Skip to main content
SpringerLink
Log in
Book cover

Transmission Electron Microscopy pp 17–43Cite as

Particle Optics of Electrons

  • Chapter

  • 1251 Accesses

Part of the book series: Springer Series in Optical Sciences ((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 spectroscopy 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 chapter.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Kessler: Polarized Electrons, 2nd edn., Springer Ser. Atom, Plasma, Voll (Springer, Berlin, Heidelberg, 1985 )

    Book  Google Scholar 

  2. W. Glaser: Grundlagen der Elektronenoptik ( Springer, Wien 1952 )

    MATH  Google Scholar 

  3. A. Septier: Focusing of Charged Particles ( Academic, New York 1967 )

    Google Scholar 

  4. P. Grivet: Electron Optics, Pt.1: Optics, Pt.2: Instruments, 2nd edn. (translated by P.W. Hawkes) ( Pergamon, Oxford 1972 )

    Google Scholar 

  5. P.W. Hawkes (ed.): Properties of Magnetic Lenses, Topics Appl. Phys., Vol. 18 ( Springer, Berlin, Heidelberg 1982 )

    Google Scholar 

  6. P.W. Hawkes, E. Kasper: Principles of Electron Optics Voll: Basic Geometrical Optics, Vol. 2: Applied Geometrical Optics (Academic, London 1989 )

    Google Scholar 

  7. W. Glaser: Strenge Berechnung magnetischer Linsen der Feldform H = Ho/[1 + (z/a)2]. Z. Physik 117, 285 (1941)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. J. Dosse: Strenge Berechnung magnetischer Linsen mit unsymmetrischer Feldform nach H = Ho/[1+ (z/a) 2]. Z. Physik 117, 316 (1941)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. E. Ruska: Über die Auflösungsgrenzen des Durchstrahlungs-Elektronenmikroskops. Optik 22, 319 (1965)

    Google Scholar 

  10. W.D. Riecke: Objective lens design for TEM. A review of the present state of the art, in Electron Microscopy 1972 ( IoP, London 1972 ) p. 98

    Google Scholar 

  11. W. Kamminga: Properties of magnetic lenses with highly saturated pole pieces. Optik 45, 39; and 46, 226 (1976)

    Google Scholar 

  12. I. Dietrich: Superconducting Electron-Optical Devices ( Plenum, New York 1976 )

    Book  Google Scholar 

  13. P.W Hawkes, U. Valdrè: Superconductivity and electron microscopy. J.Phys. E 10, 309 (1977)

    Article  ADS  Google Scholar 

  14. G. Lefranc, E. Knapek, I. Dietrich: Superconducting lens design. Ultramicroscopy 10, 111 (1982)

    Article  Google Scholar 

  15. W.D. Riecke: Practical lens design, in [2.5] p.164

    Google Scholar 

  16. J.P. Adriaanse: High T, superconductors and magnetic electron lenses, in Advances in Optical and Electron Microscopy, Vol. 14, ed. by T. Mulvey, C.J.R. Sheppard ( Academic, London 1994 ) p. 1

    Google Scholar 

  17. T. Mulvey, M.J. Wallington: Electron lenses. Rep. Prog. Phys. 36, 347 (1973)

    Article  ADS  Google Scholar 

  18. T. Mulvey: Unconventional lens design, in [2.5] p.359

    Google Scholar 

  19. P.A. Sturrock: Perturbation characteristic function and their application to electron optics. Proc. Roy. Soc. (London) A 210, 269 (1952)

    Article  ADS  MathSciNet  Google Scholar 

  20. H. Rose: Hamiltonian magnetic optics. Nucl. Instr. Meth. Phys. Res. A 258, 374 (1987)

    Article  ADS  Google Scholar 

  21. C.E. Hall: Method of measuring spherical aberration of an electron microscope objective. J. Appl. Phys. 20, 631 (1949)

    Article  ADS  Google Scholar 

  22. K. Heinemann: In-situ measurement of objective lens data of a high resolution electron microscope. Optik 34, 113 (1971)

    Google Scholar 

  23. T.F. Budinger, R.M. Glaeser: Measurement of focus and spherical aberration on electron microscope objective lens. Ultramicroscopy 2, 31 (1976)

