On Theory of Paraxial Lateral Aberrations of Electrostatic Imaging Electron Optics Based on the Asymptotic Solutions

In imaging electron optics, study of geometrical lateral aberrations of third order and paraxial lateral aberrations of second order (i.e. paraxial chromatic aberrations of second order) has traditionally been paid more attention to, but the existence of paraxial chromatic aberrations of third order and paraxial chromatic aberrations of magnification of third order was almost ignored, the general form of paraxial lateral aberration has not been studied theoretically. In the present paper, the paraxial lateral aberrations expressed in general form have been derived emphatically by using asymptotic solutions of paraxial equation. The relationship between the coefficients of asymptotic solutions of paraxial equation has been investigated, which proves that the coefficients of asymptotic solutions are related each other. Results of the present paper will have theoretical significance for studying the simple and clear form of paraxial lateral aberrations.