OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 23, Iss. 5 — May. 1, 2006
  • pp: 1179–1200

High-resolution ab initio three-dimensional x-ray diffraction microscopy

Henry N. Chapman, Anton Barty, Stefano Marchesini, Aleksandr Noy, Stefan P. Hau-Riege, Congwu Cui, Malcolm R. Howells, Rachel Rosen, Haifeng He, John C.H. Spence, Uwe Weierstall, Tobias Beetz, Chris Jacobsen, and David Shapiro  »View Author Affiliations

JOSA A, Vol. 23, Issue 5, pp. 1179-1200 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (1184 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Coherent x-ray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions limited, in principle, by only the wavelength and largest scattering angles recorded. We demonstrate x-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the three-dimensional diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct two-dimensional images of thick objects with greatly increased depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution with x-ray undulator radiation and establishes the techniques to be used in atomic-resolution ultrafast imaging at x-ray free-electron laser sources.

© 2006 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.5070) Image processing : Phase retrieval
(100.6890) Image processing : Three-dimensional image processing
(110.1650) Imaging systems : Coherence imaging
(110.6880) Imaging systems : Three-dimensional image acquisition
(180.6900) Microscopy : Three-dimensional microscopy
(340.7460) X-ray optics : X-ray microscopy

ToC Category:
X-ray Optics

Original Manuscript: August 26, 2005
Revised Manuscript: October 14, 2005
Manuscript Accepted: October 18, 2005

Virtual Issues
Vol. 1, Iss. 6 Virtual Journal for Biomedical Optics

Henry N. Chapman, Anton Barty, Stefano Marchesini, Aleksandr Noy, Stefan P. Hau-Riege, Congwu Cui, Malcolm R. Howells, Rachel Rosen, Haifeng He, John C. H. Spence, Uwe Weierstall, Tobias Beetz, Chris Jacobsen, and David Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Sayre and H. N. Chapman, "X-ray microscopy," Acta Crystallogr., Sect. A: Found. Crystallogr. 51, 237-252 (1995). [CrossRef]
  2. D. Sayre, H. N. Chapman, and J. Miao, "On the extendibility of x-ray crystallography to noncrystals," Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 232-239 (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 (London) 400, 342-344 (1999). [CrossRef]
  4. 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]
  5. G. J. Williams, M. A. Pfeifer, I. A. Vartanyants, and I. K. Robinson, "Three-dimensional imaging of microstructure in Au nanocrystals," Phys. Rev. Lett. 90, 175501 (2003). [CrossRef] [PubMed]
  6. 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 (2003). [CrossRef]
  7. S. Marchesini, H. N. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. He, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, "Coherent x-ray diffractive imaging: applications and limitations," Opt. Express 11, 2344-2353 (2003). [CrossRef] [PubMed]
  8. H. He, S. Marchesini, M. Howells, U. Weierstall, H. Chapman, S. Hau-Riege, A. Noy, and J. C. H. Spence, "Inversion of x-ray diffuse scattering to images using prepared objects," Phys. Rev. B 67, 174114 (2003). [CrossRef]
  9. M. R. Howells, T. Beetz, H. N. Chapman, C. Cui, J. M. Holton, C. J. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. A. Shapiro, and J. C. H. Spence, "An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy," arxiv.org e-print archive, physics/0502059, February 11, 2005, http://arxiv.org/pdf/physics/0502059.
  10. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, "Potential for biomolecular imaging with femtosecond x-ray pulses," Nature (London) 406, 753-757 (2000). [CrossRef]
  11. J. Miao, K. O. Hodgson, and D. Sayre, "An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images," Proc. Natl. Acad. Sci. U.S.A. 98, 6641-6645 (2001). [CrossRef] [PubMed]
  12. J. C. H. Spence and R. B. Doak, "Single molecule diffraction," Phys. Rev. Lett. 92, 198102 (2004). [CrossRef] [PubMed]
  13. W. S. Haddad, I. McNulty, J. Trebes, E. Anderson, R. Levesque, and L. Yang, "Ultrahigh-resolution x-ray tomography," Science 266, 1213-1215 (1994). [CrossRef] [PubMed]
  14. D. Weiss, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, "Computed tomography of cryogenic biological specimens based on x-ray microscopic images," Ultramicroscopy 84, 185-197 (2000). [CrossRef] [PubMed]
  15. C. A. Larabell and M. A. Le Gros, "X-ray tomography generates 3-D reconstructions of the yeast, Saccharomyces cerevisiae, at 60-nm resolution," Mol. Biol. Cell 15, 957-962 (2004). [CrossRef]
  16. N. Streibl, "Three-dimensional imaging by a microscope," J. Opt. Soc. Am. A 2, 121-127 (1985). [CrossRef]
  17. T. Beetz, M. Howells, C. Jacobsen, C. Kao, J. Kirz, E. Lima, T. Mentes, H. Miao, C. Sanchez-Hanke, D. Sayre, and D. Shapiro, "Apparatus for x-ray diffraction microscopy and tomography of cryo specimens," Nucl. Instrum. Methods Phys. Res. A 545, 459-468 (2005). [CrossRef]
  18. M. R. Howells, P. Charalambous, H. He, S. Marchesini, and J. C. H. Spence, "An off-axis zone-plate monochromator for high-power undulator radiation," in Design and Microfabrication of Novel X-Ray Optics, D.C.Mancini, ed., Proc. SPIE 4783, 65-73 (2002).
  19. C. Giacovazzo, Direct Phasing in Crystallography (Oxford U. Press, 1998), p. 468.
  20. R. Crandall, E. Jones, J. Klivington, and D. Kramer, "Gigaelement FFTs on Apple G5 clusters," Advanced Computation Group, Apple Computer (2004), http://images.apple.com/acg/pdf/20040827lowbarGigaFFT.pdf.
  21. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).
  22. R. W. James, The Optical Principles of the Diffraction of X-Rays (Bell, 1962).
  23. E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Opt. Commun. 1, 153-156 (1969). [CrossRef]
  24. J. Kirz, C. Jacobsen, and M. Howells, "Soft x-ray microscopes and their biological applications," Q. Rev. Biophys. 28, 33-130 (1995). [CrossRef] [PubMed]
  25. F. Natterer, "An error bound for the Born approximation," Inverse Probl. 20, 447-452 (2004). [CrossRef]
  26. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).
  27. J. Miao, T. Ishikawa, E. H. Anderson, and K. O. Hodgson, "Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method," Phys. Rev. B 67, 174104 (2003). [CrossRef]
  28. 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]
  29. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  30. J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004). [CrossRef] [PubMed]
