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 the single-axis tilt geometry: for instance, in medical computerized axial tomography (CAT-scan imaging), the detector-source arrangement is tilted relative to the patient around a single axis (Fig. 1a). In electron microscopy, where the beam direction is fixed, the specimen holder is tilted around a single axis (Fig. 1b). However, the usage of this term has recently become more liberal, encompassing arbitrary geometries, provided that the specimen is actively tilted into multiple angles. 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 that is tilted in multiple directions and uses these projections to reconstruct the object in its entirety. Excluded from this definition are ‘single-particle’ techniques that make use of multiple occurrences of the object in different orientations, with or without the additional aid of symmetry (Fig. 1c). These techniques are covered elsewhere (non-symmetric: Frank, 1996, 2006; symmetric: Glaeser et al., 2007).
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References
Amos, L.A., Henderson, R. and Unwin, P. N. T. (1982). Three-dimensional structure determination by electron microscopy of 2-dimensional crystals. Prog. Biophys. Mol. Biol. 39: 183–231.
Andrews, H. C. (1970). Computer Techniques in Image Processing. Academic Press, New York.
Barnard, D. P., Turner, J.N., Frank, J. and McEwen, B.F. (1992). A 360° single-axis tilt stage for the high-voltage electron microscope. J. Microsc. 167:39–48.
Bracewell, R. N. (1999). The Fourier Transform and Its Applications, 3rd edn. McGraw-Hill, New York.
Bracewell, R. N. and Riddle, A. C. (1967). Inversion of fan-beam scans in radio astronomy. Astrophys. Soc. 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. (1977). Iterative three-dimensional image reconstruction from tomographic projections. Comput. Graphics 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 226: 421–425.
Crowther, R. A., DeRosier, D. J. and Klug, A. (1970b). The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. Proc. R. Soc. B 317:319–340.
DeRosier, D. and Klug, A. (1968). Reconstruction of 3-dimensional structures from electron micrographs. Nature 217:130–134.
Frank, J. (1975). Averaging of low exposure electron micrographs of nonperiodic objects. Ultramicroscopy 1:159–162.
Frank, J. (1992). Introduction. In Electron Tomography (J. Frank, ed.) pp. 1–13. Plenum, New York.
Frank, J. (1996). Three-dimensional Electron Microscopy of Macromolecules. Academic Press, San Diego.
Frank, J. (2006). Three-dimensional Electron Microscopy of Macromolecules, 2nd edn. Oxford University Press, New York.
Frank, J. and Radermacher, M. (1986). Three-dimensional reconstruction of nonperiodic macromolecular assemblies from electron micrographs. In Advanced Techniques in Electron Microscopy III (J. K. Koehler, ed.). Springer-Verlag, New York, pp. 1–72.
Gilbert, P. F. C. (1972). The reconstruction of a three-dimensional structure from projections and its application to electron microscopy. II. Direct methods. Proc. R. Soc. B 182:89–117.
Glaeser, R. M., Downing, K. H., Chiu, W., Frank, J. and DeRosier, D. (2007). Electron Crystallography of Biological Macromolecules. Oxford University Press, New York.
Hegerl, R. and Altbauer, A. (1982). The ‘EM’ program system. Ultramicroscopy 9:109–116.
Herman, G.T. (ed.) (1979). Image Reconstruction from Projections. Springer-Verlag, Berlin.
Henderson, R. and Unwin, P. N. T. (1975). Three-dimensional model of purple membrane obtained by electron microscopy. Nature 257:28–32.
Herman, G. T. and Lewitt, R. M. (1979). Overview of image reconstruction from projections, in Image Reconstruction from Projections (G.T. Herman, ed.). Springer-Verlag, Berlin, pp. 1–7.
Hoppe, W. (1972). Drei-dimensional abbildende Elektronenmikroskope. Z. Naturforsch. 27a: 919–929.
Hoppe, W. (1981). Three-dimensional electron microscopy. Annu. 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 fatty-acid synthetase molecules from tilt series in the electron microscope. Hoppe-Seyler’s Z. Physiol. Chem. 355:1483–1487.
Klug, A. (1983). From macromolecules to biological assemblies (Nobel lecture). Angew. Chem. 22:565–636.
Koster, A. J., Chen, J.W., Sedat, J.W. and Agard, D. A. (1992). Automated microscopy for electron tomography. Ultramicroscopy 46:207–227.
Lanzavecchia, S., Cantele, F., Bellon, P. L., Zampighi, L., Kreman, M., Wright, E., and Zampighi, G. A. (2005). Conical tomography of freeze-fracture replicas: a method for the study of integral membrane proteins inserted in phospholipids bilayers. J. Struct. Biol. 149:87–98.
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.
Radermacher, M. and Hoppe, W. (1980). Properties of 3D reconstruction from projections by conical tilting compared to single axis tilting. In Proceedings of the 7th European Congress on Electron Microscopy, Den Haag, Vol. I, pp. 132–133.
Radermacher, M., Wagenknechet, T., Verschoor, A. and Frank, J. (1987a). Three-dimensional structure of the large ribosomal subunit from Escherichia coli. EMBO J. 6:1107–1114.
Radermacher, M., Wagenknecht, T., Verschoor, A. and Frank, J. (1987b). Three-dimensional reconstruction from single-exposure random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli. J. Microsc. 146:113–136.
Radon, J. (1917). Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math. Phys. Klasse 69:262–277.
Saxton, W. O. and Frank, J. (1977). Motif detection in quantum noise-limited electron micrographs by cross-correlation. Ultramicroscopy 2:219–227.
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.
Turner, J. N. (1981). Stages and stereo pair recording. Methods Cell Biol. 23:33–51.
Typke, D., Hoppe, W., Sessier, W. and Burger, M. (1976). Conception of a 3-D imaging electron microscopy. In Proceedings of the 6th European Congress on Electron Microscopy (D. G. Brandon, ed.), Vol. 1, Tal International, Israel, pp. 334–335.
Unwin, P. N. T. and Henderson, R. (1975). Molecular structure determination by electron microscopy of unstained crystalline specimens. J. Mol. Biol. 94:425–440.
Zampighi, G., Zampighi, L., Fain., N., Wright, E. M., Cantele, F. and Lanzavecchia, S. (2005). Conical tomography II: a method for the study of cellular organelles in thin sections. J. Struct. Biol. 151:263–274.
Zwick, M. and Zeitler, E. (1973). Image reconstruction from projections. Optik 38:550–565.
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Frank, J. (2007). Introduction: Principles of Electron Tomography. In: Frank, J. (eds) Electron Tomography. Springer, New York, NY. https://doi.org/10.1007/978-0-387-69008-7_1
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