    Article  Google Scholar 

  24. W. Glaser, H. Grümm: Die Kaustikfläche von Elektronenlinsen. Optik 7, 96 (1950)

    MathSciNet  Google Scholar 

  25. S. Leisegang: Zum Astigmatismus von Elektronenlinsen. Optik 10, 5 (1953)

    Google Scholar 

  26. J. Dosse: Über optische Kenngrö en starker Elektronenlinsen. Z. Phys. 117, 722 (1941)

    Article  ADS  MathSciNet  Google Scholar 

  27. V.E. Cosslett: Energy loss and chromatic aberration in electron microscopy. Z. Angew. Phys. 27, 138 (1969)

    Google Scholar 

  28. L. Reimer, P. Gentsch: Superposition of chromatic error and beam broadening in TEM of thick carbon and organic specimens. Ultramicroscopy 1, 1 (1975)

    Article  Google Scholar 

  29. S. Katagiri: Experimental investigation of chromatic aberration in the electron microscope. Rev. Sci. Instr. 26, 870 (1955)

    Article  ADS  Google Scholar 

  30. O. Rang: Der elektronenoptische Stigmator, ein Korrektiv für astigmatische Elektronenlinsen. Optik 5, 518 (1949)

    Google Scholar 

  31. O. Scherzer: Sphärische und chromatische Korrektur von Elektronenlinsen. Optik 2, 114 (1947)

    Google Scholar 

  32. 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)

    MATH  Google Scholar 

  33. H. Rose: Über den sphärischen und den chromatischen Fehler unrunder Elektronenlinsen. Optik 25, 587 (1967)

    Google Scholar 

  34. H. Rose: Elektronenoptische Aplanate. Optik 34, 285 (1971)

    Google Scholar 

  35. H. Koops, G. Kuck, O. Scherzer: Erprobung eines elektrostatischen Achromators. Optik 48, 225 (1977)

    Google Scholar 

  36. H. Rose: Outline of a spherically corrected semiaplanatic medium-voltage TEM. Optik 85, 19 (1990)

    Google Scholar 

  37. M. Haider, G. Braunshausen, E. Schwan: State of development of a C S corrected high resolution 200 kV TEM, in [Ref.1.61, Vol.1, p.195]

    Google Scholar 

  38. F. Zemlin, K. Weiss, P. Schiske, W. Kunath, K.H. Hermann: Coma-free alignment of high resolution electron microscopes with the aid of optical diffractograms. Ultramicroscopy 3, 49 (1978)

    Article  Google Scholar 

  39. F. Zemlin: A practical procedure for alignment of a high resolution electron microscope. Ultramicroscopy 4, 241 (1979)

    Article  Google Scholar 

  40. K. Ishizuka: Coma-free alignment of a high resolution electron microscope with three-fold astigmatism.. Ultramicroscopy 55, 407 (1978)

    Article  Google Scholar 

  41. D.J. Smith, W.A. Saxton, M.A. O’Keefe, G.J. Wood, W.M. Stobbs: The importance of beam alignment and crystal tilt in high resolution electron microscopy. Ultramicroscopy 11, 263 (1983)

    Article  Google Scholar 

  42. W.A. Saxton, D.J. Smith, S.J. Erasmus: Procedures for focusing, stigmating and alignment in high resolution electron microscopy. J. Microsc. 130, 187 (1983)

    Article  Google Scholar 

  43. A,J. Koster, A. van den Bos, K.D. van der Mast: An autofocus method for a TEM. Ultramicroscopy 21, 209 (1987)

    Article  Google Scholar 

  44. A.J. Koster, W.J. de Rijter, A. van den Bos, K.D. van der Mast: Autotuning of a TEM using minimum electron dose. Ultramicroscopy 27, 251 (1989)

    Article  Google Scholar 

  45. A.J. Koster, W.J. de Ruijter: Practical autoalignment of transmission electron microscopes. Ultramicroscopy 40, 89 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 10, D-48149, Münster, Germany

    Professor Dr. Ludwig Reimer

Authors
  1. Professor Dr. Ludwig Reimer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Reimer, L. (1997). Particle Optics of Electrons. In: Transmission Electron Microscopy. Springer Series in Optical Sciences, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-14824-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-14824-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-14826-6

  • Online ISBN: 978-3-662-14824-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation