OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 1 — Jan. 1, 1998
  • pp: 68–76

Design of continuous and quantized amplitude holograms by generalized projections

William C. Catino, Joseph L. LoCicero, and Henry Stark  »View Author Affiliations


JOSA A, Vol. 15, Issue 1, pp. 68-76 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000068


View Full Text Article

Enhanced HTML    Acrobat PDF (1154 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The method of generalized projections is used to design pure-amplitude diffraction holograms that generate gray-scale images. Two algorithms are presented: the direct method nonlinearly constrains the hologram transmittance to the range of real values in [0,1]; the indirect method constrains the transmittance values to the real axis and linearly transforms the resulting values to the range [0,1]. Digital amplitude holograms were simulated by quantizing the amplitude holograms resulting from the indirect method. Performance is demonstrated with objective measures (error, efficiency, and variance) as well as with subjective comparison of images. Test images included a photographic quality image of Lena, a uniform intensity spot array, and a binary amplitude block text image.

© 1998 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(090.0090) Holography : Holography
(100.0100) Image processing : Image processing

Citation
William C. Catino, Joseph L. LoCicero, and Henry Stark, "Design of continuous and quantized amplitude holograms by generalized projections," J. Opt. Soc. Am. A 15, 68-76 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-1-68


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Dou and M. K. Giles, “Phase measurement and compensation of a wave front using a twisted nematic liquid-crystal television,” Appl. Opt. 35, 3647–3652 (1996). [CrossRef] [PubMed]
  2. M. D. Missig and G. M. Morris, “Diffractive optics applied to eyepiece design,” Appl. Opt. 34, 2452–2461 (1995). [CrossRef] [PubMed]
  3. J. Khoury, P. D. Gianino, and C. L. Woods, “Nearly optimal correlations for shift-invariant associative memories,” Appl. Opt. 34, 3971–3980 (1995). [CrossRef] [PubMed]
  4. M. A. Seidowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2798 (1987). [CrossRef]
  5. H. Zhang, S. Nochte, C. H. Dietrich, and R. Manner, “Gradual and random binarization of gray-scale holograms,” Appl. Opt. 34, 5987–5995 (1995). [CrossRef] [PubMed]
  6. H. Stark, W. C. Catino, and J. L. LoCicero, “Design of phase gratings by generalized projections,” J. Opt. Soc. Am. A 8, 566–571 (1991). [CrossRef]
  7. R. W. Cohn and M. Liang, “Pseudorandom phase-only encoding of real-time spatial light modulators,” Appl. Opt. 35, 2488–2498 (1996). [CrossRef] [PubMed]
  8. F. Wyrowski, “Iterative quantization of digital amplitude holograms,” Appl. Opt. 28, 3864–3870 (1989). [CrossRef] [PubMed]
  9. F. Wyrowski, “Diffraction efficiency of analog and quantized digital amplitude holograms: analysis and manipulation,” J. Opt. Soc. Am. A 7, 383–393 (1990). [CrossRef]
  10. B. K. Jennison, J. P. Allebach, and D. W. Sweeney, “Efficient design of direct-binary-search computer-generated holograms,” J. Opt. Soc. Am. A 8, 652–660 (1991). [CrossRef]
  11. W. H. Lee, “High efficiency multiple beam gratings,” Appl. Opt. 18, 2152–2158 (1979). [CrossRef] [PubMed]
  12. F. B. McCormick, “Generation of large spot arrays from a single laser beam by multiple imaging with binary phase gratings,” Opt. Eng. 28, 299–304 (1989). [CrossRef]
  13. A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758–779 (1984). [CrossRef]
  14. D. L. Flannery and J. L. Horner, “Fourier optical signal processors,” Proc. IEEE 77, 1511–1527 (1989). [CrossRef]
  15. K. S. Urquhart, P. Marchand, and Y. Fainman, “Diffractive optics applied to free-space optical interconnects,” Appl. Opt. 33, 3670–3682 (1994). [CrossRef] [PubMed]
  16. C. Warde and A. D. Fisher, “Spatial light modulators: applications and functional capabilities,” in Optical Signal Processing, J. Horner, ed. (Academic, San Diego, Calif., 1988), pp. 478–523.
  17. R. E. Collin, Antenna and Radiowave Propagation (McGraw-Hill, New York, 1985), pp. 107–151.
  18. M. King, “Fourier optics and radar signal processing,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, New York, 1982), pp. 209–251.
  19. R. T. Compton, Jr., Adaptive Antennas (Prentice-Hall, Englewood Cliffs, N.J., 1988).
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  21. L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624 (1951). [CrossRef]
  22. R. W. Gerchberg, “Super resolution through error energy reduction,” Opt. Acta 21, 709–720 (1974). [CrossRef]
  23. A. Papoulis, “A new algorithm in spectral analysis and bandlimited extrapolation,” IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975). [CrossRef]
  24. D. C. Youla and H. Webb, “Image restoration by the method of convex projections: part I, theory,” IEEE Trans. Med. Imaging MI-1, 81–94 (1982). [CrossRef]
  25. A. Levi and H. Stark, “Image restoration by the method of generalized projections with application to restoration from magnitude,” J. Opt. Soc. Am. A 1, 932–943 (1984). [CrossRef]
  26. H. Stark, Image Recovery: Theory and Application (Academic, Orlando, Fla., 1987).
  27. A. Levi, “Image restoration by the method of projections with applications to the phase and magnitude retrieval problems,” Ph.D. dissertation (Rensselaer Polytechnic Institute, Troy, N.Y., 1983).
  28. J. P. Allebach and D. W. Sweeney, “Iterative approaches to computer generated holography,” in Computer-Generated Holography II, S. H. Lee, ed., Proc. SPIE 884, 2–9 (1988). [CrossRef]
  29. W. C. Catino, “Pure-phase and pure-amplitude hologram design using the method of generalized projections,” Ph.D. dissertation (Illinois Institute of Technology, Chicago, Ill., 1997).
  30. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990). [CrossRef]
  31. W. C. Catino, J. L. LoCicero, and H. Stark, “Design of continuous and quantized phase holograms by generalized projections,” J. Opt. Soc. Am. A 14, 2715–2725 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited