Skip to main content
SpringerLink
Log in

Electron microscopy at 1-Å resolution by entropy maximization and likelihood ranking

  • Article
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

The resolution of electron microscopy may be extended by combining the phase information in microscope images with electron diffraction intensities. A general method for obtaining structural reconstructions at a resolution greater than that of the phase information is demonstrated for crystals of perchlorocoronene. By using entropy maximization methods combined with likelihood ranking, the resolution is extended from 0.32 nm in the microscope images to 0.1 nm in the reconstruction from phase and intensity data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 1. Smith, D. J., Fryer, J. & Camps, R. A. Ultramicroscopy 19, 279-298 (1986). 2/ Fryer, J. R. & Holland, F. M. Proc. R. Soc. A393, 353-369 (1984). 3. Baird, T., Gall, J. H., MacNicol, D. D., Mallinson, P. R. & Michie, C. R. J. chem. Soc. Chem. Commun. 1471 1(988). 4. Murata, Y., Baird, T. & Fryer, J. R. J. Microsc. 108, 261-275 (1976). 5. Bricogne, G. Acta crystallogr. A40, 410-445 (1984). 6. Bricogne, G. & Gilmore, C. J. Acta crystallogr. A46, 284-297 (1990). 7. Gilmore, C. J., Bricogne, G. & Bannister, C. Acta crystallogr. A46, 297-308 1(990). 8. Gilmore, C. J., Henderson, K. & Bricogne, G. Acta crystallogr. A47, 830-841 (1991). 9. Gilmore, C. J., Henderson, A. N. & Bricogne, G. Acta crystallogr. A47, 842-846 (1991). 10. Fryer, J. R., Cleaver, J. R. A. & Smith, D. J. lnst. Phys. Conf. Ser. 52, 287-290 (1980). 11. Wang, D. N., Hovmoller, S., Kihlborg, L. & Sundberg, M. Ultramicroscopy 25, 303-316 (1988). 12. O'Keefe, M. A., Fryer, J. R. & Smith, D. J. Acta crystallogr. A39, 838-847 (1983). 13. Dorset. D. L. Acta crystallogr. A47, 510-515 (1991). 14. Bricogne, G. in Crystallographic Computing 4 (eds Isaacs, N. W. & Taylor, M. R.) 60-79 (Clarendon, Oxford, 1991). 15. Bricogne, G. Acta crystallogr. A44, 517-545 (1988). 16. Bricogne, G. in Maximum Entropy in Action (eds Buck, B. & Macaulay, V. A.) 187-216 (Clarendon, Oxford, 1991). 17. Hauptman, H. & Karle, J. The Solution of the Phase Problem: I The Centrosymmetric Crystal, ACA Monogr. No. 3. (Polycrystal Book Service, Pittsburgh, 1953). 18. Klug, A. Acta crystallogr. 11, 515-543 (1958). 19. Giacovazzo, C. Direct Methods in Crystallography (Academic, London, 1980). 20. Khinchin, A. I. Mathematical Foundations of Statistical Mechanics (Dover, New York, 1949). 21. Daniels, H. E. Ann. math. Statist. 25, 631-650 (1954). 22. Gilmore, C. J. J. appl. Crystallogr. 17, 42-46 (1984).

Download references

Author information

Authors and Affiliations

  1. Electron Microscope Centre, Chemistry Building, University of Glasgow, Glasgow, G12 8QQ, UK

    W. Dong, T. Baird & J. R. Fryer

  2. Chemistry Department, University of Glasgow, Glasgow, G12 8QQ, UK

    C. J. Gilmore & D. D. MacNicol

  3. MRC Laboratory of Molecular Biology, Hills Road, Cambridge, CB2 2QH, UK

    G. Bricogne

  4. Center for Solid State Science, Arizona State University, Tempe, Arizona, 85287, USA

    David J. Smith

  5. National Center for Electron Microscopy, University of California, LBL, Berkeley, California, 94720, USA

    M. A. O'Keefe

  6. Structural Chemistry, University of Stockholm, S-10691, Stockholm, Sweden

    S. Hövmoller

  7. LURE, Bâtiment 209D, 91405, Orsay, France

    J. R. Fryer, C. J. Gilmore & G. Bricogne

Authors
  1. W. Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Baird
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. R. Fryer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. J. Gilmore
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. D. D. MacNicol
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. Bricogne
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. David J. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. A. O'Keefe
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. S. Hövmoller
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dong, W., Baird, T., Fryer, J. et al. Electron microscopy at 1-Å resolution by entropy maximization and likelihood ranking. Nature 355, 605–609 (1992). https://doi.org/10.1038/355605a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/355605a0

  • Springer Nature Limited

This article is cited by

Search

Navigation