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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 16 — Aug. 6, 2007
  • pp: 9954–9962

A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging

S.G. Podorov, K.M. Pavlov, and D.M. Paganin  »View Author Affiliations


Optics Express, Vol. 15, Issue 16, pp. 9954-9962 (2007)
http://dx.doi.org/10.1364/OE.15.009954


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Abstract

We develop a deterministic algorithm for coherent diffractive imaging (CDI) that employs a modified Fourier transform of a Fraunhofer diffraction pattern to quantitatively reconstruct the complex scalar wavefield at the exit surface of a sample of interest. The sample is placed in a uniformly-illuminated rectangular hole with dimensions at least two times larger than the sample. For this particular scenario, and in the far-field diffraction case, our non-iterative reconstruction algorithm is rapid, exact and gives a unique analytical solution to the inverse problem. The efficacy and stability of the algorithm, which may achieve resolutions in the nanoscale range, is demonstrated using simulated X-ray data.

© 2007 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(340.0340) X-ray optics : X-ray optics
(340.7470) X-ray optics : X-ray mirrors

ToC Category:
Image Processing

History
Original Manuscript: May 4, 2007
Revised Manuscript: July 3, 2007
Manuscript Accepted: July 23, 2007
Published: July 24, 2007

Citation
S. G. Podorov, K. M. Pavlov, and D. M. Paganin, "A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging," Opt. Express 15, 9954-9962 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-9954


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References

  1. J. N. Cederquist, J. R. Fienup, J. C. Marron, and R. G. Paxman, "Phase retrival from experimental far-field speckle data," Opt. Lett. 13, 619-621 (1988). [CrossRef] [PubMed]
  2. 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]
  3. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature 400, 342-344 (1999). [CrossRef]
  4. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B 68, 140101(R) (2003). [CrossRef]
  5. J. Miao, T. Ohsuna, O. Tereasaki, K. O. Hodgson, and M. A. O'Keefe, "Atomic resolution three-dimensional electron diffraction microscopy," Phys. Rev. Lett. 89, 155502 (2002). [CrossRef] [PubMed]
  6. J. Miao, T. Ishikawa, B. Johnson, E. H. Anderson, B. Lai, K. O. Hodgson, "High resolution 3D X-ray diffraction microscopy," Phys. Rev. Lett. 89, 088303 (2002). [CrossRef] [PubMed]
  7. I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, "Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction," Phys. Rev. Lett. 87, 195505 (2001). [CrossRef] [PubMed]
  8. F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, "Neutron phase imaging and tomography," Phys. Rev. Lett. 96, 215505 (2006). [CrossRef] [PubMed]
  9. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources," Nature Physics 2, 258-261 (2006). [CrossRef]
  10. W. Pauli, "Die allgemeinen Prinzipien der Wellenmechanik" in Handbuch der Physik, ed. H. Geiger and K. Scheel (Springer, Berlin, 1933) 24(1), 83-272.
  11. 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).
  12. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  13. D. Sayre, "Some implications of a theorem due to Shannon,"Acta Cryst. 5, 843-843 (1952). [CrossRef]
  14. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege, S. Marchesini, B. W. Woods, S. Bajt, W. H. Benner, R. A. London, E. Plönjes, M. Kuhlmann, R. Treusch, S. Düesterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. M. Seibert, F. R. N.C. Maia, R. W. Lee, A. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nature Physics 2, 839-843 (2006). [CrossRef]
  15. V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Am. A 20, 40-55 (2003). [CrossRef]
  16. P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. R. Soc. A 133, 60-72 (1931). [CrossRef]
  17. M. V. Berry, "Singularities in waves and rays," in R. Balian et al. (eds), Les Houches Lecture Series, session XXXV, Physics of defects (North Holland, Amsterdam, 1981) pp. 453-543
  18. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006). [CrossRef]
  19. G. A. Korn and T. M. Korn, Mathematical handbook for scientists and engineers, 2nd ed (McGraw-Hill Book Company, 1968).
  20. R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. I: Underlying theory," Optik 61(3), 247-262 (1982).
  21. S. G. Podorov, G. Hölzer, E. Förster, and N. N. Faleev, "Fourier analysis of X-ray rocking curves from superlattices," Phys. Stat. Sol. B 213, 317-324 (1999). [CrossRef]
  22. S. G. Podorov, G. Hölzer, E. Förster, and N. N. Faleev, "Semidynamical solution of the inverse problem of X-ray Bragg diffraction on multilayered crystals," Phys. Stat. Sol. A 169, 9-16 (1998). [CrossRef]
  23. J. W. Goodman, Statistical optics (John Wiley & Sons, Inc., 2000).
  24. G. T. Herman, Image reconstruction from projections (Academic Press, 1980).
  25. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, "Fresnel coherent diffractive imaging," Phys. Rev. Lett. 97, 025506 (2006). [CrossRef] [PubMed]
  26. M. Born and E. Wolf, Principles of Optics, 7th edition (Cambridge University Press, Cambridge, 1999).
  27. Q. Shen, I. Bazarov, and P. Thibault, "Diffractive imaging of nonperiodic materials with future coherent sources,". J. Synchr. Rad. 11, 432-438 (2004). [CrossRef]
  28. D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948). [CrossRef] [PubMed]
  29. J. T. Winthrop and C. R. Worthington, "X-ray microscopy by successive Fourier transformation," Phys. Lett. 15, 124-126 (1965). [CrossRef]
  30. S. Mallick and M. L. Roblin, "Fourier transform holography using a quasimonochromatic incoherent source," Applied Optics 10, 596-598 (1971). [CrossRef] [PubMed]
  31. W. S. Haddad, D. Cullen, J. C. Solem, J. W. Longworth, A. McPherson, K. Boyer, and C. K. Rhodes, "Fourier-transform holographic microscope," Appl. Opt. 31, 4973-4978 (1992). [CrossRef] [PubMed]
  32. G. W. Stroke, "Lensless Fourier-transform method for optical holography," Appl. Phys. Lett. 6(10), 201-203 (1965). [CrossRef]
  33. G. W. Stroke and D. G. Falconer, "Attainment of high resolution in wavefront-reconstruction imaging," Phys. Lett. 13, 306-309 (1964). [CrossRef]
  34. G. W. Stroke, An introduction to coherent optics and holography, (Academic Press, New York, London, 1966).
  35. J. W. Goodman, Introduction to Fourier optics, 3rd edition (Roberts & Company, Englewood, Colorado, 2005).

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