针对用计算全息图(CGH)对非球面进行检测时出现的非对称畸变, 分析了3种基本的畸变模型, 提出了一种有效的校正非对称畸变的方法。该方法采用较少的拟合参数即可实现对非对称畸变的精确校正, 从而可以较大程度地减少畸变校正所需要的数据点对, 避免过度拟合效应。通过光学仿真模拟分析了整个干涉仪系统的畸变, 并利用以上方法对畸变进行了校正。仿真结果显示, 畸变校正的相对残差小于0.2%。最后, 设计并制作了处于离轴工作状态的CGH, 并用此CGH对非球面进行了检测。利用上述畸变校正方法对测量的非球面面形进行校正, 并用校正之后的结果进行加工迭代, 最终非球面面形的收敛精度达到1.8 nm(RMS), 得到的结果验证了提出的畸变校正方法的可靠性。

On the basis of the asymmetric distortion from asphere measurement by a Computer-generated Hologram(CGH), three basic distortion models were analyzed, and an effective correction method for asymmetric distortion was proposed. By using a few fitted parameters, the method can correct the asymmetric distortion accurately, reduce data point pairs needed by distortion correction and can avoid over-fitting effect. Furthermore, the distortion of whole interferometric system was simulated, and its distortion was corrected by the proposed method. The simulating result shows that the relative residual of the correction is less than 0.2%. Finally, an off-axis CGH was designed and fabricated to verify the reliability of the correcting method and an asphere surface was tested with this CGH. Then, the correcting method mentioned above was used to correct the testing result, and the correcting result was taken to fabricate the asphere iteratively. The experiments show that the aspheric surface figure converges at 1.8 nm RMS (Root Mean Square) eventually. These results verify the reliability of the correction method.