Scherzer Theorem
- Practical Electron Microscopy and Database -
- An Online Book -  


This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.



Immediately after an electron microscopy was invented by Knoll and Ruska, Scherzer [1] highlighted the poor properties (especially aberrations) of electron lenses and demonstrated that these imperfections are:

      i) Unavoidable for rotationally symmetric round lenses,
      ii) Free of charge on the electron-optical axis,
      iii) Time-independent fields,
      iv) Producing a real image of the object.

Because of those simultaneous factors the electron optical systems always suffer from spherical aberration and chromatic aberration. This is known as the “Scherzer theorem.” Spherical and chromatic aberrations can in principle be corrected if at least one of the four conditions has been broken, while in the most successful practices the corrections have been obtained by breaking rotational symmetry. On the other hand, time-varying fields [related to iii) mentioned above] have been applied to correct the chromatic aberration in charged particle accelerators even though it has not been applied in EMs yet.

Note that in practice to correct the spherical aberrations (Cs) one way is to break the symmetry. This has been established by using electromagnetic multipole lenses such as 2 (dipole), 4 (quadrupole), 6 (sextupole), 8 (octupole) poles, and so on, alternating North and South around the optic axis.


[1] Scherzer, O. (1936) Über einige Fehler von Elektronenlinsen, Zeitschrift Physik, 101, 593.



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