基于π/4相移平均的多光束干涉相位提取算法

Phase Extraction Algorithms of Multi-Beam Interference Based on π/4 Phase-Shifting Averaging

菲佐干涉仪中如存在多光束干涉现象,干涉光强将不再是严格的余弦分布形式。在导出菲佐干涉仪中多光束干涉光强公式的基础上,给出了将其近似为理想多光束干涉光强公式的条件。推导了对多光束相移干涉图用四幅算法求解的相位计算误差,并据此提出了基于π/4相移平均的多光束干涉相位提取算法:通过采集相移间隔π/4的两组干涉图序列,将两次计算得到的相位值平均来抑制由多光束干涉引入的误差。在存在相移随机误差的条件下,模拟了参考面具有不同反射系数时的相位计算误差。用菲佐干涉仪检测反射系数较高的反射镜,采集22幅相移干涉图计算波面数据,结果表明:常规相移算法计算得到的波面数据中存在明显的4倍条纹周期的波纹误差,而采用基于重叠四步平均法的π/4相移平均方法可以有效地抑制多光束干涉造成的波纹误差影响。

The interference intensity is not strictly cosine CllStrl0uuon 1I mulu-oeam lntenerence exists Lii rlzeau interferometer. Based on the formula of interference intensity in Fizeau interferometer, the conditions to make the interference intensity in Fizeau interferometer be approximated as the ideal formula of multi-beam interference are brought. The calculated phase errors of 4-frame phase-shifting algorithms when using multi-beam interferograms are derived, and phase extraction algorithms of multi-beam interference based on n/4 phase-shifting averaging are proposed; two sequences of phase-shifting interferograms with n/4 interval are collected, and the two calculated phases obtained from the two sequences are averaged to suppress the error induced by multibeam interference. The calculated phase errors for test surfaces with different reflection coefficients are numerically simulated in the condition of random phase-shifting errors. A mirror with high reflection coefficient is tested by Fizeau interferometer, and 22 frames of interferograms are captured to calculate the wavefront map. The results indicate that ripple errors at 4 times the modulation frequency of fringes exist in the calculated phase when using routine phase-shifting algorithms, while the proposed n/4 phase-shifting averaging method based on the overlapping averaging 4-frame algorithm can efficiently suppress the phase error caused by multi-beam interference.