非球面顶点半径和二次常数干涉测量是对二次曲面离轴子孔径在弧矢、子午和中间焦点位置直接干涉测量,拟合得到初级像差系数,并结合位置差计算出顶点曲率半径和二次常数。详细介绍了该方法的基本原理,在此基础上将子孔径中心法线与光轴夹角分解为两个倾角分量α和β引入,改进了现有模型。提出在子孔径对称情况下,可通过调整、控制特定项的泽尼克系数值,消除β分量,进而对新的模型进行了简化,只考虑α分量的影响,给出了仅存在该分量时的非球面顶点半径和二次常数的计算公式,编写了仿真程序。在α=0.03°,β=0时,直径100 mm,F数为3的抛物面反射镜离轴子孔径的初级像差系数的理论计算和数值仿真结果最大偏差仅为0.0002 λ。研究表明：在子孔径中心法线与光轴的调整存在一定误差时,在弧矢、子午和中间焦点处的初级像差系数特征关系仍然成立。

Interferometric testing the vertex radius of curvature (ROC) and conic constant (CC) of a conic surface is calculating the radius and CC with radii difference and Seidel coefficients obtained by comparing the test surface with a spherical reference wavefront having a ROC equal to the local sagittal,medial,or tangential ROC. The method is explained in detail and the angle of the optical axis and normal of the conic segment is introduced and divided into two angles α and β to improve the mathematical model. Angle β can be removed because of the symmetry of the segment according to the specific Zernike coefficients to simplify the new model. Equations about the vertex ROC and CC are derived with α and the simulation program is compiled. The maximum Seidel coefficients diffidence between theoretical calculation and simulations of a paraboloidal (=100 mm,F=3) is 0.0002 λ when α is 0.03° and β is 0. The research indicates that there are the same characteristic relations of the Seidel coefficients at the three positions even with the angle α.