迭代最小二乘法用于非线性移相器的标定

针对移相干涉仪中移相器的非线性会影响测量结果准确性的问题，提出了一种基于迭代最小二乘拟合的标定干涉仪移相器的新方法。对移相器加电压并采集若干幅干涉图后，通过在帧间和帧内迭代开展最小二乘拟合可计算出干涉图间移相值，从而得出了电压值与移相值的对应关系曲线，通过对曲线作非线性拟合并对电压值进行精密调整，完成移相器的精确标定。在改造后的干涉仪上对此标定方法进行验证，与Zygo干涉仪相比，相同元件下两者测量结果之差的RMS值为1.726 nm。该标定方法可以降低高精度面形测量干涉仪对移相器线性度的要求。

Calibration of nonlinear phase shifter with iterative least-square method

Since the measurement accuracy of a phase shifting interferometer is deeply affected by nonlinear phase shifts, a novel phase shifter calibration method based on iterative least-square-fit was proposed to cope with it. Several interferograms could be taken after applying voltages to the phase shifter, and the phase shifts between interferograms could be calculated by iterative inter-and intra-least-square-fit, so the relation curve between the applied voltages and phase shifts was obtained, then the curve was fitted and the voltages were finely adjusted and finally the phase shifter was calibrated accurately. The proposed calibration method is verified on a modified interferometer, and the measurement result is compared with that of a Zygo interferometer with the same component, the RMS of the difference between two results is 1.726 nm. It can be seen that the proposed calibration method can help to get high accuracy measurement result with a nonlinear phase shifter.