Lie algebraic aberration theory and calculation method for combined electron beam focusing-deflection systems

Lie algebraic deflection aberration theory is presented and applied to comb ined magnetic focusing-deflection systems. Employing this new algebraic too l, all third- and fifth-order canonical aberrations (including canonical po sition and momentum aberrations at arbitrary observation planes) for combin ed systems are derived. The results are complete with concise forms. An exa mple of an in-lens deflection system is calculated for high-order geometric aberrations through fifth order. This article lays the groundwork for furt her studies on the computation and optimized design for higher-order aberra tions of scanning probe systems. (C) 1998 American Vacuum Society. [S0734-2 11X(98)17306-7].