用于相移点衍射干涉仪的加权最小二乘相位提取算法

针对现有的相位提取算法只对某些特定的误差不敏感,不能满足高精度光学检测的要求,本文引入一种等间隔多步移相算法—权重待定的加权最小二乘算法。通过在最小二乘算法中添加待定的权重,分析移相点衍射干涉仪中多种误差源对算法的影响,获得多组约束方程,从而确定权重和新算法。对新算法和标准四步算法、Hariharan五步算法进行比对分析,验证了新算法对PZT线性和二阶非线性移相不准、光强的一阶二阶波动和光源频率一阶二阶波动等误差抑制能力远远优于标准四步算法和Hariharan五步算法;新算法对CCD的量化误差、光强噪声、频率噪声的抑制能力也具有一定优势,且对CCD的二阶响应非线性完全不敏感。

Weighted least square phase extraction algorithm for phase-shifting point diffraction interferometer

Existing phase extraction algorithms are just insensitive to some specifically error sources, which can't satisfy the requirements of optical testing for the high precision. An equal-phase interval multi-step phase-shifting algorithm, weighted least square algorithm with underdetermined weight, was introduced. By introducing undetermined weights to the least square algorithm and by analysing the effect of manifold error sources on the algorithm in phase-shifting point diffraction interferometer, several groups of bound equations were obtained and the undetermined weights and the new phase extraction algorithm were determined by solving these bound equations. The new phase extraction algorithm was compared with standard four-step algorithm and Hariharan five-step algorithm. The results illuminate that the new phase extraction algorithm is much more insensitive to the linearity and nonlinearity of second order of PZT, intensity fluctuation in linearity and nonlinearity of 2nd order, linearity and nonlinearity of 2nd order of frequency of light source fluctuation. The results also illunimate that the new algorithm have advantages over other two algorithms in eliminating the CCD quantization, intensity noise, and the frequency noise. Moreover, the new algorithm is insensitive to the CCD nonlinearity at all.