Magnetic Electron Lenses Based on the Uniformly Magnetized Ellipsoid

  • Adil Abdullah Alshwaikh

Student thesis: Doctoral ThesisDoctor of Philosophy


This thesis is concerned with mathematical models of magnetic pole-piece lenses. It extends the well-known square-top field model, which gives a good representation of double polepiece lenses to the calculation of spiral distortion and chromatic change in magnification and rotation.

The main aim of the project however is to propose and evaluate the uniformly magnetised ellipsoid as a possible basis for an understanding of the electron-optical properties of magnetic single pole-piece lenses. The special case of a magnetized hemisphere is shown to be of special importance since it provides a realistic model for such lenses and is adapted to mathematical analysis. For convenience, this model will be called the spherical model.

On the basis of this model, the coefficients of spherical aberration, Chromatic aberration and image distortion of single pole-piece lenses in various modes of operation have been calculated. The results so obtained enable one to select conditions of operation for minimum lens defects.

The results of this theoretical investigation give a valuable insight into the behaviour of practical single pole piece lenses, whose focal properties could not previously be accounted for in detail.

The analysis of the spherical model has also been extended to the calculation of the pre-field characteristics and the aberration coefficients of chromatic change in magnification and rotation. The results are compared with the known characteristics of conventional lenses.

Two modes of operation of single-pole lenses are considered in some detail, One is the possibility of using such a lens as a single-field condenser objective lens. The other relates to the possibility of combining two single-pole lenses in a projector system that is free from spiral distortion.

Finally, the ideas and results obtained from the theoretical analysis are compared with presently available experimental data on single-pole lenses:
Date of AwardMar 1979
Original languageEnglish


  • Aberration correction
  • electron microscopy
  • electron optics
  • lens aberration
  • lens computations
  • magnetic lens
  • magnetic lens model
  • snorkel lenses
  • spherical aberration
  • spherical field model
  • spiral distortion
  • square top field model

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