Automatic differentiation method for the aberration analysis of electron optical systems

Automatic differentiation (AD) is a new and promising method in numerical a nalysis. In this paper, the general principle of automatic differentiation method for charged particle optics is given. The aberration analysis of rot ationally symmetric systems as well as deflection systems using AD method i s thoroughly studied, and the extraction of Gaussian properties and third-o rder geometric aberration coefficients from the AD results are obtained. As examples, the Gaussian properties and the third-order geometric aberration s of bell-shaped magnetic lens and saddle-coil magnetic deflector have been calculated, and the results are of high accuracy. It is proved that the AD method is an elegant and high-accurate approach for the numerical analysis of aberrations of charged particle optical systems.