Abstract
The three-dimensional reconstruction of individual molecules from a set of electron micrographs is comparable to the “reconstruction” of structures in X-ray crystallography. Basically the electron microscope is equivalent to a diffractometer, since the specimen is illuminated by a parallel primary beam with a well-defined wavelength and orientation. The Fourier inversion of an electron micrograph delivers the distorted structure factors in a well-defined plane or weakly curved surface of the three-dimensional reciprocal space. Extraction of the undistorted structure factors and reconstruction is possible if a sufficient number of micrographs with different orientations of the object is available. Structure factors within a certain resolution in reciprocal space must be known to give a well defined reconstruction. Unlike X-ray crystallography, no “phase problem” exists since the phases of the structure factors can be deduced from the micrographs.
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References
References
W. Hoppe, D. Typke: “Three-Dimensional Reconstruction of Aperiodic Objects in Electron Microscopy”, in Advances in Structure Research by Diffraction Method, Vol.7, ed. by W. Hoppe, R. Mason (Pergamon Press, Oxford, and Vieweg, Braunschweig 1978 ) pp. 137–190
W. Hoppe, P. Bussler, A. Feltynowski, N. Hunsmann, A. Hirt: “Some Experience with Computerized Image Reconstruction Methods”, in Image Processing and Computer-Aided Design in Electron Optics, ed. by P.W. Hawkes ( Academic Press, London 1973 ) pp. 91–126
R. Hegerl, W. Hoppe: Z. Naturforsch. 31a, 1717–1721 (1976)
A. Jones: J. Appi. Cryst. 11, 268 (1978)
W. Hoppe: Acta Cryst. k26, 414–426 (1970)
W. Hoppe: Naturwiss. 61, 239–249 (1974)
J. Kieffer: Radiology 33, 560–585 (1939)
P. Edholm: The tomogram. Its formation and content. Acta Radiol., Suppl 193 (1960)
R.N. Bracewel1, A.C. Riddle: Astrophys. J. 150, 427–434 (1967)
D.W. Sweeney, C.M. Vest: Appi. Opt. 11, 205–207 (1972)
R.G. Hart: Science 159, 1464–1467 (1968)
D.J. DeRosier, A. Klug: Nature (London) 217, 130–134 (1968)
W. Hoppe, R. Langer, G. Knesch, Ch. Poppe: Naturwiss. 55, 333–336 (1968)
J.G. Colsher: Comput. Graphics Image Process. 6, 513–537 (1977)
J.G. Colsher: Thesis, University of California (1976)
R.A. Crowther, A. Klug: Ann. Rev. Biochem. 44, 161–182 (1975)
W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1090–1100 (1970); Phil. Trans. Roy. Soc. London 261, 71–94 (1971)
J. Frank, P. Bussler, R. Langer, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1105–1115 (1970)
R. Langer, J. Frank, A. Feltynowski, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1120–1126 (1970)
W. Hoppe: Manchester (1972) pp.612–617
W. Hoppe: Naturwiss. 48, 736–737 (1961)
W. Hoppe: Optik 20, 599–606 (1963)
G. Möllenstedt, R. Speidel, W. Hoppe, R. Langer, K.-H. Katerbau, F. Thon: Rome (1968) Vol. 1, pp. 125–126
W. Hoppe, H. Wenzl, H.J. Schramm: Jerusalem (1976) Vol. 2, pp. 58–60
W. Hoppe, H. Wenzl, H.J. Schramm: Hoppe-Seyler’s Z. Physiol. Chem. 358, 1069–1076 (1977)
D.F. Parsons: Science 186, 407–414 (1974)
R.M. Glaeser: J. Ultrastruct. Res. 36, 466–482 (1971)
R. Henderson, P.N.T. Unwin: Nature (London) 257, 28–32 (1975)
W. Hoppe, J. Gassmann, N. Hunsmann, H.J. Schramm, M. Sturm: Hoppe-Seyler’s Z. Physiol. Chem. 355, 1483–1487 (1974)
W. Hoppe, H.J. Schramm, M. Sturm, 31a, 1370–1379 (1976)
W. Hoppe, H.J. Schramm, M. Sturm, 31a, 645–655 (1976)
W. Hoppe, H.J. Schramm, M. Sturm, N. Hunsmann, J. Gassmann: Z. Naturforsch. 31a, 1380–1390 (1976)
W. Hoppe, B. Grill: U1tramicroscopy 2, 153–168 (1977)
