Abstract
ALTHOUGH for magnetic electron lenses the field1 
is known to permit rigorous calculation, this is not the case for electrostatic single lenses as used in electrostatic microscopes, for which up to now no type permitting exact calculation was known. We shall show in the following that the electrostatic counterpart to (1), namely: 
is also integrable. The differential equation of paraxial rays for this field, which approximates very well to the axial potential distribution of a three-aperture lens, can be transformed into an equation with constant coefficients. A magnetic field of the Glaser-type can be superposed. Inserting in 
the new variables ν, θ: 
which is well known from the bell-shaped field (1), we get: 
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References
Glaser, W., Z. Phys., 117, 285 (1941).
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SCHISKE, P. An Electrostatic Single Lens permitting Rigorous Calculation. Nature 171, 443–444 (1953). https://doi.org/10.1038/171443a0
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DOI: https://doi.org/10.1038/171443a0
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