An electron-optical system optimized by the simplex method is described. By this method

the final structure of an electron-optical system can be searched with a criterion of minimum objective parameter

i. e.

the coefficient of spherical aberration. As an example

an optimal structure and the corresponding electrical parameters of an extended field lens （EFL） are presented. In this case

the coefficient of spherical aberration is decreased from 826.9 to 393.2 where the focal length remains the same. Furthermore

the variations of this coefficient with respect to some machining tolerances might be easily obtained.