Advertisement

Particle Optics of Electrons

  • Ludwig Reimer
Chapter
  • 458 Downloads
Part of the Springer Series in Optical Sciences book series (SSOS, volume 36)

Abstract

The acceleration of electrons in the electrostatic field between cathode and anode, the action of magnetic fields with axial symmetry as electron lenses and the application of transverse magnetic and electrostatic fields for electron-beam deflection and electron spectrometry can be analysed by applying the laws of relativistic mechanics and hence calculating electron trajectories. Lens aberrations can likewise be introduced and evaluated by this kind of particle optics. In the case of spherical aberration, however, it will also be necessary to express this error in terms of a phase shift, known as the wave aberration, by using the wave-optical model introduced in the next section.

Keywords

Electron Lens Spherical Aberration Chromatic Aberration Principal Plane Homogeneous Magnetic Field 
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. 2.1
    W. Raith: “Untersuchungen zur Spin-Polarisation von Elektronenstrahlen,” in Electron Microscopy 1962, 5th Intern. Congr. Electron Microscopy, Vol.1, ed. by S.S. Breese (Academic, New York 1962) p.AA–6.Google Scholar
  2. 2.2
    K. Tradowsky: “Messungen an polarisierten Elektronenstrahlen mit Elektron-Elektron-(Möller)-Streuung,” in Electron Microscopy 1962, 5th Intern. Congr. Electron Microscopy, Vol.1, ed. by S.S. Breese (Academic, New York 1962) p.AA–5.Google Scholar
  3. 2.3
    J. Kessler: Polarized Electrons (Springer, Berlin, Heidelberg, New York 1976).CrossRefGoogle Scholar
  4. 2.4
    W. Glaser: Grundlagen der Elektronenoptik (Springer, Wien 1952).zbMATHGoogle Scholar
  5. 2.5
    A. Septier: Focusing of Charged Particles (Academic, New York 1967).Google Scholar
  6. 2.6
    P. Grivet: Electron Optics, Part 1: Optics, Part 2: Instruments, 2nd ed., (translated by P.W. Hawkes) (Pergamon, Oxford 1972).Google Scholar
  7. 2.7
    P.W. Hawkes (ed.): Properties of Magnetic Electron Lenses, Topics Appl. Phys., Vol.18 (Springer, Berlin, Heidelberg, New York 1982).Google Scholar
  8. 2.8
    W. Glaser: Strenge Berechnung magnetischer Linsen der Feldform H= H0/[1 + (z/a)2]. Z. Phys. 117, 285 (1941).MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 2.9
    J. Dosse: Strenge Berechnung magnetischer Linsen mit unsymmetrischer Feldform nach H=H0/[1 + (z/a)2]. Z. Phys. 117, 316 (1941).MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 2.10
    W.D. Riecke: “Ein Kondensorsystem für eine starke Objektivlinse,” in Electron Microscopy 1962, 5th Intern. Congr. Electron Microscopy, Vol.1, ed. by S.S. Breese (Academic, New York 1962) p.KK–5.Google Scholar
  11. 2.11
    E. Ruska: Über die Auflösungsgrenzen des Durchstrahlungs-Elektronenmikroskops. Optik 22, 319 (1965).Google Scholar
  12. 2.12
    S. Suzuki, K. Akashi, H. Tochigi: “Objective Lens Properties of Very High Excitation,” in 26th Annual Meeting of EMSA (Claitor’s Publ. Div., Baton Rouge, LO 1968) p.320.Google Scholar
  13. 2.13
    W.D. Riecke: “Objective Lens Design for TEM. A Review of the Present State of the Art,” in Electron Microscopy 1972 (The Institute of Physics, London 1972) p.98.Google Scholar
  14. 2.14
    W. Kamminga: Properties of magnetic objective lenses with highly saturated pole pieces. Optik 45, 39 and 46, 226 (1976).Google Scholar
  15. 2.15
    A. Septier: “Superconducting Lenses,” in Electron Microscopy 1972 (The Institute of Physics, London 1972) p.104.Google Scholar
  16. 2.16
    P. Bonjour: “Superconducting Lenses: Present Trends and Design,” in Electron Microscopy 1976, Vol.1, ed. by D.G. Brandon (Tal International, Jerusalem 1976) p.73.Google Scholar
  17. 2.17
    I. Dietrich: “Superconducting Lenses,” in Electron Microscopy 1978, Vol.3, ed. by J.M. Sturgess (Microscopical Soc. Canada, Toronto 1978) p.173.Google Scholar
  18. 2.18
    W.D. Riecke: “Practical Lens Design”, in [Ref.2.7, p.164].Google Scholar
  19. 2.19
    T. Mulvey, C.D. Newman: “Versatile Miniature Electron Lenses,” in Electron Microscopy 1972 (The Institute of Physics, London 1972) p.116.Google Scholar
  20. 2.20
    T. Mulvey, M.J. Wallington: Electron lenses. Rep. Prog. Phys. 36, 347 (1973).ADSCrossRefGoogle Scholar
  21. 2.21
