针对相移算法中以双光束干涉为基础的余弦依赖算法的算法误差,以菲佐干涉仪精密测长为应用背景进行了研究。利用干涉光学的基本原理导出了在多束光干涉(经光学面多次反射、透射)的情况下干涉光强随相位分布的精确公式;通过数值分析得出了在给定参量条件下忽略次级反射光所引入的光强误差达到14.4%;对余弦依赖算法所引起的光强误差分别就四步算法、五步算法得出了不同的依赖关系:由于四步算法比五步算法对光强误差更为敏感,因而五步算法具有更高的准确度;对于两个反射面均具有较高反射率的情况,必须考虑算法误差;当测长准确度要求不太高时,在两个或至少其中一个反射面反射率较低的情况下可以忽略算法误差的影响。

Aiming at the application of precision length measurement, the error of phase-shifting algorithm based on the cosine dependent algoritm by means of double-beam interference is explored, and the precision formula of intensity distribution of multiple-beam interference (multiple reflection and transmission by the optical surface) with the basic principle of interference optics is derived. Based on this formula and the numerical analysis, the maximum error of the interference intensity is found to reach 14.4% due to ignoring the second multiple-beam interference in the precision measurement, and the different dependences between the reflection coefficients of the two surface and the phase difference for the four-step algorithm and the five-step algorithm are listed: the latter possesses higher accuracy than the former since the former is more sensitive to the intensity error; and the error of the algorithm can be ignored while the reflection coefficient of the two surfaces or one of them is low, unless the reflectivity of the two surfaces is high.