基于多点平均频率校正的多表面波长调谐移相干涉测量

为实现多表面干涉测量中强度叠加干涉信号的分离和相位解调，提出了一种基于频率校正的多表面波长移相干涉测量算法，可实现透明被测件各表面面形的同时重建。波长移相干涉技术可以根据各干涉谐波光程差(optical path difference, OPD)的不同使各表面干涉谐波具有不同的移相值，该差异为各信号分离和相位解调提供了基础。在现有的多表面测量技术中，往往通过被测件的腔长和光学厚度等信息对谐波频率进行粗估，但估计精度较低，且无法应对移相误差。因此，本文通过多点平均和频率校正实现了各干涉谐波频率的精确提取，能够有效消除异常值和加性高斯噪声(additive Gaussian noise, AGN)对频率求解精度的影响，并且仅通过干涉图之间的加权操作便可同时对各谐波相位进行解调，对比分析和实验结果验证了所提出的算法的可靠性。

Multi-surface wavelength-tuning phase-shifting interferometry based on multi-point average frequency correction

To realize separation and phase demodulation of superimposed interference intensity signals in multi-surface interferometry measurements,a frequency-corrected-based multi-surface wavelength-shifting interferometry algorithm is proposed,which can realize the simultaneous reconstruction of the surface shapes of the measured transparent plates.The wavelength-shifting interferometry technique can enable each interference harmonic to feature different phase-shifting values according to the corresponding optical path difference (OPD),which provides the basis for the separation and phase demodulation of each signal.In existing multi-surface measurement techniques,the harmonic frequencies are often roughly estimated from information such as the cavity length and optical thickness of the measured plates, but the estimation accuracy is low and cannot cope with phase-shifting errors.Therefore,this paper realizes the accurate extraction of each interference harmonic frequency by multi-point averaging and frequency correction,which can effectively eliminate the influence of abnormal value and additive Gaussian noise (AGN) on the frequency solution accuracy,and can demodulate each harmonic phase simultaneously only by the weighting operation between interferograms.The comparative analysis and experimental results verify the reliability of the proposed algorithm.