Abstract Fringe analysis using phase modulation through wavelength scanning is extensively utilized for profiling the surface and thickness variation of glass plates. However, the nonlinearity of the phase-modulation error during wavelength scanning causes an offset error in the calculated phase. Therefore, in this research, two types of 19-frame phase-extraction formulas were derived for simultaneous profiling of the thickness variation and surface of a glass plate, focusing on eliminating the offset phase error. These new formulas were visualized in the frequency domain using the Fourier description. The ability of these formulas to eliminate the offset error was confirmed through numerical error analysis. Finally, the surface and thickness variation of a glass plate were simultaneously profiled using the large-aperture Fizeau interferometer and the new 19-frame formulas. The standard deviations obtained for thickness variation and surface profiling were 4.687 and 14.421 nm, respectively, which were lower than those obtained when using other phase-extraction formulas.

中文翻译：

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使用 Fizeau 干涉仪同时测量玻璃板的厚度变化和表面轮廓并消除偏移相位误差

摘要 通过波长扫描使用相位调制的条纹分析被广泛用于分析玻璃板的表面和厚度变化。然而，波长扫描期间相位调制误差的非线性会导致计算相位中的偏移误差。因此，在本研究中，推导出两种19帧相位提取公式，用于同时分析玻璃板的厚度变化和表面，重点消除偏移相位误差。这些新公式使用傅立叶描述在频域中可视化。通过数值误差分析证实了这些公式消除偏移误差的能力。最后，使用大孔径斐索干涉仪和新的 19 帧公式同时分析玻璃板的表面和厚度变化。获得的厚度变化和表面轮廓的标准偏差分别为 4.687 和 14.421 nm，低于使用其他相提取公式时获得的标准偏差。