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Calculation of Aberration Coefficients by Ray Tracing

Basic optical properties as well as aberration coefficients of electrostatic and magnetic round lenses and multipoles can be easily and quickly calculated with a standard program packaged like ELD or MLD [1]. They calculate cardinal elements and aberration coefficients of a lens directly by solving paraxial trajectory equation and aberration integrals from axial potential and fields, obtained from the computations by the first order finite element method. From known values of transfer matrix and aberration components we can evaluate positions and slopes of particle trajectories in a plane after a lens.