Numerical calculation of electron optical aberrations

A numerical method for the accurate calculation of aberration figures in systems with a straight optical axis is concisely outlined. The method involves computing a fundamental set of paraxial rays, and then directly ray-tracing a judiciously chosen set of deviations from these paraxial rays, that enable the direct plotting of aberration figures. This method avoids using complicated aberration integrals, and can directly handle the effects of high-order aberrations and asymmetry errors. A fast general predictor–corrector method for the numerical ray-tracing is also presented.