OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 21, Iss. 15 — Aug. 1, 1982
  • pp: 2758–2769

Phase retrieval algorithms: a comparison

J. R. Fienup  »View Author Affiliations

Applied Optics, Vol. 21, Issue 15, pp. 2758-2769 (1982)

View Full Text Article

Enhanced HTML    Acrobat PDF (1740 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input–output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.

© 1982 Optical Society of America

Original Manuscript: February 19, 1982
Published: August 1, 1982

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  2. W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978).
  3. R. A. Gonsalves, J. Opt. Soc. Am. 66, 961 (1976). [CrossRef]
  4. J. R. Fienup, Opt. Lett. 3, 27 (1978). [CrossRef] [PubMed]
  5. J. R. Fienup, Opt. Eng. 18, 529 (1979). [CrossRef]
  6. J. R. Fienup, Opt. Eng. 19, 297 (1980). [CrossRef]
  7. J. R. Fienup, “Reconstruction and Synthesis Applications of an Iterative Algorithm,” in Transformations in Optical Signal Processing, W. T. Rhodes, J. R. Fienup, B. E. A. Saleh, Eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1982), to be published.
  8. P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of Making an Object-Dependent Diffuser,” U.S. Patent3,619,022 (9Nov., 1971).
  9. N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973). [CrossRef] [PubMed]
  10. J. R. Fienup, T. R. Crimmins, W. Holsztynski, J. Opt. Soc. Am. 72, 610 (1982). [CrossRef]
  11. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  12. R. H. Boucher, Proc. Soc. Photo-Opt. Instrum. Eng. 231, 130 (1980).
  13. M. T. Manry, J. K. Aggarwal, IEEE Trans. Circuits Syst. CAS-23, 185 (1976). [CrossRef]
  14. D. P. Feder, Appl. Opt. 2, 1209 (1963). [CrossRef]
  15. D. R. Buchele, Appl. Opt. 7, 2433 (1968). [CrossRef] [PubMed]
  16. B. R. Frieden, D. G. Currie, J. Opt. Soc. Am. 66, 1111 (1976) (Abstract). [CrossRef]
  17. J. R. Fienup, “Improved Synthesis and Computational Methods for Computer-Generated Holograms,” Ph.D. Thesis, Stanford University, May, 1975 (University Microfilms No. 75-25523), Chap. 5.
  18. G. B. Feldkamp, J. R. Fienup, Proc. Soc. Photo-Opt. Instrum. Eng. 231, 84 (1980).
  19. J. R. Fienup, “Fourier Modulus Image Construction,” Report RADC-TR-81-63 (1981).
  20. A. Labeyrie, Astron. Astrophys. 6, 85 (1970); D. Y. Gezari, A. Labeyrie, R. V. Stachnik, Astrophys. J. Lett. 173, L1 (1972). [CrossRef]
  21. J. W. Goodman, J. F. Belsher, Proc. Soc. Photo-Opt. Instrum. Eng. 75, 141 (1976).
  22. A. M. J. Huiser, A. J. J. Drenth, H. A. Ferwerda, Optik 45, 303 (1976); A. M. J. Huiser, H. A. Ferwerda, Optik 46, 407 (1976).
  23. A. J. Devaney, R. Chidlaw, J. Opt. Soc. Am. 68, 1352 (1978). [CrossRef]
  24. Yu. M. Bruck, L. G. Sodin, Opt. Commun. 30, 304 (1979). [CrossRef]
  25. W. Lawton, Proc. Soc. Photo-Opt. Instrum. Eng. 231, 94 (1980).
  26. A. M. J. Huiser, P. Van Toorn, Opt. Lett. 5, 499 (1980). [CrossRef] [PubMed]
  27. T. R. Crimmins, J. R. Fienup, J. Opt. Soc. Am. 71, 1026 (1981). [CrossRef]
  28. J. R. Fienup, “Image Reconstruction for Stellar Interferometry,” in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, Eds. (Taylor & Francis, London, 1981), pp. 95–102.

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