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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 12 — Dec. 1, 2013
  • pp: 2627–2634

Diffraction by nanocrystals

Joe P. J. Chen and Rick P. Millane  »View Author Affiliations

JOSA A, Vol. 30, Issue 12, pp. 2627-2634 (2013)

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X-ray femtosecond nanocrystallography is a new, potentially powerful technique for imaging biological macromolecules that uses ensemble-averaged measurements of diffraction of x-ray free-electron laser pulses from nanocrytalline specimens. Nanocrystals have some diffraction characteristics that are distinct from those of macroscopic crystals, due to the presence of different kinds of unit cell in the crystal and of truncated unit cells on the crystal surface. Expressions are derived for diffraction by nanocrystals with variable and incomplete unit cells, averaged over a distribution of crystal sizes and shapes. The diffraction contains differently modulated Bragg components that are due to interference effects within and between the full and incomplete unit cells. Estimates are obtained for the relative magnitudes of the components. The nature of the diffraction is illustrated by two-dimensional simulations. Implications for molecular imaging are discussed.

© 2013 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1960) Diffraction and gratings : Diffraction theory
(110.7440) Imaging systems : X-ray imaging

ToC Category:
Diffraction and Gratings

Original Manuscript: July 11, 2013
Revised Manuscript: October 22, 2013
Manuscript Accepted: October 23, 2013
Published: November 27, 2013

Virtual Issues
Vol. 9, Iss. 2 Virtual Journal for Biomedical Optics

Joe P. J. Chen and Rick P. Millane, "Diffraction by nanocrystals," J. Opt. Soc. Am. A 30, 2627-2634 (2013)

