在随机和倾斜移相下光强归一化的迭代移相算法

由于存在振动和导向误差，干涉仪移相器在移相过程中产生随机的平移误差和倾斜误差，会给测量结果带来影响。因此高精度测量中对环境的稳定性和移相器的性能要求很苛刻。为了降低此种要求，针对随机和倾斜移相下干涉图背景光强和调制度的不均匀会影响移相平面计算的问题，对采集得到的干涉图做归一化处理，并利用迭代最小二乘法对归一化的干涉图做相位求解。迭代过程中，将干涉图分块来求解移相值，并对各移相值做平面拟合得到移相平面。仿真结果表明，该方法消除了背景光强和调制度的不均匀对倾斜系数计算的耦合作用，能够有效补偿倾斜移相误差对面形相位的影响，与其他方法相比,具有收敛速度快、求解精度高的特点。实验结果进一步验证了该方法的有效性。

Abstract

Since there exist vibration and orientation errors, a phase shifter usually suffers from both random translational error and tilt-shift error during phase shifting in an interferometer, and it will influence the accuracy of measurement result. So the environmental stability and the performance of phase shifter are subject to rigorous requirements in high accuracy measurement. To reduce these requirements, focusing on the problem that the nonuniformity of the background intensity and modulation will affect the calculation of phase-shift plane in random and tilt phase shifting interferograms, the acquired interferograms are normalized, and phase distribution is determined with least-squares-based iterative algorithm. During iteration, the interferograms are divided into small blocks to calculate local phase shifts, and then these phase shifts are fitted to a phase-shift plane. Results of computer simulation indicate that the proposed method can eliminate the coupling effect of background intensity and modulation on the calculation of the tilt coefficients, so it can compensate tilt phase shift errors during phase shifting. Compared with other methods, the proposed method has faster convergence as well as higher accuracy. Experimental results further demonstrate the validity of this method.

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苏志德, 史振广, 苏东奇, 隋永新, 杨怀江. 在随机和倾斜移相下光强归一化的迭代移相算法[J]. 光学学报, 2013, 33(1): 0112001. Su Zhide, Shi Zhenguang, Su Dongqi, Sui Yongxin, Yang Huaijiang. Iterative Phase Shifting Algorithm with Normalized Intensity in the Presence of Random and Tilt Phase Shifts[J]. Acta Optica Sinica, 2013, 33(1): 0112001.

在随机和倾斜移相下光强归一化的迭代移相算法

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