施密特光学系统由施密特校正板和球面反射镜组成，校正板设置在球面反射镜的球心处，系统的焦点不一定和反射镜的焦点重合。为了得到精确的校正板面形初始结构参数，基于波像差函数建立了带有离焦量的大口径施密特校正板的数学模型，同时校正了系统的三级和五级球差。利用光学设计软件对校正板口径为1000 mm、主镜的曲率半径为2000 mm、F数为1的系统进行了设计和分析，来验证校正板面形数学模型的正确性。结果显示此校正板的数学模型与优化后结果吻合得较好，校正板面形初始结构参数的精度得到了极大的提高，这为大口径、大相对孔径的施密特光学系统的设计提供了理论基础。

A Schmidt optical system consists of a Schmidt corrector plate and a spherical primary mirror, in which the corrector plate lies at the center of the spherical mirror. The focus of the system is not necessarily coincident with the one of the mirror. To precisely find the initial surface parameters of the corrector, a mathematical model based on wavefront aberration functions with the corrector plate surface varying as a function of defocusing amount is established. This model simultaneously corrects both the third-order and the 5th-order spherical aberrations for the system. A Schmidt optical system with aperture size 1000 mm, the mirror radius of curvature 2000 mm and the F number 1 is designed as an example to analyze and test the correctness of the mathematical model of the corrector. The results show that the mathematical model for the corrector agrees with the optimized result of the optical design software Zemax very well. The initial parameters of the optical system are improved greatly. It provided the theoretical foundation of the Schmidt optical systems design with the large aperture and the large relative aperture.