Abstract

For the optimization of non-Fourier-type computer-generated phase holograms (kinoform lenses), a method based on the Monte Carlo procedure is suggested. This method can be regarded as analogous to the iterative Fourier transform algorithm method that is widely used for the optimization of Fourier-type computer-generated phase holograms (kinoforms).

© 1998 Optical Society of America

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References

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  1. J. P. Waters, “Three-dimensional Fourier-transform method for synthesizing binary holograms,” J. Opt. Soc. Am. 58, 1284–1288 (1968).
    [CrossRef]
  2. D. Leseberg and Ch. Frère, “Computer-generated holograms of 3-D objects composed of tilted planar segments,” Appl. Opt. 27, 3020–3023 (1988).
    [CrossRef] [PubMed]
  3. J. A. Jordan, Jr., P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9, 1883–1887 (1970).
    [PubMed]
  4. J.-J. Clair, “New methods to synthesize kinoforms,” Opt. Commun. 6, 135–137 (1972).
    [CrossRef]
  5. N. Bokor and Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
    [CrossRef]
  6. J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
    [CrossRef]
  7. H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
    [CrossRef]
  8. F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
    [CrossRef]

1997 (1)

N. Bokor and Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

1992 (1)

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

1989 (1)

J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

1988 (2)

1972 (1)

J.-J. Clair, “New methods to synthesize kinoforms,” Opt. Commun. 6, 135–137 (1972).
[CrossRef]

1970 (1)

1968 (1)

Bokor, N.

N. Bokor and Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

Bryngdahl, O.

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

Clair, J.-J.

J.-J. Clair, “New methods to synthesize kinoforms,” Opt. Commun. 6, 135–137 (1972).
[CrossRef]

Frère, Ch.

Hirsch, P. M.

Jordan, Jr., J. A.

Leseberg, D.

Lesem, L. B.

Lüpken, H.

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

Papp, Zs.

N. Bokor and Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

Peter, Th.

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

Turunen, J.

J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

Van Rooy, D. L.

Vasara, A.

J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

Waters, J. P.

Westerholm, J.

J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

Wyrowski, F.

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

F. Wyrowski and O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

H. Lüpken, Th. Peter, F. Wyrowski, and O. Bryngdahl, “Phase synthesis for array illuminator,” Opt. Commun. 91(3, 4), 163–167 (1992).
[CrossRef]

J.-J. Clair, “New methods to synthesize kinoforms,” Opt. Commun. 6, 135–137 (1972).
[CrossRef]

Opt. Eng. (2)

N. Bokor and Zs. Papp, “Monte Carlo method in computer holography,” Opt. Eng. 36, 1014–1020 (1997).
[CrossRef]

J. Turunen, A. Vasara, and J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1989).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Diagram of the iterative Monte Carlo method.

Fig. 2
Fig. 2

Monte Carlo reconstruction of a kinoform lens. The object is 10 × 10 points.

Fig. 3
Fig. 3

Performance of the iterative Monte Carlo method: 10,000 reconstruction pixels are used.

Fig. 4
Fig. 4

Performance of the iterative Monte Carlo method: 50,000 reconstruction pixels are used.

Equations (3)

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i = 1 N a i r i exp j kr i + ϕ i ,
G X ,   Y = i = 1 N a i r i X ,   Y exp j kr i X ,   Y + ϕ i ,
g x ,   y ,   z = m = 1 n exp j kr x ,   y ,   z ,   X m ,   Y m + G X m ,   Y m r x ,   y ,   z ,   X m ,   Y m ,

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