A differential algebra method for aberration analysis of variable-axis lens system

Abstract

A variable-axis lens (VAL) is an effective method for achieving a large field of view with high resolution because it can preserve small aberrations by shifting the optical axis according to the deflection of the electron beam, even when the beam is deflected to regions far from the central straight optical axis. However, for systems consisting of such a VAL, conventional methods for calculating aberration coefficients that refer to the central straight optical axis could be meaningless. Here, we propose a novel approach, based on the differential algebraic(DA) method, for calculating high-order aberration coefficients for VAL systems. Instead of using the straight optical axis as a reference, we trace only one electron trajectory in such a system. Then, the linear optical properties and the geometric aberration and chromatic aberration coefficients up to 5th rank are calculated (with high accuracy) and analyzed with reference to the reference trajectory. In comparison with conventional methods, the proposed DA approach shows overwhelming advantages in having analyzed the dispersion, focus error and 2nd rank aberration coefficients. A new software package was developed, and an example was shown to demonstrate the proposed approach.