Differential algebraic description for third- and fifth-order aberrations of electromagnetic lenses

In this paper the modern map method is applied to the third- and fifth-order aberration analysis of electromagnetic lenses, focusing on the high order. It is also emphasized that there exist three types of differential algebraic (DA) descriptions for electron optical aberrations. The numerical results of third- and fifth-order aberrations of a given electromagnetic lens computed through the DA technique are shown to be in excellent agreement with those evaluated using electron optical aberration integrals. In conclusion, the DA technique is concise, efficient, and precise for electron optical aberration analysis and the code COSY INFINITY has been proved to be an excellent computer code for such purposes.