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.
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
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.
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.
J. Kessler: Polarized Electrons (Springer, Berlin, Heidelberg, New York 1976).
W. Glaser: Grundlagen der Elektronenoptik (Springer, Wien 1952).
A. Septier: Focusing of Charged Particles (Academic, New York 1967).
P. Grivet: Electron Optics, Part 1: Optics, Part 2: Instruments, 2nd ed., (translated by P.W. Hawkes) (Pergamon, Oxford 1972).
P.W. Hawkes (ed.): Properties of Magnetic Electron Lenses, Topics Appl. Phys., Vol.18 (Springer, Berlin, Heidelberg, New York 1982).
W. Glaser: Strenge Berechnung magnetischer Linsen der Feldform H= H0/[1 + (z/a)2]. Z. Phys. 117, 285 (1941).
J. Dosse: Strenge Berechnung magnetischer Linsen mit unsymmetrischer Feldform nach H=H0/[1 + (z/a)2]. Z. Phys. 117, 316 (1941).
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.
E. Ruska: Über die Auflösungsgrenzen des Durchstrahlungs-Elektronenmikroskops. Optik 22, 319 (1965).
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.
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.
W. Kamminga: Properties of magnetic objective lenses with highly saturated pole pieces. Optik 45, 39 and 46, 226 (1976).
A. Septier: “Superconducting Lenses,” in Electron Microscopy 1972 (The Institute of Physics, London 1972) p.104.
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.
I. Dietrich: “Superconducting Lenses,” in Electron Microscopy 1978, Vol.3, ed. by J.M. Sturgess (Microscopical Soc. Canada, Toronto 1978) p.173.
W.D. Riecke: “Practical Lens Design”, in [Ref.2.7, p.164].
T. Mulvey, C.D. Newman: “Versatile Miniature Electron Lenses,” in Electron Microscopy 1972 (The Institute of Physics, London 1972) p.116.
T. Mulvey, M.J. Wallington: Electron lenses. Rep. Prog. Phys. 36, 347 (1973).
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.
T. Mulvey: “Unconventional Lens Design,” in [Ref.2.7, p.359].
V.E. Cosslett: Probe size and probe current in the scanning transmission electron microscope. Optik 36, 85 (1972).
W. Kunath, W.D. Riecke: Zur Bestimmung der Öffnungsfehlerkoeffizienten magnetischer Objektivlinsen. Optik 23, 322 (1966).
L. Albert: Zur Phasenschiebung starker Elektronenlinsen bei endlicher Vergrößerung. Optik 24, 18 (1966).
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.
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.
C.E. Hall: Method of measuring spherical aberration of an electron microscope objective. J. Appl. Phys. 20, 631 (1949).
K. Heinemann: In-situ measurement of objective lens data of a high resolution electron microscope. Optik 34, 113 (1971).
G. Liebmann: Measured properties of strong “unipotential” electron lenses. Proc. Phys. Soc. B 62, 213 (1949).
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).
S. Leisegang: Zum Astigmatismus von Elektronenlinsen. Optik 10, 5 (1953).
W. Glaser, H. Grümm: Die Kaustikfläche von Elektronenlinsen. Optik 7, 96(1950).
D. Kynaston, T. Mulvey: The correction of distortion in the electron microscope. Br. J. Appl. Phys. 14, 199 (1963).
J. Dosse: Über optische Kenngrößen starker Elektronenlinsen. Z. Phys. 117, 722 (1941).
V.E. Cosslett: Energy loss and chromatic aberration in electron microscopy. Z. Angew. Phys. 27, 138 (1969).
L. Reimer, P. Gentsch: Superposition of chromatic error and beam broadening in TEM of thick carbon and organic specimens. Ultramicroscopy 1, 1 (1975).
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.
S. Katagiri: Experimental investigation of chromatic aberration in the electron microscope. Rev. Sci. Instrum. 26, 870 (1955).
O. Scherzer: Sphärische und chromatische Korrektur von Elektronen-Linsen. Optik 2, 114 (1947).
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).
H. Rose: Über den sphärischen und den chromatischen Fehler unrunder Elektronenlinsen. Optik 25, 587 (1967).
H. Rose: Elektronenoptische Aplanate. Optik 34, 285 (1971).
H. Koops, G. Kuck, O. Scherzer: Erprobung eines elektronenoptischen Achromators. Optik 48, 225 (1977).
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.
O. Rang: Der elektrostatische Stigmator, ein Korrektiv für astigmatische Elektronenlinsen. Optik 5, 518 (1949).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Reimer, L. (1984). Particle Optics of Electrons. In: Transmission Electron Microscopy. Springer Series in Optical Sciences, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13553-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-13553-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-13555-6
Online ISBN: 978-3-662-13553-2
eBook Packages: Springer Book Archive