旋转法是一种用于获得被测面旋转非对称面形的绝对检测技术。旋转平均补偿算法是在N次等间隔旋转的基础上增加一次不同角度的旋转测量，称为N+1次旋转法。通过附加的一次旋转测量，采用泽尼克多项式拟合求解旋转平均法的丢失面形。推导了理论计算公式，仿真分析了存在旋转角度和偏心误差时，补偿算法的有效性以及附加旋转角度对补偿面形计算精度的影响。验证实验的结果与仿真相符，表明在选择合适的附加角度之后，该算法可有效补偿丢失信息。与旋转平均法相比，只需增加一次旋转，就能得到更完整的面形，极大地提高了检测效率和精度，实验中补偿率达到61%，检测精度提高了约1倍。

The rotation method is an absolute testing to obtain rotationally asymmetric surface. A compensation method based on rotation-averaging needs a different rotation measurement besides N equally spaced azimuthal measurements, which is called N+1 rotation method. The losing surface of rotation-averaging method can be obtained with the additional measurement data and Zernike polynomial fitting. The theoretical formulas are derived and the validity of compensation method is simulated. The impact of additional rotation angle on algorithm accuracy is presented. The experimental result is consistent with simulation very well which proves that the losing surface can be compensated effectively by this method with an appropriate angle. Compared with the rotation-averaging method, this method can greatly improve the testing efficiency and accuracy by just adding one additional measurement. The compensation ratio is 0.61 and the accuracy is improved by a factor of 1.