基于多光束干涉原理的相移算法研究

针对多光束干涉原理的相移算法包括算法误差及步长优化等问题，以菲索干涉仪精密测长为 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；在此基础上，通过数值分析的方法得出了利 用菲索干涉仪精密测长的相移步长的优化取值范围和干涉光束最佳初相位差的范围；对余弦 依赖算法所引起的光强误差分别就四步法、五步法得出了不同的依赖关系；并对多光束干涉 算法中几种主要的误差来源进行了不确定度评估. 关键词： 相移算法 多光束干涉 精密测长 不确定度

Phase-shift algorithm research based on multiple-beam interference principle

Aiming at the application of precision measurement of length, the phase shift algorithm including algorithm error and optimum range of the phase shift step was studied by using the multiple beam interference principle in this paper. We have derived an accurate formula for the intensity distribution of multiple beam interference (multiple reflection by and transmission through the optical surface) in the basic principle of interference optics. Based on this formula and the numerical analysis technique, we have found the optimum value of the phase shift step and the applicable range of the initial phase difference between interference beams by using the precision measurement of length with Fizeau interferometer.We also found the respective relationships between the original phase error and the phase of four step algorithm (and of the five step algorithm) due to the intensity error from cosine dependence. We have assessed the uncertainty from several main error sources of the multiple beam interference.