A complex of mathematical problems of electron optics could be subdivided into two classes: a problem of analysis and a problem of synthesis. The problems of the first type consist in finding distribution of electrostatic field of a EOS for specific electrodes configuration and given potentials on them. The problems of the second type aim at determining configuration of electrodes and potentials on them, which provide sought electron-optical parameters.

There are considered two approaches for building algorithm of numerical solving the problem of synthesis of a field with a given axial distribution, that is reduced to finding configuration of electrodes and potentials on them. An axial distribution of the field can be obtained as solution of a problem of synthesis of another type [1] or can be given among initial data of the problem.