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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19330–19339

Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging

Tatiana Latychevskaia, Jean-Nicolas Longchamp, and Hans-Werner Fink  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19330-19339 (2011)
http://dx.doi.org/10.1364/OE.19.019330


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Abstract

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.

© 2011 OSA

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(110.7440) Imaging systems : X-ray imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

History
Original Manuscript: July 19, 2011
Revised Manuscript: August 25, 2011
Manuscript Accepted: August 27, 2011
Published: September 20, 2011

Citation
Tatiana Latychevskaia, Jean-Nicolas Longchamp, and Hans-Werner Fink, "Novel Fourier-domain constraint for fast phase retrieval in coherent diffraction imaging," Opt. Express 19, 19330-19339 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19330


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References

  1. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr.5(6), 843–843 (1952). [CrossRef]
  2. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.)35, 237–246 (1972).
  3. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A15(6), 1662–1669 (1998). [CrossRef]
  4. B. W. J. McNeil and N. R. Thompson, “X-ray free-electron lasers,” Nature Photon.4(12), 814–821 (2010). [CrossRef]
  5. H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nature Photon.4(12), 833–839 (2010). [CrossRef]
  6. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt.21(15), 2758–2769 (1982). [CrossRef] [PubMed]
  7. 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. B68(14), 140101 (2003). [CrossRef]
  8. G. Oszlányi and A. Süto, “Ab initio structure solution by charge flipping,” Acta Crystallogr. A60(2), 134–141 (2004). [CrossRef] [PubMed]
  9. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier-transform using a support constraint,” J. Opt. Soc. Am. A4(1), 118–123 (1987). [CrossRef]
  10. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A.102(43), 15343–15346 (2005). [CrossRef] [PubMed]
  11. P. Thibault and I. C. Rankenburg, “Optical diffraction microscopy in a teaching laboratory,” Am. J. Phys.75(9), 827–832 (2007). [CrossRef]
  12. W. J. Huang, J. M. Zuo, B. Jiang, K. W. Kwon, and M. Shim, “Sub-angstrom-resolution diffractive imaging of single nanocrystals,” Nature Phys.5(2), 129–133 (2009). [CrossRef]
  13. 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(2), 025506 (2006). [CrossRef] [PubMed]
  14. D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A80(6), 063823 (2009). [CrossRef]
  15. S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szoke, C. W. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J. Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nature Photon.2(9), 560–563 (2008). [CrossRef]
  16. R. A. Dilanian, G. J. Williams, L. W. Whitehead, D. J. Vine, A. G. Peele, E. Balaur, I. McNulty, H. M. Quiney, and K. A. Nugent, “Coherent diffractive imaging: a new statistically regularized amplitude constraint,” New J. Phys.12(9), 093042 (2010). [CrossRef]
  17. F. C. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010). [CrossRef]
  18. M. Valle, A. Zavialov, W. Li, S. M. Stagg, J. Sengupta, R. C. Nielsen, P. Nissen, S. C. Harvey, M. Ehrenberg, and J. Frank, “Incorporation of aminoacyl-tRNA into the ribosome as seen by cryo-electron microscopy,” Nat. Struct. Mol. Biol.10(11), 899–906 (2003). [CrossRef] [PubMed]
  19. O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, and K. Gohara, “10-kV diffractive imaging using newly developed electron diffraction microscope,” Ultramicroscopy110(2), 130–133 (2010). [CrossRef] [PubMed]
  20. E. Steinwand, J.-N. Longchamp, and H.-W. Fink, “Coherent low-energy electron diffraction on individual nanometer sized objects,” Ultramicroscopy111(4), 282–284 (2011). [CrossRef] [PubMed]

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