Differential algebraic theory and calculation for arbitrary high order aberrations of a bipotential electrostatic lens

Abstract

The principle of differential algebra was applied to the arbitrary high order aberration analysis and calculation of bipotential electrostatic lens systems. By employing the effective tool, the differential algebraic expressions of arbitrary order geometric aberrations were obtained. As an example, a real bipotential electrostatic electron lens was studied, and all of the third geometric aberration coefficients were calculated. The patterns of the third order aberrations and the fifth order aberrations were given as well. The differential algebraic aberration method was confirmed to be an effective tool for high order aberration analysis and calculation of the bipotential electrostatic lenses.