由复合电磁同心球系统的近轴方程两个特解出发, 通过展开理想成像位置处图像转角表达式的途径, 探讨了复合电磁同心球系统的近轴纵向像差和近轴横向像差。主要贡献是求得了近轴方程的两个特解在理想像面位置处的解析表达式, 由此证明决定极限空间分辨率的二级近轴色球差能以Recknagel-Artimovich公式描述。导出了近轴横向像差的表达式, 该像差由近轴色球差、近轴放大率色差和近轴各向异性色差等组成。

Starting from the two special solutions of the paraxial equation of the combined electromagnetic concentric spherical system, the paraxial longitudinal and lateral aberrations of the combined electromagnetic concentric spherical system have been explored by expanding the representation of the image rotation angle at the ideal imaging position. The main contribution of this paper is to obtain the analytical expression of the two special solutions of paraxial equation at ideal image plane, and it has proved that the paraxial spherical-chromatic aberration of second order that determines the limited spatial resolution of imaging can still be characterized in terms of the Recknagel-Artimovich formula. Expressions of the paraxial lateral aberration composed of paraxial spherical-chromatic aberration, paraxial magnification chromatic aberration, and paraxial anisotropic chromatic aberration have been deduced.