Analytical and numerical analysis of third-order geometric and first-order chromatic aberrations in a bi-potential electrostatic lens

Glaser and Robl (Z. Angew. Math. Phys. 2 (1951) 444) first proposed a theoretical model for a bi-potential electrostatic lens, whose axial potential distribution satisfies the law of electrostatics and whose paraxial trajectory equation is soluble. In this paper, the Gaussian optical property in the bi-potential electrostatic lens has been thoroughly studied. Meanwhile, based on electron optical canonical aberration theory, analytical formulas of third-order geometrical and first-order chromatic aberration coefficients have first been derived and their computational results obtained for this bi-potential electrostatic lens. It is to be 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 electrostatic immersion lens.