Abstract

An iterative discrete on-axis encoding method for computer-generated holograms (termed IDO encoding) has been developed. The binary IDO method employs simulated annealing to optimize the hologram phase delay and reduce sensitivity to fabrication tolerances. Computer-simulation results indicate that binary phase IDO encoding is capable of generating two-dimensional spot arrays with diffraction efficiencies larger than 70%. An experimentally fabricated hologram, designed to account for a 6% manufacturing hologram thickness tolerance, produced a 3 × 3 array of spots with 59% diffraction efficiency. The binary IDO algorithm can be employed to encode arbitrary images with twofold rotation symmetry.

© 1989 Optical Society of America

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References

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1988

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

1987

1986

1983

S. Kirkpatric, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

1980

J. R. Fienup, Opt. Eng. 19, 297 (1980).

1977

H. Dammann, E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

1975

1971

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Allebach, J. P.

Dammann, H.

H. Dammann, E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Eschbach, R.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

Fainman, Y.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

Feldman, M.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

Feldman, M. R.

Fienup, J. R.

J. R. Fienup, Opt. Eng. 19, 297 (1980).

Gelatt, C. D.

S. Kirkpatric, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Gortler, K.

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Guest, C. C.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

M. R. Feldman, C. C. Guest, Appl. Opt. 26, 4377 (1987).
[CrossRef] [PubMed]

Kirkpatric, S.

S. Kirkpatric, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Klotz, E.

H. Dammann, E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Lee, S. H.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

Liu, B.

Seldowitz, M. A.

Sweeney, D. W.

Vecchi, M. P.

S. Kirkpatric, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Walker, A. C.

Appl. Opt.

Opt. Acta

H. Dammann, E. Klotz, Opt. Acta 24, 505 (1977).
[CrossRef]

Opt. Commun.

H. Dammann, K. Gortler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Opt. Eng.

J. R. Fienup, Opt. Eng. 19, 297 (1980).

Proc. Soc. Photo-Opt. Instrum. Eng.

C. C. Guest, M. Feldman, R. Eschbach, Y. Fainman, S. H. Lee, Proc. Soc. Photo-Opt. Instrum. Eng. 884, 33 (1988).

Science

S. Kirkpatric, C. D. Gelatt, M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

(a) Computer plot of one period of an IDO hologram designed to reconstruct a 3 × 3 array of spots. The pattern was replicated eight times in each direction. (b) Photograph of the reconstruction produced by the hologram in (a).

Tables (3)

Tables Icon

Table 1 Computer-Simulation Results for Binary IDO Encoding of a 3 × 3 Signal Spot Array

Tables Icon

Table 2 Computer-Simulation Results for Binary IDO Encodinga

Tables Icon

Table 3 Effects of Various Features of IDO Encodinga

Equations (7)

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h m n = k - 1 K l = 1 L H k l C k l m n ,             m = - M - 1 2 , , M - 1 2 ,             n = - N - 1 2 , , N - 1 2 ,
C k l m n = - 1 4 π 2 m n × { exp [ - j 2 π m ( k + 1 ) / K ] - exp ( - j 2 π m k / K ) } × { exp [ - j 2 π n ( l + 1 ) / L ] - exp ( - j 2 π n l / L ) } .
h m n = ( 1 - e j ϕ ) h m n ,             m 0 ,             n 0 , h 00 = ( 1 - e j ϕ ) h 00 + e j ϕ ,
E = E 1 + E 2 ,             E 1 = C E ( P max - P min ) 2 , E 2 = m n ( η N M - P m n ) 2 ,
P ( Δ E ) = 1 / [ 1 + exp ( Δ E / T ) ] ,
ϕ - δ ϕ ϕ ϕ + δ ϕ ,
E ( ϕ ) = E 2 ( ϕ ) + max [ E 1 ( ϕ - δ ϕ ) , E 1 ( ϕ ) , E 1 ( ϕ + δ ϕ ) ] ,

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