Advertisement

Introduction: Principles of Electron Tomography

  • Joachim Frank

Abstract

Tomography is a method for reconstructing the interior of an object from its projections. The word tomography literally means the visualization of slices, and is applicable, in the strict sense of the word, only in the narrow context of a single-axis tilt geometry: e.g., in medical computerized axial tomography (CAT-scan imaging), the detector-source arrangement is tilted relative to the patient around a single axis. In electron microscopy, where the beam direction is fixed, the specimen holder is tilted around a single axis (Fig. 1). However, the usage of this term has recently become more liberal, encompassing arbitrary geometries. In line with this relaxed convention, we will use the term electron tomography for any technique that employs the transmission electron microscope to collect projections of an object and uses these projections to reconstruct the object in its entirety.

Keywords

Fourier Space Single Axis Word Tomography Macromolecular Assembly Angular Increment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amos, L. A., Henderson, R., and Unwin, P. N. T. (1982). Three-dimensional structure determination by electron microscopy of two-dimensional crystals. Prog. Biophys. Mol. Biol. 39:183–231.Google Scholar
  2. Andrews, H. C. (1970). Computer Techniques in Image Processing. Academic Press, New York.Google Scholar
  3. Bracewell, R. N. and Riddle, A. C. (1967). Inversion of fan-beam scans in radio astronomy. Astrophys. J. 150:427–434.CrossRefGoogle Scholar
  4. Chalcroft, J. P. and Davey, C. L. (1984). A simply constructed extreme-tilt holder for the Philips eucentric goniometer stage. J. Microsc. 134:41–48.CrossRefGoogle Scholar
  5. Colsher, J. G. (1976). Iterative three-dimensional image reconstruction from tomographic projections. Comput. Gr. Image Process 6:513–537.CrossRefGoogle Scholar
  6. Cormack, A. M. (1964). Representation of a function by its line integrals, with some radiological applications. I. J. Appl. Phys. 35:2908–2912.CrossRefGoogle Scholar
  7. Crowther, R. A., Amos, L. A., Finch, J. T., and Klug, A. (1970a). Three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs. Nature (London) 226:421–425.CrossRefGoogle Scholar
  8. Crowther, R. A., DeRosier, D. J., and Klug, A. (1970b). The reconstruction of a three-dimensional structure from its projections and its application to electron microscopy. Proc. R. Soc. LondonA 317:319–340.Google Scholar
  9. DeRosier, D. and Klug, A. (1968). Reconstruction of three-dimensional structures from electron micrographs. Nature (London) 217:130–134.CrossRefGoogle Scholar
  10. Frank, J. (1989). Three-dimensional imaging techniques in electron microscopy. BioTechniques 7:164–1 /3.Google Scholar
  11. Frank, J. and Radermacher, M. (1986). Three-dimensional reconstruction of nonperiodic macro-molecular assemblies from electron micrographs. In: Advanced Techniques in Biological Electron Microscopy. J. Koehler, ed. Springer-Verlag, Berlin, pp. 1–72.CrossRefGoogle Scholar
  12. Frank, J., Goldfarb, W., Eisenberg, D. and Baker, T. S. (1978). Reconstruction of glutamine synthetase using computer averaging. Ultramicroscopy 3:283–290.PubMedCrossRefGoogle Scholar
  13. Gilbert, P. F. C. (1972). Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36:105–117.PubMedCrossRefGoogle Scholar
  14. Hegerl, R. and Altbauer, A. (1982). The “EM” program system. Ultramicroscopy 9:109–116.PubMedCrossRefGoogle Scholar
  15. Henderson, R. and Unwin, P. N. T. (1975). Three-dimensional model of purple membrane obtained by electron microscopy. Nature (London) 257:28–32.CrossRefGoogle Scholar
  16. Herman, G. T., ed. (1979). Image Reconstruction from Projections. Springer-Verlag, Berlin.Google Scholar
  17. Herman, G. T. and Lewitt, R. M. (1979). Overview of image reconstruction from projections, in Image Reconstruction from Projections (G. T. Herman, ed.), pp. 1–7, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  18. Hoppe, W. (1972). Dreidimensional abbildende Elektronenmikroskope. Z. Naturforsch. 27a:919–929.Google Scholar
