Abstract

Computer-generated holograms suffer from a limited space–bandwidth product. A pulse-density coding technique is presented that efficiently uses the capabilities of binary raster-scan devices. An active sequential procedure to generate the pulse-density modulation based on hard clipping and error correction is implemented.

© 1984 Optical Society of America

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References

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  1. W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232; “Holography—a dedication to D. Gabor,” Opt. Eng. 19, 631–796 (1980).
    [Crossref]
  2. B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966); A. W. Lohmann, D. P. Paris, “Binary Fraunhofer hologram generated by computer,” Appl. Opt. 6, 1739–1748 (1967); W.-H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [Crossref] [PubMed]
  3. W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, Vol. 41 of Topics in Applied Physics, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), pp. 291–366.
    [Crossref]
  4. J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
    [Crossref]
  5. J. C. Stoffel, J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. TOC-29, 1898–1925 (1981).
    [Crossref]
  6. T. C. Strand, “Signal/noise in analog and binary holograms,” Opt. Eng. 13, 219–227 (1974).
    [Crossref]
  7. P. Chavel, J.-P. Hugonin, “High quality computer holograms: The problem of phase representation,” J. Opt. Soc. Am. 66, 989–996 (1976).
    [Crossref]
  8. J. P. Allebach, “Representation-related errors in binary digital holograms: a unified analysis,” Appl. Opt. 20, 290–299 (1981).
    [Crossref] [PubMed]
  9. B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.
  10. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. SID 17, 78–84 (1976).
  11. C. Billotet-Hoffmann, O. Bryngdahl, “On the error diffusion technique in electronic halftoning,” Proc. SID (to be published).
  12. D. C. Chu, J. R. Fienup, J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12, 1386–1388 (1973); B. Braunecker, R. Hauck, W. T. Rhodes, “Pupil function replication in OTF synthesis,” Appl. Opt. 18, 44–51 (1979).
    [Crossref] [PubMed]
  13. J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
    [Crossref]

1981 (2)

J. C. Stoffel, J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. TOC-29, 1898–1925 (1981).
[Crossref]

J. P. Allebach, “Representation-related errors in binary digital holograms: a unified analysis,” Appl. Opt. 20, 290–299 (1981).
[Crossref] [PubMed]

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[Crossref]

1976 (2)

P. Chavel, J.-P. Hugonin, “High quality computer holograms: The problem of phase representation,” J. Opt. Soc. Am. 66, 989–996 (1976).
[Crossref]

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. SID 17, 78–84 (1976).

1974 (1)

T. C. Strand, “Signal/noise in analog and binary holograms,” Opt. Eng. 13, 219–227 (1974).
[Crossref]

1973 (1)

1967 (1)

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[Crossref]

1966 (1)

Allebach, J. P.

Bayer, B. E.

B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.

Billotet-Hoffmann, C.

C. Billotet-Hoffmann, O. Bryngdahl, “On the error diffusion technique in electronic halftoning,” Proc. SID (to be published).

Brown, B. R.

Bryngdahl, O.

C. Billotet-Hoffmann, O. Bryngdahl, “On the error diffusion technique in electronic halftoning,” Proc. SID (to be published).

Burch, J. J.

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[Crossref]

Chavel, P.

Chu, D. C.

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, Vol. 41 of Topics in Applied Physics, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), pp. 291–366.
[Crossref]

Fienup, J. R.

Floyd, R. W.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. SID 17, 78–84 (1976).

Goodman, J. W.

Hugonin, J.-P.

Lee, W.-H.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232; “Holography—a dedication to D. Gabor,” Opt. Eng. 19, 631–796 (1980).
[Crossref]

Lohmann, A. W.

Moreland, J. F.

J. C. Stoffel, J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. TOC-29, 1898–1925 (1981).
[Crossref]

Steinberg, L.

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. SID 17, 78–84 (1976).

Stoffel, J. C.

J. C. Stoffel, J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. TOC-29, 1898–1925 (1981).
[Crossref]

Strand, T. C.

T. C. Strand, “Signal/noise in analog and binary holograms,” Opt. Eng. 13, 219–227 (1974).
[Crossref]

Appl. Opt. (3)

IEEE Trans. Commun. (1)

J. C. Stoffel, J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. TOC-29, 1898–1925 (1981).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
[Crossref]

T. C. Strand, “Signal/noise in analog and binary holograms,” Opt. Eng. 13, 219–227 (1974).
[Crossref]

Proc. IEEE (1)

J. J. Burch, “A computer algorithm for synthesis of spatial frequency filters,” Proc. IEEE 55, 599–601 (1967).
[Crossref]

Proc. SID (1)

R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. SID 17, 78–84 (1976).

Other (4)

C. Billotet-Hoffmann, O. Bryngdahl, “On the error diffusion technique in electronic halftoning,” Proc. SID (to be published).

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), Vol. 16, pp. 119–232; “Holography—a dedication to D. Gabor,” Opt. Eng. 19, 631–796 (1980).
[Crossref]

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, Vol. 41 of Topics in Applied Physics, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), pp. 291–366.
[Crossref]

B. E. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” in Proceedings of the IEEE International Conference on Communication (Institute of Electrical and Electronics Engineers, New York, 1973), pp. 26-11–26-15.

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Figures (9)

Fig. 1
Fig. 1

One-dimensional generation of a pulse-density modulation using error diffusion and correction. Arrows indicate how hard-clipping errors are transported to the nearest neighbors before they are binarized and produce new errors that are further transported.

Fig. 2
Fig. 2

Weight factors of the 2-D error-diffusion and -correction scheme.

Fig. 3
Fig. 3

Examples of converting constant gray levels (left-hand column) into binary structures (right-hand column) using pulse-density modulation.

Fig. 4
Fig. 4

Magnified portion of a pulse-density modulation Fourier hologram. Raster period, 10 μm.

Fig. 5
Fig. 5

Optical reconstruction of the CGH of Fig. 4.

Fig. 6
Fig. 6

Magnified portion of the reconstructed image of Fig. 5.

Fig. 7
Fig. 7

Optical reconstruction of a CGH using the 1-D binarization algorithm in y direction.

Fig. 8
Fig. 8

Two-dimensional error-diffusion and -correction scheme with adaption to the hologram structure.

Fig. 9
Fig. 9

Optical reconstruction of CGH’s with inclined carrier function: (a) using the 1-D diffusion algorithm in y direction and (b) adaption of the error-diffusion direction to the carrier geometry.

Equations (4)

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

ũ M ( ν , μ ) = ũ ( ν , μ ) cos [ 2 π x 0 ν + ϕ ( ν , μ ) ] ,
ũ ( ν , μ ) = ũ ( ν , μ ) exp [ i ϕ ( ν , μ ) ] .
ũ H ( ν , μ ) = ũ M ( ν , μ ) + b ˜ ( ν , μ ) 0.
b ˜ ( ν , μ ) = - min ( ν , μ ) ũ M ( ν , μ ) .

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