Scherzer theorem

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The Scherzer theorem is a theorem from the field of electron microscopy . It says that the resolution of electronic lenses is limited. The reason for this are unavoidable imaging errors (so-called aberrations).

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In 1936, the German physicist Otto Scherzer showed that the electromagnetic fields that are used to focus the electron beam in electron microscopy result in unavoidable imaging errors . These aberrations are both spherical and chromatic, that is, the spherical aberration coefficient C s and the chromatic aberration coefficient C c are always positive.

Scherzer solved the system of Laplace equations for electromagnetic potentials under the following conditions:

  1. The electromagnetic fields are rotationally symmetrical .
  2. The electromagnetic fields are static.
  3. There are no space charges.

The aberrations that arise in such a lens system worsen the resolution of an electron microscope by fifty to one hundred times the wavelength of the electron. The aberrations cannot be corrected with a combination of rotationally symmetrical lenses.

In his work, Otto Scherzer summarized his findings as follows:

“Chromatic and spherical aberration are unavoidable defects in the space-charge-free electron lens. Distortion (stretching and twisting) and (all types of) coma can in principle be eliminated. Because spherical aberration is inevitable, there is a practical, but not a fundamental, limit for the resolution of the electron microscope. "

In order to correct spherical aberrations, the task of rotational symmetry in electronic lenses helps. The correction of chromatic aberration is achieved in particle accelerators with time-dependent, i.e. non-static, electromagnetic fields. Scherzer himself experimented with space charges (e.g. with charged foils), dynamic lenses and combinations of lenses and mirrors in order to minimize the aberrations in electron microscopes.

Individual evidence

  1. ↑ a b Otto Scherzer: About some defects in electron lenses . In: Journal of Physics . No. 101 . Springer, September 1936, p. 593-603 .
  2. ↑ G. Schönhense, HJ Elmers, SA Nepijko, CM Schneider: Time-Resolved Photoemission Electron Microscopy . In: Advances in Imaging and Electron Physics . tape 142 . Elsevier, 2006, p. 159–323 , doi : 10.1016 / S1076-5670 (05) 42003-0 .
  3. ^ H. Rose, W. Wan: Aberration Correction in Electron Microscopy. (PDF) In: Proceedings of 2005 Particle Accelerator Conference. 2005, accessed April 3, 2020 .
  4. ↑ Otto Scherzer: The father of aberration correction. (PDF) Microscopy Society of America, accessed April 3, 2020 .
  5. ↑ Jon Orloff (Ed.): Handbook of Charged Particle Optics . 1st edition. CRC Press, 1997, ISBN 0-8493-2513-7 , pp. 234 .
  6. ↑ Frank Ernst, Manfred Rühle (Ed.): High-Resolution Imaging and Spectrometry of Materials (=  Springer Series in Materials Science . Volume 50 ). Springer Science & Business Media, 2003, ISBN 3-540-41818-0 , pp. 237 .
  7. ↑ Yougui Liao: Correction of Chromatic aberration in Charged Particle Accelerators with Time-varying fields. In: Practical Electron Microscopy and Database. 2018, accessed on April 3, 2020 .
  8. ↑ Otto Scherzer: Spherical and chromatic correction of electron lenses . In: Optics . tape 2 . Elsevier, 1947, ISSN  0030-4026 , p. 114-132 .