Analytical calculation of geometric and chromatic aberrations in a bi-potential electrostatic and bell-shaped magnetic combined lens

In the present paper, Gaussian optical property in the bi-potential electrostatic and the bell-shaped magnetic combined lens – a new theoretical model first proposed in electron optics – has been thoroughly studied. Meanwhile, based on electron optical canonical aberration theory, analytical formulas of third-order geometrical and first-order chromatic aberration coefficients and their computational results have first been derived for this bi-potential electrostatic and bell-shaped magnetic combined lens. It is to emphasized that this theoretical study can be used to estimate third-order geometric and first-order chromatic aberrations and to provide a theoretical criterion for numerical computation in a rotationally symmetric electromagnetic lens.