Canonical Aberration Theory in Electron Optics Up to Ultrahigh-Order Approximation

Abstract

Publisher Summary This chapter discusses the canonical aberration theory in electron optics up to ultrahigh-order approximation. The Lagrangian theory allows for solving a series of important mechanical problems, including problems in charged-particle optics. However, Lagrangian mechanics is contained in Hamiltonian mechanics as a special case. The Hamiltonian theory allows to solve a series of more general mechanical problems, and it has greater value for seeking approximate solutions to perturbation theory, for understanding the general characteristics of motion in a complicated mechanical system, and for developing canonical aberration theory and charged-particle beam optics. The chapter derives not only the power series for Hamiltonian functions up to the tenth-order approximation, but also the important recursive formulas for straightforward derivation of higher-order Hamiltonian functions by successive approximation. In higher-order canonical aberration theory, calculation of combined higher-order aberrations is the most complicated problem.