Wavelength-tuning phase-shifting interferometry plays a significant role in the measurements of transparent parallel plates. The difficulty of multi-surface measurements is that the harmonics with different frequencies and phases make the captured interference signal mixed. In multi-surface measurements, the demodulation of phases builds on the determination of the frequency of each signal, which is traditionally estimated from the prior information including the cavity length and the optical thickness of the measured plate. However, the estimation accuracy of this method is not satisfactory. In order to accurately obtain the signal frequencies and demodulate the initial phases of the measured surfaces simultaneously, this paper proposes a total least squares wavelength-tuning phase-shifting algorithm (TLSWPA). The developed TLSWPA includes two steps: Firstly, considering the influence of the Gaussian noise on the captured interferograms, the signal frequencies are obtained based on the total least squares principle with high accuracy; Secondly, introducing the Householder transformation, the least squares error based on the 2-Norm is used to demodulate the initial phase distribution for each signal. Comparison of the obtained results of the frequency solution and the accuracy of wavefront reconstruction shows that the developed TLSWPA allows obtaining results with an accuracy 2 orders of magnitude higher than the algorithm based on the fast Fourier transform and 1 order of magnitude higher than the advanced iterative algorithm. Experimental study on a borosilicate crown glass using a Fizeau wavelength-tuning interferometer further verifies its effectiveness.

波长调谐相移干涉测量在透明平行板的测量中起着重要作用。多面测量的难点在于不同频率和相位的谐波使捕获的干扰信号混合。在多表面测量中，相位的解调建立在确定每个信号的频率的基础上，该频率通常是根据先验信息（包括被测板的腔长和光学厚度）来估计的。然而，这种方法的估计精度并不令人满意。为了准确获取信号频率并同时解调被测表面的初始相位，本文提出了一种全最小二乘波长调谐相移算法（TLSWPA）。所开发的TLSWPA包括两个步骤：首先，考虑高斯噪声对捕获的干涉图的影响，基于全最小二乘原理高精度地获取信号频率；其次，引入Householder变换，利用基于2-范数的最小二乘误差来解调每个信号的初始相位分布。频率解的结果和波前重建精度的比较表明，所开发的 TLSWPA 允许获得的结果精度比基于快速傅立叶变换的算法高 2 个数量级，比高级迭代算法高 1 个数量级。算法。