Differential algebraic method for aberration analysis of electron optical systems

Abstract

Differential algebraic method is a powerful technique in computer numerical analysis. It presents a straightforward method for computing arbitrary order derivatives of functions with extreme high accuracy limited only by the machine error. When applied to nonlinear dynamics systems, the arbitrary high order transfer properties of the system can be derived directly. In this paper, the principle of differential algebraic method is applied to calculate high order aberrations of electron optical systems. As an example, an electrostatic lens with an analytical expression has been calculated using this method. Relative errors of the Gaussian properties and spherical aberration coefficient of the lens compared with the analytic solutions are of the order 10-11 or smaller. It is proved that differential algebraic aberration method is very helpful with high accuracy for high order aberration analysis and computation of electron optical systems. © Springer-Verlag Berlin Heidelberg 2004.