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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
Andrews, H. C. (1970). Computer Techniques in Image Processing. Academic Press, New York.
Bracewell, R. N. and Riddle, A. C. (1967). Inversion of fan-beam scans in radio astronomy. Astrophys. J. 150:427–434.
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.
Colsher, J. G. (1976). Iterative three-dimensional image reconstruction from tomographic projections. Comput. Gr. Image Process 6:513–537.
Cormack, A. M. (1964). Representation of a function by its line integrals, with some radiological applications. I. J. Appl. Phys. 35:2908–2912.
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.
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.
DeRosier, D. and Klug, A. (1968). Reconstruction of three-dimensional structures from electron micrographs. Nature (London) 217:130–134.
Frank, J. (1989). Three-dimensional imaging techniques in electron microscopy. BioTechniques 7:164–1 /3.
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.
Frank, J., Goldfarb, W., Eisenberg, D. and Baker, T. S. (1978). Reconstruction of glutamine synthetase using computer averaging. Ultramicroscopy 3:283–290.
Gilbert, P. F. C. (1972). Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36:105–117.
Hegerl, R. and Altbauer, A. (1982). The “EM” program system. Ultramicroscopy 9:109–116.
Henderson, R. and Unwin, P. N. T. (1975). Three-dimensional model of purple membrane obtained by electron microscopy. Nature (London) 257:28–32.
Herman, G. T., ed. (1979). Image Reconstruction from Projections. Springer-Verlag, Berlin.
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.
Hoppe, W. (1972). Dreidimensional abbildende Elektronenmikroskope. Z. Naturforsch. 27a:919–929.
Hoppe, W. (1981). Three-dimensional electron microscopy. Ann. Rev. Biophys. Bioeng. 10:563–592.
Hoppe, W. (1983). Elektronenbeugung mit dem Transmissions-Elektronenmikroskop als phasenbestimmendem Diffraktometer-von der Ortsfrequenzfilterung zur dreidimensionalen Strukturanalyse an Ribosomen. Angew. Chem. 95:465–494.
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.
Hoppe, W., Langer, R., Knesch, G., and Poppe, Ch. (1968). Protein-Kristallstrukturanalyse mit Elektronenstrahlen. Naturwissenschaften 55:333–336.
Klug, A. (1983). From macromolecules to biological assemblies. Angew. Chem. 22:565–582.
Lewitt, R. M. and Bates, R. H. T. (1978a). Image reconstruction from projections I: General theoretical considerations. Optik (Stuttgart) 50:19–33.
Lewitt, R. M. and Bates, R. H. T. (1978b). Image reconstruction from projections. III: Projection completion methods (theory). Optik (Stuttgart) 50:189–204.
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.
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.
OE Reports (1990). The development of computerized axial tomography. No. 79 (July 1990), p. 1.
Radermacher, M. (1980). Dreidimensionale Rekonstruktion bei kegelförmiger Kippung im Elektronenmikroskop. Thesis, Technical University, Munich.
Radermacher, M. (1988). Three-dimensional reconstruction of single particles from random and nonrandom tilt series. J. Electron. Microsc. Tech. 9:359–394.
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.
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.
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.
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.
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.
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.
Unwin, P. N. T. and Henderson, R. (1975). Molecular structure determination by electron microscopy of unstained crystalline specimens. J. Mol. Biol. 94:425–440.
Vogel, R. H. and Provencher, S. W. (1988). Three-dimensional reconstruction from electron micrographs of disordered snecimens. tUltramicro.scnnv 25:223–240
Zwick, M. and Zeitler, E. (1973). Image reconstruction from projections. Optik 38:550–565.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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