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Analytical equations of electron optics could describe general properties of an optical component but normally could not suggest any optimum dimension. For a very long time, theory had been just theory and design of instrument had been another thing until a numerical magnetic field calculation by the finite element method [1] was achieved (FEM).

[1] Munro E (1973) Computer-aided design of electron lenses by the finite element method. In: Image Processing and Computer-aided Design in Electron Optics, ed. Hawkes P W, pp. 284-323, (Academic Press, London).