Abstract

An algorithm incorporating a stochastic approach is proposed for reducing the computation time of the direct-binary-search algorithm for hologram synthesis. Two variants of this new algorithm are considered for a number of hologram-generation problems. Both variants can reduce the computation time significantly with a very small increase in the reconstruction error on average. The effectiveness of the proposed algorithm is found to improve with the increasing computational complexity of the design problem. Also, the algorithm is able to generate the hologram in a time that is relatively independent of the initial conditions.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (1)

1995 (2)

1994 (1)

1992 (2)

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Commun. 94, 491–496 (1992).
[CrossRef]

1991 (3)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Efficient design of direct-binary search computer-generated holograms,” J. Opt. Soc. Am. A 8, 652–660 (1991).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.1481–1570 (1991).
[CrossRef]

D. Just, D. T. Ling, “Neural networks for binarizing computer-generated holograms,” Opt. Commun. 81, 1–5 (1991).
[CrossRef]

1989 (2)

F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[CrossRef]

F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 2, 3864–3870 (1989).
[CrossRef]

1988 (1)

E. Barnard, “Optimal error diffusion for computer-generated hologram,” J. Opt. Soc. Am. 5, 1803–1817 (1988).
[CrossRef]

1987 (1)

1984 (1)

Allebach, J. P.

Barnard, E.

E. Barnard, “Optimal error diffusion for computer-generated hologram,” J. Opt. Soc. Am. 5, 1803–1817 (1988).
[CrossRef]

Bryngdahl, O.

Chevallier, R.

Dietrich, C. H.

Ersoy, O. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

Hall, T. J.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Commun. 94, 491–496 (1992).
[CrossRef]

Hauck, R.

Heggarty, K.

Jennison, B. K.

Just, D.

D. Just, D. T. Ling, “Neural networks for binarizing computer-generated holograms,” Opt. Commun. 81, 1–5 (1991).
[CrossRef]

Kirk, A. G.

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Commun. 94, 491–496 (1992).
[CrossRef]

Ling, D. T.

D. Just, D. T. Ling, “Neural networks for binarizing computer-generated holograms,” Opt. Commun. 81, 1–5 (1991).
[CrossRef]

Man¨ner, R.

Noehte, S.

Seldowitz, M. A.

Sweeney, D. W.

Wyrowski, F.

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.1481–1570 (1991).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[CrossRef]

F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 2, 3864–3870 (1989).
[CrossRef]

Yatagai, T.

Yoshikawa, N.

Zhang, E.

Zhuang, J.-Y.

Appl. Opt. (4)

J. Mod. Opt. (1)

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: observation of metastable states,” J. Mod. Opt. 39, 2531–2539 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

E. Barnard, “Optimal error diffusion for computer-generated hologram,” J. Opt. Soc. Am. 5, 1803–1817 (1988).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (2)

D. Just, D. T. Ling, “Neural networks for binarizing computer-generated holograms,” Opt. Commun. 81, 1–5 (1991).
[CrossRef]

A. G. Kirk, T. J. Hall, “Design of binary computer generated holograms by simulated annealing: coding density and reconstruction error,” Opt. Commun. 94, 491–496 (1992).
[CrossRef]

Rep. Prog. Phys. (1)

F. Wyrowski, O. Bryngdahl, “Digital holography as part of diffractive optics,” Rep. Prog. Phys.1481–1570 (1991).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

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Figures (12)

Fig. 1
Fig. 1

Fourier-transform hologram-reconstruction geometry.

Fig. 2
Fig. 2

DBS algorithm.

Fig. 3
Fig. 3

(a) Desired reconstruction with pattern “F”; (b) binary hologram generated by the DBS.

Fig. 4
Fig. 4

Fraction of total pixels not reducing the MSE versus the iteration number.

Fig. 5
Fig. 5

Fraction of total pixels that did not change versus the number of iterations for which they did not change till the end.

Fig. 6
Fig. 6

Average value of the increase in the MSE and the midrange value of the increase in the MSE by pixels that did not change versus the iteration number.

Fig. 7
Fig. 7

FDBS algorithm.

Fig. 8
Fig. 8

Reconstructions from the holograms generated with the standard DBS, FDBS1, and FDBS2 for the hologram-generation problem of Fig. 3.

Fig. 9
Fig. 9

Flip-and-test probability of marked pixels for FDBS1 and FDBS2.

Fig. 10
Fig. 10

Variations of the number of marked pixels and the number of pixels that do not go through the flip-and-test operation, for FDBS1 and FDBS2.

Fig. 11
Fig. 11

MSE versus iteration number for the standard DBS, FDBS1, and FDBS2.

Fig. 12
Fig. 12

(a) Desired reconstruction with spot array; (b) binary hologram generated with DBS; (c) reconstruction from the hologram.

Tables (2)

Tables Icon

Table 1 Comparison of Results for DBS, FDBS1, and FDBS2 in Generating 100 Holograms with Different Initial Conditions for the Hologram-Design Problem of Fig. 3 with Pattern “F”

Tables Icon

Table 2 Comparison of Results for DBS, FDBS1, and FDBS2 in Generating 50 Holograms with Different Initial Conditions for the Hologram-Design Problem of Fig. 12 with Spot Array

Equations (9)

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

gx0, y0=Ajλf  hx, yexp-j2πξx+ηydxdy,
gpq=AΔxΔyjλfsinπp/Nxπp/Nxsinπq/Nyπq/Ny×m=0Nx-1n=0Ny-1hmn exp-j2πmpNx+nqNy,
MSE=1Nx0WNy0WpqWFpq-F¯σF-Gpq-G¯σG2,
F¯=1Nx0WNy0WpqW Fpq,
G¯=1Nx0WNy0WpqW Gpq,
σF2=1Nx0WNy0WpqW |Fpq-F¯|2,
σG2=1Nx0WNy0WpqW |Gpq-G¯|2.
η=ΣpqWGpqΣpqRGpq,
Pj=1.0-exp-MSEj-2-MSEcurrentMSEj-1,

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