J. Frank: Jerusalem (1976) Vol. 1, pp. 273–274
J. Frank: U1tramicroscopy 1, 159–162 (1975)
J. Frank: “Optical Use of Image Information Using Signal Detection and Averaging Techniques”, in Short Wavelength Microscopy, Ann. N.Y. Acad. Sei. 306, 112–120 (1978)
W. Hoppe: Z. Naturforsch. 30a, 1188–1199 (1975)
W. Hoppe: “Trace Structure Analysis”, in Short Wavelength Microscopy, Ann. N.Y. Acad. Sei. 306, 121–144 (1978)
O Scherzer: Optik 501–516 (1971)
H. Rose: Optik 1–24 (1971); Optik 34, 285–311 (1971)
E. Plies, W. Hoppe: Optik 46, 75–92 (1976)
W. Hoppe, R. Guckenberger: Z. Naturforsch. 29a, 1931–1932 (1974)
W. Hoppe: Naturwiss. 61, 534–536 (1974)
P. Schiske: Rome (1968) Vol. 1, pp. 145–146
W. Hoppe, R. Langer, F. Thon: Optik 30, 538–545 (1970)
W. Hoppe: Z. Naturforsch. 26a, 1155–1168 (1971)
W. Hoppe: Optik 29, 617–621 (1969)
C. E. Shannon, W. Weaver: The Mathematical Theory of Communication (University of Illinois Press 1975 )
J.L. Harris: J. Opt. Soc. Am. 54, 931–936 (1964)
R.A. Crowther, D.J. DeRosier, A. Klug: Proc. Roy. Soc. Lond. (1970)
V. Knauer: Diplomarbeit, TU München (1976)
W. Hoppe: Z. Naturforsch. 27a, 919–929 (1972)
D. Typke, W. Hoppe, W. Sessler, M. Burger: Jerusalem (1976) Vol.1
W. Hoppe, N. Hunsmann, H.J. Schramm, M. Sturm, B. Grill, J. Gassmann: Jerusalem (1976) Vol. 1, pp.8–13
M. Radermacher, W. Hoppe: Toronto (1978) Vol.1, pp.218–219
R.A. Crowther, L.A. Amos, A. Klug: Manchester (1972) pp. 593–597
A.M. Cormack: J. Appl. Phys. 35, 2908–2913 (1964)
P.R. Smith, T.M. Peters, R.H.T. Bates: J. Phys. Äff, 361–382 (1973)
E. Zeitler: Optik 39, 396–415 (1974)
A. Klug, R.A. Crowther: Nature 235, 435–440 (1972)
N. Hunsmann: Thesis, TU München (1975)
R. Gordon, R. Bender, G.T. Herman: J. Theor. Biol. 29, 471–481 (1970)
P.F.C. Gilbert: J. Theor. Biol. 36, 105–117 (1972)
R.A. Crowther, A. Klug: Nature 251, 490–492 (1974)
M. Goitein: Nucl. Instrum. Methods 101, 509–518 (1971)
W. Hoppe, R. Huber, J. Gassmann: Acta Cryst. 16, A4 (1963)
W. Hoppe, J. Gassmann: Acta Cryst. B24, 97–107 (1968)
W. Hoppe, J. Gassmann, K. Zechmeister: “Some Automatic Procedures for the Solution of Crystal Structures with Direct Methods and Phase Correction”, Cvystallogvaphic Computing IX, ed. by F.R. Ahmed ( Munksgaard, Copenhagen 1970 ) pp. 26–36
J. Gassmann: “Improvement and Extension of Approximate Phase Sets in Struc ture Determination”, in Crystallographies Computing II, ed. by F.R. Ahmed ( Munksgaard, Copenhagen 1976 ) pp. 144–154
E. Zeitler, M.G.R. Thomson: Optik 31, 258–280 (1970)
O Scherzer: Ber. Bunsenges. Phys. Chem. 74, 1154–1167 (1970)
W. Hoppe: Acta Cryst. k25, 508–514 (1969)
W. Hoppe: Acta Cryst. A25, 495–501 (1969)
R. Hegerl, W. Hoppe: Ber. Bunsenges. Phys. Chem. 74, 1148–1154 (1970)
H. Rose: Optik 416–436 (1974)
L.H. Veneklasen: Optik 44, 447–468 (1975)
D. Gabor: Nature 161, 777–778 (1948)
Additonal References
W. Hoppe, J. Gassmann: “Comments on the 3-D reconstruction of periodic structures”, in Electronic Microscopy in Molecular Dimensions. State of the Art and Strategies for the Future, ed. by W. Baumeister (Springer, Berlin, Heidelberg, New York 1980 ) In preparation
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Hoppe, W., Hegerl, R. (1980). Three-Dimensional Structure Determination by Electron Microscopy (Nonperiodic Specimens). In: Hawkes, P.W. (eds) Computer Processing of Electron Microscope Images. Topics in Current Physics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81381-8_4
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DOI: https://doi.org/10.1007/978-3-642-81381-8_4
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