  31. R. Crowther, D. DeRosier, and A. Klug, "The reconstruction of a three-dimensional structure from its projections and its applications to electron microscopy," Proc. R. Soc. London A317, 319-340 (1970).
  32. E. Salerno, "Superresolution capabilities of the Gerchberg method in the band-pass case: an eigenvalue analysis," Int. J. Imaging Syst. Technol. 90, 181-188 (1998). [CrossRef]
  33. Y. Nishino, J. Miao, and T. Ishikawa, "Image reconstruction of nanostructured nonperiodic objects only from oversampled hard x-ray diffraction intensities," Phys. Rev. B 68, 220101 (2003). [CrossRef]
  34. T. Sato, S. J. Norton, M. Linzer, O. Ikeda, and M. Hirama, "Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces," Appl. Opt. 20, 395-399 (1981). [CrossRef] [PubMed]
  35. M. Bertero and E. R. Pike, "Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination," Opt. Acta 29, 727-746 (1982). [CrossRef]
  36. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neimann, and D. Sayre, "Biological imaging by soft x-ray diffraction microscopy," Proc. Natl. Acad. Sci. U.S.A. 102, 15343-15346 (2005). [CrossRef] [PubMed]
  37. A. Szoke, H. Szoke, and J. R. Somoza, "Holographic methods in x-ray crystallography. V. Multiple isomorphous replacement, multiple anomalous dispersion and noncrystallographic symmetry," Acta Crystallogr., Sect. A: Found. Crystallogr. 53, 291-313 (1997). [CrossRef]
  38. S. P. Hau-Riege, H. Szoke, H. N. Chapman, A. Szoke, S. Marchesini, A. Noy, H. He, M. Howells, U. Weierstall, and J. C. H. Spence, "SPEDEN: reconstructing single particles from their diffraction patterns," Acta Crystallogr., Sect. A: Found. Crystallogr. 60, 294-305 (2004). [CrossRef]
  39. D. Potts, G. Steidl, and M. Tasche, "Fast Fourier transforms for nonequispaced data: a tutorial," in Modern Sampling Theory: Mathematics and Applications, J.J.Benedetto and P.Ferreira, eds. (Springer, 2001), Chap. 12, pp. 249-274.
  40. H. Choi and D. C. Munson, Jr., "Direct-Fourier reconstruction in tomography and synthetic aperture radar," Int. J. Imaging Syst. Technol. 9, 1-13 (1998). [CrossRef]
  41. F. Natterer, The Mathematics of Computerized Tomography (SIAM, 2001). [CrossRef]
  42. A. J. Devaney, "A filtered backpropagation algorithm for diffraction tomography," Ultrason. Imaging 4, 336-350 (1982). [CrossRef] [PubMed]
  43. S. Pan and A. Kak, "A computational study of reconstruction algorithms for diffraction tomography: interpolation versus filtered-backpropagation," IEEE Trans. Acoust., Speech, Signal Process. SP- 31, 1262-1275 (1983). [CrossRef]
  44. 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., Sect. A: Found. Crystallogr. 59, 143-152 (2003). [CrossRef]
  45. J. R. Fienup, "Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint," J. Opt. Soc. Am. A 4, 118-123 (1987). [CrossRef]
  46. J. R. Fienup, "Phase retrieval and support estimation in x-ray diffraction," in Coherence 2005: International Workshop on Phase Retrieval and Coherent Scattering (ESRF, 2005), http://www.esrf.fr/NewsAndEvents/Conferences/Coherence2005/Proceedings/files/Talks/Fienup.pdf.
  47. T. R. Crimmins, J. Fienup, and B. J. Thelen, "Improved bounds on object support from autocorrelation support and application to phase retrieval," J. Opt. Soc. Am. A 7, 3-13 (1990). [CrossRef]
  48. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  49. V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Am. A 20, 40-55 (2003). [CrossRef]
  50. D. R. Luke, "Relaxed averaged alternating reflections for diffraction imaging," Inverse Probl. 21, 37-50 (2005). [CrossRef]
  51. M. Frigo and S. G. Johnson, "The design and implementation of FFTW3," Proc. IEEE 93, 216-231 (2005). (Special issue on "Program Generation, Optimization, and Platform Adaptation"). [CrossRef]
  52. "The message passing interface (MPI) standard," http://www-unix.mcs.anl.gov/mpi/.
  53. A. J. Ladd, J. H. Kinney, D. L. Haupt, and S. A. Goldstein, "Finite-element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus," J. Orthop. Res. 16, 622-628 (1998). [CrossRef] [PubMed]
  54. "Movies of three-dimensional diffraction data and reconstruction of the pyramid test object," http://als.lbl.gov/esglowbarbeamlines/cxdi.
  55. J. M. Cowley, Diffraction Physics (North-Holland,1981).
  56. J. C. H. Spence, U. Weierstall, and M. Howells, "Phase recovery and lensless imaging by iterative methods in optical, x-ray and electron diffraction," Philos. Trans. R. Soc. London, Ser. A 360, 875-895 (2002). [CrossRef]
  57. G. Huldt, Biomedical Centre, Uppsala Universitet (personal communication, 2005).
  58. J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies (Academic, 1996).
  59. J. R. Fienup and C. Wackerman, "Phase-retrieval stagnation problems and solutions," J. Opt. Soc. Am. A 3, 1897-1907 (1986). [CrossRef]
  60. J. R. Fienup, "Invariant error metrics for image reconstruction," Appl. Opt. 36, 8352-8357 (1997). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited