Analysis of a range of symmetrical three-aperture electrostatic lenses

The three-aperture electrostatic lens was investigated in great detail. The potential along the axis was obtained using the relaxation technique. The cardinal points and coefficients of spherical and chromatic aberration were numerically calculated from the axial potential distribution using the classical Scherzer and Glaser formulas. The results are given for a range of lenses and for a series of voltage ratios
V_{1}/V_{2}
where V
1
and V
2
are the potentials of the inner and outer electrodes, respectively. The ratio of the aperture radii
R_{2}/R_{1}
is varied from 0.25 to 1 in steps of 0.25. The separation of the electrodes
S/R_{1}
is varied from 0.5 to 3 in steps of 0.5, and the thickness of the central electrode
T/R_{1}
is varied from 0.25 to 2 in steps of 0.25. The influence of all these parameters on the cardinal points and aberration coefficients is discussed and comparison is made with published experimental and theoretical results.