OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 32 — Nov. 10, 2001
  • pp: 5886–5893

Optimal multicriteria approach to the iterative Fourier transform algorithm

Laurent Bigué and Pierre Ambs  »View Author Affiliations

Applied Optics, Vol. 40, Issue 32, pp. 5886-5893 (2001)

View Full Text Article

Enhanced HTML    Acrobat PDF (1063 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a unified approach to the multicriteria design of diffractive optics. A multicriteria version of the direct binary search that allows the user to adjust the compromise between the diffraction efficiency and the signal-to-noise ratio already exists. This technique has proved to be extremely powerful but also very time consuming. We extend this multicriteria approach to the iterative Fourier transform algorithm, which helps to reduce the computation time dramatically, especially for multilevel domains. Simulations as well as experimental validations are provided.

© 2001 Optical Society of America

OCIS Codes
(090.1760) Holography : Computer holography
(090.1970) Holography : Diffractive optics

Original Manuscript: January 12, 2001
Revised Manuscript: June 5, 2001
Published: November 10, 2001

Laurent Bigué and Pierre Ambs, "Optimal multicriteria approach to the iterative Fourier transform algorithm," Appl. Opt. 40, 5886-5893 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. 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]
  2. D. C. Youla, “Image restoration by the method of alternating projections,” IEEE Trans. Circuits Syst. CAS-25, 694–702 (1978). [CrossRef]
  3. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  4. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [CrossRef]
  5. L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997). [CrossRef]
  6. P. Réfrégier, “Filter design for optical pattern recognition: multicriteria optimization approach,” Opt. Lett. 15, 854–856 (1990). [CrossRef] [PubMed]
  7. F. Wyrowski, “Diffraction efficiency of analog and quantized digital amplitude holograms: analysis and manipulation,” J. Opt. Soc. Am. A 7, 383–393 (1990). [CrossRef]
  8. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990). [CrossRef]
  9. H. Stark, M. I. Sezan, “Image processing using projection methods,” in Real-Time Optical Information Processing, B. Javidi, J. L. Horner, eds. (Academic, San Diego, Calif., 1994), pp. 185–232.
  10. J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer generated holography,” in Computer Generated Holography II, S. H. Lee, ed., Proc. SPIE884, 2–9 (1988). [CrossRef]
  11. F. Fetthauer, C. Stroot, O. Bryngdahl, “On the quantization of holograms with the iterative Fourier transform algorithm,” Opt. Commun. 136, 7–10 (1997). [CrossRef]
  12. K.-H. Brenner, “Method for designing arbitrary two-dimensional continuous phase elements,” Opt. Lett. 25, 31–33 (2000). [CrossRef]
  13. L. Legeard, “Étude et optimisation d’hologrammes synthétisés par ordinateur: application au stockage d’informations et aux éléments diffractifs,” Ph.D. dissertation (Université de Haute Alsace, Alsace, France, 1995).
  14. R. Bräuer, F. Wyrowski, O. Bryngdahl, “Diffusers in digital holography,” J. Opt. Soc. Am. A 8, 572–578 (1991). [CrossRef]
  15. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  16. P. Ambs, L. Bigué, C. Stolz, “Dynamic computer generated hologram displayed on a spatial light modulator for information processing,” in Euro American Workshop on Optoelectronic Information Processing, P. Réfrégier, B. Javidi, eds., Vol. CR74 of SPIE Critical Review Series (SPIE Press, Bellingham, Wash., 1999), pp. 151–170.
  17. I. Moreno, C. Gorecki, J. Campos, M. J. Yzuel, “Comparison of computer-generated holograms produced by laser printers and lithography: application to pattern recognition,” Opt. Eng. 31, 3520–3525 (1995).

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