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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 11 — Nov. 1, 1983
  • pp: 1421–1426

Reconstruction of objects having latent reference points

J. R. Fienup  »View Author Affiliations


JOSA, Vol. 73, Issue 11, pp. 1421-1426 (1983)
http://dx.doi.org/10.1364/JOSA.73.001421


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Abstract

A simple recursive algorithm is proposed for reconstructing certain classes of two-dimensional objects from their autocorrelation functions (or equivalently from the modulus of their Fourier transforms—the phase-retrieval problem). The solution is shown to be unique in some cases. The objects contain reference points not satisfying the holography condition but satisfying weaker conditions. Included are objects described by Fiddy et al. [ Opt. Lett. 8, 96 ( 1983)] satisfying Eisenstein’s thorem.

© 1983 Optical Society of America

Citation
J. R. Fienup, "Reconstruction of objects having latent reference points," J. Opt. Soc. Am. 73, 1421-1426 (1983)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-11-1421


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References

  1. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978).
  2. C. Y. C. Liu and A. W. Lohmann, "High resolution image formation through the turbulent atmosphere," Opt. Commun. 8, 372–377 (1973). [CrossRef]
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  4. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237–246 (1972); W. O. Saxton, Computer Techniques for Image Processing in Electron Microscopy (Academic, New York, 1978); R. H. Boucher, "Convergence of algorithms for phase retrieval from two intensity distributions," Proc. Soc. Photo-Opt. Instrum. Eng. 231, 130–141 (1980).
  5. W. J. Dallas, "Digital computation of image complex amplitude from image- and diffraction-intensity: an alternative to holography," Optik 44, 45–59 (1975).
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  7. J. R. Fienup, "Reconstruction of an object from the modulus of its Fourier transform," Opt. Lett. 3, 27–29 (1978); J. R. Fienup, "Space object imaging through the turbulent atmosphere," Opt. Eng. 18, 529–534 (1979). [CrossRef] [PubMed]
  8. P. J. Napier and R. H. T. Bates, "Inferring phase information from modulus information in two-dimensional aperture synthesis," Astron. Astrophys. Suppl. 15, 427–430 (1974).
  9. G. H. Stout and L. H. Jensen, X-Ray Structure Determination (Macmillan, London, 1968).
  10. J. R. Fienup, T. R. Crimmins, and W. Holsztynski, "Reconstruction of the support of an object from the support of its autocorrelation," J. Opt. Soc. Am. 72, 610–624 (1982). [CrossRef]
  11. Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979). [CrossRef]
  12. A. Walther, "The question of phase retrieval in optics," Opt. Acta 10,41–49 (1963); E. M. Hofstetter, "Construction of time-limited functions with specified autocorrelation functions," IEEE Trans. Inf. Theory IT-10, 119–126 (1964). [CrossRef]
  13. M. A. Fiddy, B. J. Brames and J. C. Dainty, "Enforcing irreducibility for phase retrieval in two dimensions," Opt. Lett. 8,96–98 (1983). [CrossRef] [PubMed]
  14. M. H. Hayes and T. F. Quatieri, "The importance of boundary conditions in the phase retrieval problem," IEEE Trans. Acoust. Speech Signal Process. ASSP-82, 1545 (1982).
  15. J. R. Fienup, "Image reconstruction for stellar interferometry," in Current Trends in Optics, F. T. Arecchi and F. R. Aussenegg, eds. (Taylor and Francis, London, 1981), pp. 95–102

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