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Introduction: Principles of Electron Tomography

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Book cover Electron Tomography

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.

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References

  • 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 

  • Andrews, H. C. (1970). Computer Techniques in Image Processing. Academic Press, New York.

    Google Scholar 

  • Bracewell, R. N. and Riddle, A. C. (1967). Inversion of fan-beam scans in radio astronomy. Astrophys. J. 150:427–434.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Colsher, J. G. (1976). Iterative three-dimensional image reconstruction from tomographic projections. Comput. Gr. Image Process 6:513–537.

    Article  Google Scholar 

  • Cormack, A. M. (1964). Representation of a function by its line integrals, with some radiological applications. I. J. Appl. Phys. 35:2908–2912.

    Article  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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 

  • DeRosier, D. and Klug, A. (1968). Reconstruction of three-dimensional structures from electron micrographs. Nature (London) 217:130–134.

    Article  Google Scholar 

  • Frank, J. (1989). Three-dimensional imaging techniques in electron microscopy. BioTechniques 7:164–1 /3.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Frank, J., Goldfarb, W., Eisenberg, D. and Baker, T. S. (1978). Reconstruction of glutamine synthetase using computer averaging. Ultramicroscopy 3:283–290.

    Article  PubMed  CAS  Google Scholar 

  • Gilbert, P. F. C. (1972). Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36:105–117.

    Article  PubMed  CAS  Google Scholar 

  • Hegerl, R. and Altbauer, A. (1982). The “EM” program system. Ultramicroscopy 9:109–116.

    Article  PubMed  CAS  Google Scholar 

  • Henderson, R. and Unwin, P. N. T. (1975). Three-dimensional model of purple membrane obtained by electron microscopy. Nature (London) 257:28–32.

    Article  CAS  Google Scholar 

  • Herman, G. T., ed. (1979). Image Reconstruction from Projections. Springer-Verlag, Berlin.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Hoppe, W. (1972). Dreidimensional abbildende Elektronenmikroskope. Z. Naturforsch. 27a:919–929.

    Google Scholar 

  • Hoppe, W. (1981). Three-dimensional electron microscopy. Ann. Rev. Biophys. Bioeng. 10:563–592.

    Article  CAS  Google Scholar 

  • Hoppe, W. (1983). Elektronenbeugung mit dem Transmissions-Elektronenmikroskop als phasenbestimmendem Diffraktometer-von der Ortsfrequenzfilterung zur dreidimensionalen Strukturanalyse an Ribosomen. Angew. Chem. 95:465–494.

    Article  CAS  Google Scholar 

  • 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.

    CAS  Google Scholar 

  • Hoppe, W., Langer, R., Knesch, G., and Poppe, Ch. (1968). Protein-Kristallstrukturanalyse mit Elektronenstrahlen. Naturwissenschaften 55:333–336.

    Article  PubMed  CAS  Google Scholar 

  • Klug, A. (1983). From macromolecules to biological assemblies. Angew. Chem. 22:565–582.

    Article  Google Scholar 

  • Lewitt, R. M. and Bates, R. H. T. (1978a). Image reconstruction from projections I: General theoretical considerations. Optik (Stuttgart) 50:19–33.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • OE Reports (1990). The development of computerized axial tomography. No. 79 (July 1990), p. 1.

    Google Scholar 

  • Radermacher, M. (1980). Dreidimensionale Rekonstruktion bei kegelförmiger Kippung im Elektronenmikroskop. Thesis, Technical University, Munich.

    Google Scholar 

  • Radermacher, M. (1988). Three-dimensional reconstruction of single particles from random and nonrandom tilt series. J. Electron. Microsc. Tech. 9:359–394.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  CAS  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Unwin, P. N. T. and Henderson, R. (1975). Molecular structure determination by electron microscopy of unstained crystalline specimens. J. Mol. Biol. 94:425–440.

    CAS  Google Scholar 

  • Vogel, R. H. and Provencher, S. W. (1988). Three-dimensional reconstruction from electron micrographs of disordered snecimens. tUltramicro.scnnv 25:223–240

    Article  CAS  Google Scholar 

  • Zwick, M. and Zeitler, E. (1973). Image reconstruction from projections. Optik 38:550–565.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Wadsworth Center for Laboratories and Research, New York State Department of Health, Albany, New York, 12201-0509, USA

    Joachim Frank

  2. Department of Biomedical Sciences, School of Public Health, State University of New York at Albany, Albany, New York, 12222, USA

    Joachim Frank

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  1. Joachim Frank
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Editors and Affiliations

  1. Wadsworth Center for Laboratories and Research, New York State Department of Health, Albany, New York, USA

    Joachim Frank

  2. Department of Biomedical Sciences, School of Public Health, State University of New York at Albany, Albany, New York, USA

    Joachim Frank

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© 1992 Springer Science+Business Media New York

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Frank, J. (1992). Introduction: Principles of Electron Tomography. In: Frank, J. (eds) Electron Tomography. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2163-8_1

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  • DOI: https://doi.org/10.1007/978-1-4757-2163-8_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-2165-2

  • Online ISBN: 978-1-4757-2163-8

  • eBook Packages: Springer Book Archive

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