OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 2866–2873

Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals

John C. H. Spence, Richard A. Kirian, Xiaoyu Wang, Uwe Weierstall, Kevin E. Schmidt, Thomas White, Anton Barty, Henry N. Chapman, Stefano Marchesini, and James Holton  »View Author Affiliations

Optics Express, Vol. 19, Issue 4, pp. 2866-2873 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1023 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The scattering between Bragg reflections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if sufficiently finely-sampled “snap-shot” diffraction data (as provided a free-electron X-ray laser) are available from many nanocrystals of different sizes lying in random orientations. By using information on the particle-size distribution within the patterns, this digital method succeeds, using all the data, without knowledge of the distribution of particle size or requiring atomic-resolution data.

© 2011 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(260.1960) Physical optics : Diffraction theory
(290.5840) Scattering : Scattering, molecules
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Image Processing

Original Manuscript: December 15, 2010
Revised Manuscript: January 26, 2011
Manuscript Accepted: January 27, 2011
Published: January 31, 2011

John C. H. Spence, Richard A. Kirian, Xiaoyu Wang, Uwe Weierstall, Kevin E. Schmidt, Thomas White, Anton Barty, Henry N. Chapman, Stefano Marchesini, and James Holton, "Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals," Opt. Express 19, 2866-2873 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. N. Kasai, and M. Kakudo, “X-ray diffraction by macromolecules” (Springer New York 2005).
  2. W. A. Barletta, J. Bisognano, J. N. Corlett, P. Emma, Z. Huang, K. J. Kim, R. Lindberg, J. B. Murphy, G. R. Neil, D. C. Nguyen, C. Pellegrini, R. A. Rimmer, F. Sannibale, G. Stupakov, R. P. Walker, A. A. Zholents, “Free electron lasers: Present status and future challenges,” Nucl. Instrum. Methods A618, 69–96 (2010).
  3. R. A. Kirian, X. Y. Wang, U. Weierstall, K. E. Schmidt, J. C. H. Spence, M. Hunter, P. Fromme, T. White, H. N. Chapman, J. Holton, “Femtosecond protein nanocrystallography-data analysis methods,” Opt. Express 18(6), 5713–5723 (2010). [CrossRef] [PubMed]
  4. H. N. Chapman, P. Fromme, A. Barty, T. A. White, R. A. Kirian, A. Aquila, M. S. Hunter, J. Schulz, D. P. DePonte, U. Weierstall, R. B. Doak, F. Maia, A. V. Martin, I. Schlichting, L. Lomb, N. Coppola, R. L. Shoeman, S. W. Epp, R. Hartmann, D. Rolles, A. Rudenko, L. Foucar, N. Kimmel, G. Weidenspointner, P. Holl, M. Liang, M. Barthelmess, C. Caleman, S. Boutet, M. J. Bogan, J. Krzywinski, C. Bostedt, S. Bajt, L. Gumprecht, B. Rudek, B. Erk, C. Schmidt, A. Hömke, C. Reich, D. Pietschner, L. Strüder, G. Hauser, H. Gorke, J. Ullrich, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K. Kühnel, M. Messerschmidt, J. D. Bozek, S. P. Hau-Riege, M. Frank, C. Y. Hampton, R. Sierra, D. Starodub, G. J. Williams, J. Hajdu, N. Timneanu, M. Seibert, J. Andreasson, A. Rocker, O. Jönsson, S. Stern, K. Nass, R. Andritschke, C. Schröter, F. Krasniqi, M. Bott, K. E. Schmidt, X. Wang, I. Grotjohann, J. Holton, S. Marchesini, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, M. Svenda, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, J. C. H. Spence, “Femtosecond X-ray protein nanocrystallography,” Nature. in press. [PubMed]
  5. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952). [CrossRef]
  6. M. F. Perutz, “The structure of haemoglobin,” Proc. Royal Soc. A264, 264–286 (1954). [CrossRef]
  7. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension,” Optik (Stuttg.) 61, 247–262 (1982).
  8. J. C. H. Spence, in Science of Microscopy, eds., P. Hawkes and J. C. H. Spence, (Springer, 2006. New York).
  9. J. C. H. Spence, R. B. Doak, “Single molecule diffraction,” Phys. Rev. Lett. 92(19), 198102 (2004). [CrossRef] [PubMed]
  10. C. Riekel. “Recent developments in microdiffraction on protein crystals,” J. Synchrontron Radiat. 11, 4–6 (2004). Also R. Von Dreele (2009) Personal communication: Results of powder X-ray diffraction from growth media. [CrossRef]
  11. M. von Laue, “The external shape of crystals and its influence on interference phenomena in crystalline lattices,” Ann. Phys. 26, 55–68 (1936).
  12. I. K. Robinson, R. Harder, “Coherent X-ray diffraction imaging of strain at the nanoscale,” Nat. Mater. 8(4), 291–298 (2009). [CrossRef] [PubMed]
  13. M. G. Rossmann, J. W. Erickson, “Oscillation photography of radiation-sensitive crystals using a synchrotron source,” J. Appl. Cryst. 16(6), 629–636 (1983). [CrossRef]
  14. A. G. Leslie, “The integration of macromolecular diffraction data,” Acta Crystallogr. D Biol. Crystallogr. 62(1), 48–57 (2006). [CrossRef]
  15. F. Maia, C. Yang, S. Marchesini, “Compressive auto-indexing in femotsecond nanocrystallography,” Proc. SPIE 7800, 78000F (2010). [CrossRef]
  16. G. Xu, G. Zhou, X. Zhang, “Phase recovery for X-ray crystallography,” Phys. Rev. B 59(14), 9044–9047 (1999). [CrossRef]
  17. W. Press, B. P. Flannery, A. A. Teukolsky, and W. T. Vetterling, Numerical Recipes. C.U.P. (2007).
  18. A. Brunettia, M. Sanchez del Rioc, B. Golosiob, A. Simionovicic, A. Somogyi, “A library for X-ray-matter interaction cross sections for X-ray fluorescence applications,” Spectrochim. Acta [A] B59, 1725–1731 (2004).
  19. D. A. Shapiro, H. N. Chapman, D. DePonte, R. B. Doak, P. Fromme, G. Hembree, M. Hunter, S. Marchesini, K. Schmidt, J. Spence, D. Starodub, U. Weierstall, J. Synchrotron Radiat. 15, 593–599 (2008). [CrossRef] [PubMed]
  20. S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci Inst. 78(1), 011301 (2007). [CrossRef]
  21. V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. U.S.A. 104(2), 418–423 (2007). [CrossRef] [PubMed]
  22. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. A 62(4), 248–261 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited