中文摘要：

为了在制造过程中保证离轴非球面的光学特性，需要对其主要的面型参数进行严格控制，除了常规形式的顶点曲率半径和非球面系数外，还需要控制镜面的离轴量和离轴角。本文基于普通的二次曲面方程，推导了在新坐标系下的二次曲面表达式，并在这个坐标系下，利用Powell共轭方向法求取镜面的顶点曲率半径、二次曲面系数、离轴量和离轴角。通过对抛物面和双曲面两种形式不同外形的镜面数据的计算，拟合的RMS值可以达到10nm的精度，从而表明该测量计算方法可以有效地控制离轴面加工时的参数误差。

英文摘要：

To ensure the accuracy of conic surface in the fabrication of off - axis aspheric section, it is important to control the current surface parameters, such as the lateral displacement, tilt angle, the paraxial radius and the conic constant. From the normal equation for conic aspheric, new equation of conic aspheric was derived in new correlation system. Base on the new equation, the lateral displacement, tilt angle and the paraxial radius can be calculated with Conjugate Direction Method to minimize the RMS of deviation. The experimental result of the paraboloid and hyperboloid with different shapes are presented, the fitting accuracy arrived to 10nm rms. Thus the deviation of the off- axis aspheric section can be controlled effectively.