Wavelength-modulation Fourier interferometry has been employed to measure the thickness of a glass plate. However, nonlinear phase-modulation error causes a DC error in the evaluated phase distribution. In this study, a 5 N–2 phase-extraction algorithm was derived for the simultaneous measurement of the thickness and surface shape of a glass plate with eliminating the DC phase error. First, the condition for the error elimination on a complex plane was derived and a new algorithm polynomial was proposed to satisfy this condition. Next, using this condition and 5 N–4 algorithm, 5 N–2 algorithm was derived. The newly developed 5 N–2 algorithm was visualized in the frequency domain using the Fourier transform method. The DC error elimination ability of the 5 N–2 algorithm was confirmed through numerical error analysis. Finally, the surface shape and thickness of the glass plate were simultaneously measured using a large-aperture Fizeau interferometer and the 5 N–2 algorithm. The standard deviations of the thickness and surface shape profiling were 3.113 nm and 10.689 nm, respectively, which were smaller than those obtained using other phase-extraction algorithms.

波长调制傅里叶干涉法已被用于测量玻璃板的厚度。但是，非线性相位调制误差会在评估的相位分布中引起直流误差。在这项研究中，导出了一种5  N –2相位提取算法，用于同时测量玻璃板的厚度和表面形状，同时消除了DC相位误差。首先，推导了消除复杂平面误差的条件，并提出了满足该条件的新算法多项式。接下来，使用该条件和5  N -4算法，得出5  N -2算法。新开发的5  N–2算法使用傅里叶变换方法在频域中可视化。通过数值误差分析证实了5 N –2算法的DC误差消除能力 。最后，使用大孔径Fizeau干涉仪和5 N –2算法同时测量玻璃板的表面形状和厚度 。厚度和表面形状轮廓的标准偏差分别为3.113 nm和10.689 nm，小于使用其他相提取算法获得的标准偏差。