High order aberrations calculations of Wien filters using differential algebra methods

In this paper, a novel scheme based on the differential algebraic (DA) method is proposed to analyze the electron optics properties of the Wien fillers. A new software package is then developed, to compute the geometrical and chromatic aberrations up to the fifth order of the Wien fillers. For examples, the aberrations of single filter and the double filters are calculated. The calculated geometrical aberration coefficients are comparable with the counterpart calculated by Tang's theory. However, both theories can only match with each other in the calculation of the chromatic aberration coefficient when the dispersion ray is taken into consideration in Tang's theory.