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  1. J. Drenth, Principles of Protein X-ray Crystallography (Springer-Verlag, 1994).
  2. R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990). [CrossRef]
  3. 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]
  4. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutet, M. Frank, S. P. Hau-Riege, S. Marchesini, B. W. Woods, S. Bajt, H. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, 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. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006). [CrossRef]
  5. A. Barty, C. Caleman, A. Aquila, N. Timneanu, L. Lomb, T. A. White, J. Andreasson, D. Arnlund, S. Bajt, T. R. M. Barends, M. Barthelmess, M. J. Bogan, C. Bostedt, J. D. Bozek, R. Coffee, N. Coppola, J. Davidsson, D. P. DePonte, B. R. Doak, T. Ekeberg, V. Elser, S. W. Epp, B. Erk, H. Fleckenstein, L. Foucar, P. Fromme, H. Graafsma, L. Gumprecht, J. Hajdu, C. Y. Hampton, R. Hartmann, A. Hartmann, G. Hauser, H. Hirsemann, P. Holl, M. S. Hunter, L. Johansson, S. Kassemeyer, N. Kimmel, R. A. Kirian, M. N. Liang, F. R. N. C. Maia, E. Malmerberg, S. Marchesini, A. V. Martin, K. Nass, R. Neutze, C. Reich, D. Rolles, B. Rudek, A. Rudenko, H. Scott, I. Schlichting, J. Schulz, M. M. Seibert, R. L. Shoeman, R. G. Sierra, H. Soltau, J. C. H. Spence, F. Stellato, S. Stern, L. Struder, J. Ullrich, X. Wang, G. Weidenspointner, U. Weierstall, C. B. Wunderer, and H. N. Chapman, “Self-terminating diffraction gates femtosecond x-ray nanocrystallography measurements,” Nat. Photonics 6, 35–40 (2011). [CrossRef]
  6. 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, B. R. Doak, F. R. N. C. 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. N. 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. Homke, C. Reich, D. Pietschner, L. Struder, G. Hauser, H. Gorke, J. Ullrich, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K. U. Kuhnel, M. Messerschmidt, J. D. Bozek, S. P. Hau-Riege, M. Frank, C. Y. Hampton, R. G. Sierra, D. Starodub, G. J. Williams, J. Hajdu, N. Timneanu, M. M. Seibert, J. Andreasson, A. Rocker, O. Jonsson, M. Svenda, S. Stern, K. Nass, R. Andritschke, C. D. Schroter, F. Krasniqi, M. Bott, K. E. Schmidt, X. Y. Wang, I. Grotjohann, J. M. Holton, T. R. M. Barends, R. Neutze, S. Marchesini, R. Fromme, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, I. Andersson, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, and J. C. H. Spence, “Femtosecond x-ray protein nanocrystallography,” Nature 470, 73–77 (2011). [CrossRef]
  7. R. A. Kirian, X. Y. Wang, U. Weierstall, K. E. Schmidt, J. C. H. Spence, M. Hunter, P. Fromme, T. A. White, H. N. Chapman, and J. M. Holton, “Femtosecond protein nanocrystallography: data analysis methods,” Opt. Express 18, 5713–5723 (2010). [CrossRef]
  8. T. A. White, A. Barty, F. Stellato, J. M. Holton, R. A. Kirian, N. A. Zatsepin, and H. N. Chapman, “Crystallographic data processing for free-electron laser sources,” Acta Crystallogr. Sect. D 69, 1231–1240 (2013).
  9. S. Boutet, L. Lomb, G. J. Williams, T. R. M. Barends, A. Aquila, R. B. Doak, U. Weierstall, D. P. DePonte, J. Steinbrener, R. L. Shoeman, M. Messerschmidt, A. B arty, T. A. White, S. Kassemeyer, R. A. Kirian, M. M. Seibert, P. A. Montanez, C. Kenney, R. Herbst, P. Hart, J. Pines, G. Haller, S. M. Gruner, H. T. Philipp, M. W. Tate, M. Hromalik, L. J. Koerner, N. vanBakel, J. Morse, W. Ghonsalves, D. Arnlund, M. J. Bogan, C. Caleman, R. Fromme, C. Y. Hampton, M. S. Hunter, L. C. Johansson, G. Katona, C. Kupitz, M. N. Liang, A. V. Martin, K. Nass, L. Redecke, F. Stellato, N. Timneanu, D. J. Wang, N. A. Zatsepin, D. Schafer, J. Defever, R. Neutze, P. Fromme, J. C. H. Spence, and H. N. Chapman, “High-resolution protein structure determination by serial femtosecond crystallography,” Science 337, 362–364 (2012). [CrossRef]
  10. L. Redecke, K. Nass, D. P. DePonte, T. A. White, D. Rehders, A. Barty, F. Stellato, M. N. Liang, T. R. M. Barends, S. Boutet, G. J. Williams, M. Messerschmidt, M. M. Seibert, A. Aquila, D. Arnlund, S. Bajt, T. Barth, M. J. Bogan, C. Caleman, T. C. Chao, R. B. Doak, H. Fleckenstein, M. Frank, R. Fromme, L. Galli, I. Grotjohann, M. S. Hunter, L. C. Johansson, S. Kassemeyer, G. Katona, R. A. Kirian, R. Koopmann, C. Kupitz, L. Lomb, A. V. Martin, S. Mogk, R. Neutze, R. L. Shoeman, J. Steinbrener, N. Timneanu, D. J. Wang, U. Weierstall, N. A. Zatsepin, J. C. H. Spence, P. Fromme, I. Schlichting, M. Duszenko, C. Betzel, and H. N. Chapman, “Natively inhibited Trypanosoma brucei Cathepsin B structure determined by using an x-ray laser,” Science 339, 227–230 (2013). [CrossRef]
  11. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
  12. J. Miao and D. Sayre, “On possible extensions of x-ray crystallography through diffraction-pattern oversampling,” Acta Crystallogr. Sect. A 56, 596–605 (2000).
  13. V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003). [CrossRef]
  14. S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007). [CrossRef]
  15. A. V. Martin, A. J. Morgan, T. Ekeberg, N. D. Loh, F. R. N. C. Maia, F. Wang, J. C. H. Spence, and H. N. Chapman, “The extraction of single-particle diffraction patterns from a multiple-particle diffraction pattern,” Opt. Express 21, 15102–15112 (2013). [CrossRef]
  16. R. P. Millane and V. L. Lo, “Iterative projection algorithms in protein crystallography. I. Theory,” Acta Crystallogr. Sect. A 69, 517–527 (2013).
  17. J. C. H. Spence, R. A. Kirian, X. Y. Wang, U. Weierstall, K. E. Schmidt, T. A. White, A. Barty, H. N. Chapman, S. Marchesini, and J. Holton, “Phasing of coherent femtosecond x-ray diffraction from size-varying nanocrystals,” Opt. Express 19, 2866–2873 (2011). [CrossRef]
  18. J. P. J. Chen, J. C. H. Spence, and R. P. Millane, “Direct phasing in femtosecond nanocrystallography I. Diffraction characteristics,” Acta Cryst. A (in press).
  19. J. P. J. Chen, J. C. H. Spence, and R. P. Millane, “Direct phasing in femtosecond nanocrystallography II. Phase retrieval,” Acta Cryst. A (in press–).
  20. V. Elser, “Direct phasing of nanocrystal diffraction,” Acta Crystallogr. Sect. A 69, 559–569 (2013).
  21. R. A. Dilanian, V. A. Streltsov, H. M. Quiney, and K. A. Nugent, “Continuous x-ray diffractive field in protein nanocrystallography,” Acta Crystallogr. Sect. A 69, 108–118 (2013).
  22. V. Elser and R. P. Millane, “Reconstruction of an object from its symmetry-averaged diffraction pattern,” Acta Crystallogr. Sect. A 64, 273–279 (2008).

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