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. 11, Iss. 7 — Jul. 1, 1994
  • pp: 2016–2026

Phase retrieval and estimation with use of real-plane zeros

Christopher C. Wackerman and Andrew E. Yagle  »View Author Affiliations


JOSA A, Vol. 11, Issue 7, pp. 2016-2026 (1994)
http://dx.doi.org/10.1364/JOSAA.11.002016


View Full Text Article

Enhanced HTML    Acrobat PDF (1719 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Locations at which the Fourier transform F(u, υ) of an image equals zero have been called real-plane zeros, since they are the intersections of the zero curves of the analytic extension of F(u, υ) with the real–real (u, υ) plane. It has been shown that real-plane zero locations have a significant effect on the Fourier phase in that they are the end points of phase branch cuts, and it has been shown that real-plane zero locations can be estimated from Fourier magnitude data. Thus real-plane zeros can be utilized in phase retrieval algorithms to help constrain the possible Fourier phases. First we show a simplified procedure for estimating real-plane zeros from the Fourier magnitude. Then we present a new phase retrieval algorithm that uses real-plane zero locations to generate a simple parameterization of the Fourier phase and uses knowledge about the image to estimate the Fourier phase parameters. We show by example that this algorithm generates improved phase retrieval results when it is used as an initial guess into existing iterative algorithms. We assume that the image is real valued.

© 1994 Optical Society of America

History
Original Manuscript: September 13, 1993
Revised Manuscript: January 21, 1994
Manuscript Accepted: February 1, 1994
Published: July 1, 1994

Citation
Christopher C. Wackerman and Andrew E. Yagle, "Phase retrieval and estimation with use of real-plane zeros," J. Opt. Soc. Am. A 11, 2016-2026 (1994)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-11-7-2016


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. Y. C. Lui, A. W. Lohmann, “High resolution image formation through the turbulent atmosphere,” Opt. Commun. 8, 372–377 (1973). [CrossRef]
  2. J. Karle, “Recovering phase information from intensity data,” Science 232, 837–843 (1986). [CrossRef] [PubMed]
  3. D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973). [CrossRef]
  4. E. J. Akutowicz, “On the determination of the phase of a Fourier integral,” Trans. Am. Math. Soc. 83, 179–192 (1956).
  5. Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–308 (1979). [CrossRef]
  6. H. V. Deighton, M. S. Scivier, M. A. Fiddy, “Solution of the two-dimensional phase retrieval problem,” Opt. Let. 10, 250–251 (1985). [CrossRef]
  7. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982). [CrossRef] [PubMed]
  8. 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).
  9. D. Izraelevitz, J. S. Lim, “A new direct algorithm for image reconstruction from Fourier transform magnitude,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 511–519 (1987). [CrossRef]
  10. R. G. Lane, W. R. Fright, R. H. T. Bates, “Direct phase retrieval,” IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520–525 (1987). [CrossRef]
  11. N. E. Hurt, Phase Retrieval and Zero Crossings (Kluwer, Dordrecht, The Netherlands, 1989). [CrossRef]
  12. H. Stark, ed., Image Recovery: Theory and Applications (Academic, San Diego, Calif., 1987).
  13. I. Manolitsakis, “Two-dimensional scattered fields: a description in terms of the zeros of entire functions,” J. Math. Phys. 23, 2291–2298 (1982). [CrossRef]
  14. I. S. Stefanescu, “On the phase retrieval problem in two dimensions,” J. Math. Phys. 26, 2141–2159 (1985). [CrossRef]
  15. M. S. Scivier, M. A. Fiddy, “Phase ambiguities and the zeros of multidimensional band-limited functions,” J. Opt. Soc. Am. A 2, 693–697 (1985). [CrossRef]
  16. J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. 3, 1897–1907 (1986). [CrossRef]
  17. C. C. Wackerman, A. E. Yagle, “Use of Fourier domain real-plane zeros to overcome a phase retrieval stagnation,” J. Opt. Soc. Am. A 8, 1898–1904 (1991). [CrossRef]
  18. S. Weissbach, F. Wyrowski, O. Byngdahl, “Errordiffusion algorithm in phase synthesis and retrieval techniques,” Opt. Lett. 17, 235–237 (1992). [CrossRef] [PubMed]
  19. F. Wyrowski, O. Bryngdahl, “Iterative Fourier-transform algorithm applied to computer holography,” J. Opt. Soc. Am. A 5, 1058–1065 (1988). [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