Third-rank chromatic aberrations of electron lenses

First- and third-order chromatic aberrations in Glaser magnetic lens for object magnetic immersion

In this paper, the Gaussian optical properties and the first- and third-order isotropic and anisotropic chromatic aberrations of the Glaser magnetic lens have been derived analytically and then calculated numerically based on two methods: the differential-algebraic DA and the electron optical aberration integrals. These coefficients have been recalculated for object magnetic immersion OMI. The expressions of chromatic aberration coefficients with the inclusion of the OMI effect of round electron lenses were not published in the literature until the present work. The numerical results of high-order chromatic aberration coefficients of Glaser magnetic lenses calculated using the DA method are shown to be in excellent agreement with those calculated using the integral aberration method and with the minor relative errors of order (10-7- 10-8), indicating that all the formulas for the chromatic aberration coefficients are entirely correct. For this purpose, COSY INFINITY 10 and Mathematica 11 were used, and both proved to be excellent computer programs for this work.