

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Table 1 Diffraction Efficiencies of the Designed DOE

Equations (3)

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

U1x, y=A1x, yexpjϕ1x, y,
U2fx, fy=A2fx, fyexpjϕ2fx, fy.
U2fx, fy= U1x, yGx, yexpj 2πλLxfx+yfy×dxdy.

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