基于渐近解的静电成像电子光学近轴横向像差理论

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

在迄今为止的成像电子光学研究中,备受关注的是二级近轴横向像差(即二级近轴色差)和三级几何横向像差,几乎忽略了三级近轴色差和三级近轴放大率色差的存在,理论上也没有给出近轴横向像差的一般形式.作者基于近轴方程的渐近解研究近轴横向像差的一般理论,探讨了近轴方程渐近解系数之间的关系式,证明其间是相互关联的.所得结果为研究简明形式的近轴横向像差提供理论基础.

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.