Lie algebraic method for calculating high-order canonical magnetic deflection aberrations

Lie algebraic aberration theory is developed and applied to magnetic deflection systems. Employing this new algebraic tool, all third- and fifth-order canonical magnetic deflection aberrations (including canonical position and momentum aberrations at arbitrary observation planes) are derived. The results are in exactly agreement with those obtained by the conventional successive approximation aberration theory. The present paper lays a theoretical groundwork for further studies on Lie algebraic theory for calculating higher-order aberrations of scanning probe systems.