Abstract
We discuss a computerized systematic investigation to find axially symmetric electrostatic lens potentials with acceptable first-order properties and small spherical aberrations. The calculation of the spherical aberration is based on the direct solution of the relativistic trajectory equation in paraxial and nonparaxial approximation. The potentials are characterized by their properties in infinite magnification mode. Conditions for the computations and constraints to satisfy practical requirements are prescribed. A successful axial potential distribution and its relativistic spherical aberration coefficient, the spherical disk radius, and some first-order optical parameters, are also presented in the paper as an example.
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