    T. Mulvey: “Imaging System for Conventional Electron Microscopes,” in Electron Microscopy 1974, Vol.1, ed. by J.V. Sanders, D.J. Goodchild (Australian Acad. Sci., Canberra 1974) p.16.Google Scholar
  22. 2.22
    T. Mulvey: “Unconventional Lens Design,” in [Ref.2.7, p.359].Google Scholar
  23. 2.23
    V.E. Cosslett: Probe size and probe current in the scanning transmission electron microscope. Optik 36, 85 (1972).Google Scholar
  24. 2.24
    W. Kunath, W.D. Riecke: Zur Bestimmung der Öffnungsfehlerkoeffizienten magnetischer Objektivlinsen. Optik 23, 322 (1966).Google Scholar
  25. 2.25
    L. Albert: Zur Phasenschiebung starker Elektronenlinsen bei endlicher Vergrößerung. Optik 24, 18 (1966).Google Scholar
  26. 2.26
    W. Kunath, W.D. Riecke, E. Ruska: “Spherical Aberration of Saturated Strong Objective Lenses,” in Electron Microscopy 1966, Vol.1, ed. by R. Uyeda (Maruzen, Tokyo 1966) p.139.Google Scholar
  27. 2.27
    T. Yanaka, M. Watanabe: “Aberration Coefficients of Extremely Asymmetrical Objective Lenses,” in Electron Microscopy 1966, Vol.1, ed. by R. Uyeda (Maruzen, Tokyo 1966) p.141.Google Scholar
  28. 2.28
    C.E. Hall: Method of measuring spherical aberration of an electron microscope objective. J. Appl. Phys. 20, 631 (1949).ADSCrossRefGoogle Scholar
  29. 2.29
    K. Heinemann: In-situ measurement of objective lens data of a high resolution electron microscope. Optik 34, 113 (1971).Google Scholar
  30. 2.30
    G. Liebmann: Measured properties of strong “unipotential” electron lenses. Proc. Phys. Soc. B 62, 213 (1949).ADSCrossRefGoogle Scholar
  31. 2.31
    K.J. Hanszen: Vergleichende Betrachtungen liber den Öffnungsfehler symmetrischer und asymmetrischer Elektronen-Einzel linsen auf Grund von Vermessungen der Austrittsstrahltangenten. Z. Naturforsch. A13, 409 (1958).ADSGoogle Scholar
  32. 2.32
    S. Leisegang: Zum Astigmatismus von Elektronenlinsen. Optik 10, 5 (1953).Google Scholar
  33. 2.33
    W. Glaser, H. Grümm: Die Kaustikfläche von Elektronenlinsen. Optik 7, 96(1950).MathSciNetGoogle Scholar
  34. 2.34
    D. Kynaston, T. Mulvey: The correction of distortion in the electron microscope. Br. J. Appl. Phys. 14, 199 (1963).ADSCrossRefGoogle Scholar
  35. 2.35
    J. Dosse: Über optische Kenngrößen starker Elektronenlinsen. Z. Phys. 117, 722 (1941).MathSciNetADSCrossRefGoogle Scholar
  36. 2.36
    V.E. Cosslett: Energy loss and chromatic aberration in electron microscopy. Z. Angew. Phys. 27, 138 (1969).Google Scholar
  37. 2.37
    L. Reimer, P. Gentsch: Superposition of chromatic error and beam broadening in TEM of thick carbon and organic specimens. Ultramicroscopy 1, 1 (1975).CrossRefGoogle Scholar
  38. 2.38
    M. Fotino: “Evaluation of Factors Affecting the Resolution in Thick Biological Specimens in High-Voltage TEM,” in Electron Microscopy 1976, Vol.1, ed. by D.G. Brandon (Tal International, Jerusalem 1976) p.277.Google Scholar
  39. 2.39
    S. Katagiri: Experimental investigation of chromatic aberration in the electron microscope. Rev. Sci. Instrum. 26, 870 (1955).ADSCrossRefGoogle Scholar
  40. 2.40
    O. Scherzer: Sphärische und chromatische Korrektur von Elektronen-Linsen. Optik 2, 114 (1947).Google Scholar
  41. 2.41
    A. Septier: Lentille quadrupolaire magnéto-électrique corrigée de l’aberration chromatique. Aberration d’ouverture de ce type de lentilles. C.R. Acad. Sci. Paris 256, 2325 (1963).zbMATHGoogle Scholar
  42. 2.42
    H. Rose: Über den sphärischen und den chromatischen Fehler unrunder Elektronenlinsen. Optik 25, 587 (1967).Google Scholar
  43. 2.43
    H. Rose: Elektronenoptische Aplanate. Optik 34, 285 (1971).Google Scholar
  44. 2.44
    H. Koops, G. Kuck, O. Scherzer: Erprobung eines elektronenoptischen Achromators. Optik 48, 225 (1977).Google Scholar
  45. 2.45
    H. Koops: “Aberration Correction in Electron Microscopy,” in Electron Microscopy 1978, Vol.3, ed. by J.M. Sturgess (Microscopical Soc. Canada, Toronto 1978) p.185.Google Scholar
  46. 2.46
    O. Rang: Der elektrostatische Stigmator, ein Korrektiv für astigmatische Elektronenlinsen. Optik 5, 518 (1949).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Ludwig Reimer
    • 1
  1. 1.Physikalisches InstitutWestfälische Wilhelms-Universität MünsterMünsterFed. Rep. of Germany

Personalised recommendations