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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 11 — Nov. 1, 2008
  • pp: 2784–2790

Phase retrieval by propagation for localized images

David Montiel, Mark Sutton, and Martin Grant  »View Author Affiliations


JOSA A, Vol. 25, Issue 11, pp. 2784-2790 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002784


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Abstract

We present an algorithm for phase retrieval based on improvements to the methods developed by Bates [see Optik 61, 247 (1982) ]. Specifically, we have developed a more precise way of calculating phase differences between adjacent actual sampling points. This leads to a reduction in the error buildup in a recursive phase propagation scheme. Our approach has the advantage of having no adjustable parameters. We present a few examples of how this method can lead to improved image reconstructions.

© 2008 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval

ToC Category:
Image Processing

History
Original Manuscript: June 12, 2008
Manuscript Accepted: August 17, 2008
Published: October 21, 2008

Citation
David Montiel, Mark Sutton, and Martin Grant, "Phase retrieval by propagation for localized images," J. Opt. Soc. Am. A 25, 2784-2790 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-11-2784


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References

  1. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237-246 (1972).
  2. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27-29 (1978). [CrossRef] [PubMed]
  3. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I: Underlying theory,” Optik (Stuttgart) 61, 247-262 (1982).
  4. K. L. Garden and R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. II: One-dimensional considerations,” Optik (Stuttgart) 62, 131-142 (1982).
  5. W. R. Fright and R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. III: Computational examples for two dimensions,” Optik (Stuttgart) 62, 219-230 (1982).
  6. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  7. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40-55 (2003). [CrossRef]
  8. Y. M. Bruck and L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304-308 (1979). [CrossRef]
  9. M. H. Hayes, “The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-30, 140-154 (1982). [CrossRef]
  10. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662-1669 (1998). [CrossRef]
  11. R. H. T. Bates, “Uniqueness of solutions to two-dimensional Fourier phase problems for localized and positive images,” Comput. Vis. Graph. Image Process. 25, 205-217 (1984). [CrossRef]
  12. C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C. Chen, T. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B 75, 012102 (2007). [CrossRef]
  13. The solution to the phase problem is not unique in 1D. In the most general case (for a complex image), there can be up to 22M−1 different sets of phases compatible with a set of 2M+1 given magnitudes al. This is consistent with the fact that there are two possible choices for the sign of each phase difference (ωl) between adjacent samples .
  14. K. T. Knox and B. J. Thompson, “Recovery of images from atmospherically degraded short exposure images,” Astrophys. J. 193, L45-L48 (1974). [CrossRef]
  15. R. H. T. Bates and W. R. Fright, “Composite two-dimensional phase-restoration procedure,” J. Opt. Soc. Am. 73, 358-365 (1983). [CrossRef]

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