研究了用Zernike环多项式分析光电经纬仪主反射镜变形的方法。首先推导了将有限元分析的变形结果转换成基于波前坐标系的数据形式的转换公式，然后用Zernike环多项式对某光电经纬仪主反射镜的变形进行拟合，计算了主反射镜变形引起的面形误差的峰谷值(30.7 nm)和面形误差均方根值(6.3 nm)，与实际测量结果相比误差分别为9.2%和10.5%。根据Zernike环多项式系数与Seidel多项式系数的关系，得到了主反射镜变形对光学系统像差造成的影响。将Zernike环多项式系数导入光学系统分析软件Zemax中，可对主反射镜变形后的光学系统进行综合分析，为光学系统修正提供参考。

A method for analyzing the primary mirror deformation of photo-electronic theodolite with Zernike annular polynomials is researched. Firstly, a formula used to convert the finite element method (FEM) analysis results into the data based on the wave-front coordinate is deduced. Then, the deformation of the primary mirror in a photo-electronic theodolite is fitted with Zernike annular polynomials, and the peak-to-valley (PV) value (30.7 nm) and root-mean-square (RMS) value (6.3 nm) of surface error are calculated. Their error are 9.2% and 10.5% compared with actual inspection results. The influence of the primary mirror deformation on the aberration of optical system is obtained based on the relationship between Zernike annular polynomial coefficients and Seidel polynomial coefficients. Importing the Zernike annular polynomials into the Zemax software, a comprehensive analysis of the optical system can be realized. It provides information for optimizing the optical system.