  19. Hoppe, W. (1981). Three-dimensional electron microscopy. Ann. Rev. Biophys. Bioeng. 10:563–592.CrossRefGoogle Scholar
  20. Hoppe, W. (1983). Elektronenbeugung mit dem Transmissions-Elektronenmikroskop als phasenbestimmendem Diffraktometer-von der Ortsfrequenzfilterung zur dreidimensionalen Strukturanalyse an Ribosomen. Angew. Chem. 95:465–494.CrossRefGoogle Scholar
  21. Hoppe, W., Gassmann, J., Hunsmann, N., Schramm, H. J., and Sturm, M. (1974). Three-dimensional reconstruction of individual negatively stained yeast fatty-acid synthetase molecules from tilt series in the electron microscope. Hoppe-Seyler’s Z. Physiol. Chemm. 355:1483–1487.Google Scholar
  22. Hoppe, W., Langer, R., Knesch, G., and Poppe, Ch. (1968). Protein-Kristallstrukturanalyse mit Elektronenstrahlen. Naturwissenschaften 55:333–336.PubMedCrossRefGoogle Scholar
  23. Klug, A. (1983). From macromolecules to biological assemblies. Angew. Chem. 22:565–582.CrossRefGoogle Scholar
  24. Lewitt, R. M. and Bates, R. H. T. (1978a). Image reconstruction from projections I: General theoretical considerations. Optik (Stuttgart) 50:19–33.Google Scholar
  25. Lewitt, R. M. and Bates, R. H. T. (1978b). Image reconstruction from projections. III: Projection completion methods (theory). Optik (Stuttgart) 50:189–204.Google Scholar
  26. Lewitt, R. M., Bates, R. H. T., and Peters, T. M. (1978). Image reconstruction from projections. II: Modified back-projection methods. Optik (Stuttgart) 50:85–109.Google Scholar
  27. McEwen, B. F. and Frank, J. (1990). Application of tomographic 3D reconstruction to a diverse range of biological preparations, in Proc. XII Int. Congr. Electron Microscopy (L. D. Peachey and D. B. Williams, eds.), Vol. I, pp. 516–517, San Francisco Press, San Francisco.Google Scholar
  28. OE Reports (1990). The development of computerized axial tomography. No. 79 (July 1990), p. 1.Google Scholar
  29. Radermacher, M. (1980). Dreidimensionale Rekonstruktion bei kegelförmiger Kippung im Elektronenmikroskop. Thesis, Technical University, Munich.Google Scholar
  30. Radermacher, M. (1988). Three-dimensional reconstruction of single particles from random and nonrandom tilt series. J. Electron. Microsc. Tech. 9:359–394.PubMedCrossRefGoogle Scholar
  31. Radermacher, M. and Hoppe, W. (1980). Properties of 3D reconstruction from projections by conical tilting compared to single axis tilting, in Proc. 7th European Congr. Electron Microscopy, Den Haag, Vol. I. pp. 132–133.Google Scholar
  32. Radermacher, M., Wagenknecht, T., Verschoor, A., and Frank, J. (1987a). Three-dimensional structure of the laree subunit from Escherichia coli. EMBO J. 6:1107–1114.Google Scholar
  33. Radermacher, M., Wagenknecht, T., Verschoor, A., and Frank, J. (1987b). Three-dimensional reconstruction from a single-exposure random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli. J. Microsc. 146:113–136.CrossRefGoogle Scholar
  34. Radon, J. (1917). ÜÜber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math. Phys. Klasse 69:262–277.Google Scholar
  35. Smith, P. R., Peters, T. M., and Bates, R. H. T. (1973). Image reconstruction from a finite number of projections. J. Phys. A 6:361–382.CrossRefGoogle Scholar
  36. Typke, D., Hoppe, W., Sessler, W., and Burger, M. (1976). Conception of a 3-D imaging electron microscope, in Proc. Sixth European Congr. Electron Microscopy (D. G. Brandon, ed.), Vol. I, pp. 334–335, Tal International, Israel.Google Scholar
  37. Unwin, P. N. T. and Henderson, R. (1975). Molecular structure determination by electron microscopy of unstained crystalline specimens. J. Mol. Biol. 94:425–440.Google Scholar
  38. Vogel, R. H. and Provencher, S. W. (1988). Three-dimensional reconstruction from electron micrographs of disordered snecimens. tUltramicro.scnnv 25:223–240CrossRefGoogle Scholar
  39. Zwick, M. and Zeitler, E. (1973). Image reconstruction from projections. Optik 38:550–565.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Joachim Frank
    • 1
    • 2
  1. 1.Wadsworth Center for Laboratories and ResearchNew York State Department of HealthAlbanyUSA
  2. 2.Department of Biomedical Sciences, School of Public HealthState University of New York at AlbanyAlbanyUSA

Personalised recommendations