基于平移旋转的球面绝对检测技术是一种实现高精度面形测量的有效手段。通过绕光轴多次等角度旋转被测球面测得被测面面形误差的旋转非对称部分，并由共心平移被测球面恢复出被测面面形误差的旋转对称部分，合成即可得到被测球面完整的面形信息。详细推导了平移旋转法的理论公式，并进行了仿真分析。仿真结果表明，基于上述方法获得的被测球面面形误差与初始面形误差残差图的均方根值为5.300 0×10-12 nm，其与初始面形误差均方根值的比值为1.164 1×10-12，理论误差极小，满足高精度面形检测要求。surfaces with shift-rotation method

The absolute testing of spherical surfaces with the shift-rotation method is an effective way to test spherical surfaces with high accuracy. In the testing, the spherical surface under test is rotated to N equally spaced positions about the optical axis and the results of testing are averaged, to obtain the rotational asymmetric component. The spherical surface is also shifted to a confocal position with a shift, to derive the rotational symmetric component. Then full surface shape information can be obtained by synthesizing the above rotational asymmetric and rotational symmetric components. The formulas of shift-rotation method are derived and a simulation of the testing is presented. The results of simulation show that the root-mean-square(RMS) of residual figure error is 5.300 0×10-12 nm and its ratio to the RMS of original figure error is 1.164 1×10-12. Thus the method can realize high accuracy measurement of spherical surfaces.