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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 19 — Sep. 22, 2003
  • pp: 2335–2343

Tomographic diffractive imaging of monolayer crystals at atomic resolution with one-dimensional compact support

U. Weierstall, J. Spence, and G. Hembree  »View Author Affiliations

Optics Express, Vol. 11, Issue 19, pp. 2335-2343 (2003)

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A solution to the phase problem for diffraction by two-dimensional crystalline slabs is described, based on the application of a compact support normal to the slab. Specifically we apply the iterative Gerchberg-Saxton-Fienup algorithm to simulated three-dimensional transmission electron diffraction data from monolayer organic crystals. We find that oversampling normal to the monolayer alone does not solve the phase problem in this geometry in general. However, based on simulations for a crystalline monolayer (tetracyanoethylene), we find that convergence is obtained if phases are supplied from a few high-resolution electron microscope images recorded at small tilts to the beam direction. Since current cryomicroscopy methods required a large number of images to phase tomographic diffraction data, this method should greatly reduce the labor involved in data acquisition and analysis in cryo-electron microscopy of organic thin crystals by avoiding the need to record images at high tilt angles. We discuss also the use of laser tweezers as a method of supporting nanoparticles in TEM for diffractive imaging

© 2003 Optical Society of America

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

ToC Category:
Focus Issue: Coherent x-ray optics

Original Manuscript: July 28, 2003
Revised Manuscript: August 29, 2003
Published: September 22, 2003

U. Weierstall, J. Spence, and G. Hembree, "Tomographic diffractive imaging of monolayer crystals at atomic resolution with onedimensional compact support," Opt. Express 11, 2335-2343 (2003)

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  1. J. R. Fienup, "Phase Retrieval Algorithms - a Comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  2. J. W. 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]
  3. H. He, S. Marchesini, M. Howells, U. Weierstall, H. Chapman, S. Hau-Riege, A. Noy, and Spence,, "Inversion of X-ray diffuse scattering to images using prepared objects," Phys. Rev. B 67, 174114 (2003). [CrossRef]
  4. H. He, S. Marchesini, M. Howells, U. Weierstall, G. Hembree, and J. C. H. Spence, "Experimental lensless soft-X-ray imaging using iterative algorithms: phasing diffuse scattering," Acta Crystallogr. A 59, 143-152 (2003). [CrossRef] [PubMed]
  5. H. H. S. Marchesini , H. N. Chapman , S. P. Hau-Riege A. Noy, M. R. Howells , U. Weierstall , J.C.H. Spence, "Imaging without lenses," <a href=http://arxiv.org/abs/physics/0306174 (2003).>http://arxiv.org/abs/physics/0306174 (2003).</a>
  6. U. Weierstall, Q. Chen, J. C. H. Spence, M. R. Howells, M. Isaacson, and R. R. Panepucci, "Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation," Ultramicroscopy 90, 171-195 (2002). [CrossRef] [PubMed]
  7. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, "Atomic resolution imaging of a carbon nanotube from diffraction intensities," Science 300, 1419-1421 (2003). [CrossRef] [PubMed]
  8. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, "Potential for biomolecular imaging with femtosecond X-ray pulses," Nature 406, 752-757 (2000). [CrossRef] [PubMed]
  9. L.D. Marks, �??General solution for three-dimensional surface structures using direct methods,�?? Phys. Rev. B 60, 2771-2780 (1999). [CrossRef]
  10. S. Lindaas, B. Calef, K. Downing, M. Howells, C. Magowan, D. Pinkas, and C. Jacobsen, "X-ray Holography of Fast-Frozen Hydrated Biological Samples," in X-ray Microscopy and Spectromicroscopy, J. Thieme, ed. (Springer, Berlin, 1998), pp. II-75.
  11. R. P. Millane and W. J. Stroud, "Reconstructing symmetric images from their undersampled Fourier intensities," J. Opt. Soc. Am. A 14, 568-579 (1997). [CrossRef]
  12. H. Stark, Image recovery : theory and application (Academic Press, Orlando, 1987).
  13. D. Sayre, "Some implications of a theorem due to Shannon", Acta Crystallogr. 5, 843 (1952). [CrossRef]
  14. D. Belemlilga, J. M. Gillet, and P. J. Becker, "Charge and momentum densities of cubic tetracyanoethylene and its insertion compounds," Acta Crystallogr. B 55, 192-202 (1999). [CrossRef]
  15. P. A. Doyle and P. S. Turner, "Relativistic Hartree-Fock X-Ray and Electron Scattering Factors", Acta Crystallogr. A 24, 390 (1968).
  16. R. J. Read, "Improved Fourier Coefficients for Maps Using Phases from Partial Structures with Errors," Acta Crystallogr. A 42, 140-149 (1986). [CrossRef]
  17. A. Ashkin and J. M. Dziedzic "Optical levitation in high vacuum", Appl. Phys. Lett. 28, 333-335 (1976). [CrossRef]
  18. A. Ashkin, J. M. Dziedzic, J.E. Bjorkholm, and Steven Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986). [CrossRef] [PubMed]
  19. J.C.H.Spence, U. Weierstall, T.T.Fricke, K.H.Downing and R.M.Glaeser, "Three-dimensional diffractive imaging for crystalline monolayers with one-dimensional compact support," J. Struct. Biol., submitted (2003). [CrossRef] [PubMed]
  20. E. Nogales, S. G. Wolf, and K. H. Downing, "Structure of the alpha beta tubulin dimer by electron crystallography," Nature 393, 191-191 (1998). [CrossRef]
  21. N. Grigorieff, T. A. Ceska, K. H. Downing, J. M. Baldwin, and R. Henderson, "Electron-crystallographic refinement of the structure of bacteriorhodopsin," J. Mol. Biol. 259, 393-421 (1996). [CrossRef] [PubMed]
  22. M. J. Buerger, Vector space, and its application in crystal-structure investigation (Wiley, New York, 1959).
  23. J. H. Seldin and J. R. Fienup, "Numerical Investigation of the Uniqueness of Phase Retrieval," J. Opt. Soc. Am. A 7, 412-427 (1990). [CrossRef]

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