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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 5, Iss. 11 — Nov. 1, 1988
  • pp: 1803–1817

Optimal error diffusion for computer-generated holograms

Etienne Barnard  »View Author Affiliations

JOSA A, Vol. 5, Issue 11, pp. 1803-1817 (1988)

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A probabilistic model is introduced to describe error diffusion (a method of binarization). This model is solved for general error-diffusion coefficients. The solution leads to an analytic error expression that is minimized to optimize the quality of binarization. It is shown that this procedure is useful in the production of computer-generated holograms. Simulations are presented to verify both the theoretical development and the optimization procedure.

© 1988 Optical Society of America

Original Manuscript: March 21, 1988
Manuscript Accepted: June 22, 1988
Published: November 1, 1988

Etienne Barnard, "Optimal error diffusion for computer-generated holograms," J. Opt. Soc. Am. A 5, 1803-1817 (1988)

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  1. H. S. Watkins, J. S. Moore, “A survey of color graphics printing,” IEEE Spectrum 21, 26–37 (1984).
  2. T. S. Perry, P. Wallich, eds., “Displays (Applications Topic),” IEEE Spectrum 22, 52–73 (1985).
  3. J. C. Stoffel, J. F. Moreland, “A survey of electron techniques for pictorial image reproduction,” IEEE Trans. Commun. C-29, 1898–1925 (1981). [CrossRef]
  4. R. W. Floyd, L. Steinberg, “An adaptive algorithm for spatial grayscale,” Proc. Soc. Inf. Disp. 17, 78–84 (1976).
  5. R. Ulichney, Digital Halftoning (MIT Press, Cambridge, Mass., 1987).
  6. J. R. Jarvis, C. N. Judice, W. H. Ninke, “A survey of techniques for the display of continuous tone pictures on bilevel displays,” Comput Graph. Image Process. 5, 13–40 (1976). [CrossRef]
  7. J. G. Kim, G. Kim, “Design of optimal filters for error-feedback quantization of monochrome pictures,” Inf. Sci. 39, 285–298 (1986). [CrossRef]
  8. J. A. G. Hale, “Dot spacing modulation for the production of pseudo grey pictures,” Proc. Soc. Inf. Disp. 17, 63–74 (1976).
  9. R. Eschbach, R. Hauck, “Analytic description of the 1-D error diffusion technique for halftoning,” Opt. Commun. 52, 165–168 (1984). [CrossRef]
  10. R. Hauck, O. Bryngdahl, “Computer-generated holograms with pulse-density modulation,” J. Opt. Soc. Am. A 1, 5–10 (1984). [CrossRef]
  11. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987). [CrossRef] [PubMed]
  12. S. H. Algie, “Resolution and tonal continuity in bilevel printed picture continuity,” Comput. Vision Graph. Image Process. 24, 329–346 (1983). [CrossRef]
  13. W. H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1978), p. 121.
  14. J. P. Allebach, “Representation-related errors in binary digital holograms: a unified analysis,” Appl. Opt. 20, 290–299 (1981). [CrossRef] [PubMed]
  15. G. Neugebauer, R. Hauck, O. Bryngdahl, “Computer-generated holograms: carrier of polar geometry,” Appl. Opt. 24, 777–784 (1985). [CrossRef] [PubMed]
  16. J. Richards, P. Vermeulen, E. Barnard, D. P. Casasent, “Parallel holographic generation of multiple Hough transform slices,” submitted to Appl. Opt.
  17. M. H. Kuhn, W. Menhardt, I. C. Carlsen, “Real time interactive NMR image synthesis,” IEEE Trans. Med. Imag. MI-4, 160–164 (1985). [CrossRef]
  18. C. Billotet-Hoffmann, O. Bryngdahl, “Optical pseudocolor encoding using adaptive electronic halftoning,” Opt. Commun. 45, 327–330 (1983). [CrossRef]
  19. D. Kermisch, P. G. Roetling, “Fourier spectrum of halftone images,” J. Opt. Soc. Am. 65, 716–723 (1975). [CrossRef]
  20. M. Broja, R. Eschbach, O. Bryngdahl, “Stability of active binarization processes,” Opt. Commun. 60, 353–358 (1986). [CrossRef]
  21. J. P. Allebach, B. Liu, “Minimax spectrum shaping with a bandwidth constraint,” Appl. Opt. 14, 3062–3072 (1975). [CrossRef] [PubMed]

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