White light interferometry micro measurement algorithm based on principal component analysis
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摘要:
为了解决白光干涉相位求解问题，实现微观形貌的高度测量，提出了基于主成分分析（Principal Component Analysis，PCA）的白光干涉（White Light Interferometry，WLI）微观形貌测量算法。通过搭建的白光干涉显微系统采集多幅干涉图，将其重构成向量形式。从一组干涉图中，用时间平均值来估计背景照明，消除背景光成分。然后，通过矩阵运算得到代表原始数据的特征值及其特征向量。最后，通过反正切函数计算物体的压包相位分布。实验结果表明，本文所提方法对标定高度为956.05 nm台阶的测量结果为953.66 nm，且可以获得与迭代算法近似一致的解，而本文所提方法与迭代算法相比，平均时长快2个数量级。分析了表面粗糙度为0.025 µm样块的干涉条纹，本文所提方法计算得到表面粗糙度均值为24.83 nm，标准差为0.3831 nm。本文提出的方法解决了单色光干涉测量中的不足，还具有计算简单、速度快及精度高等优势。
Abstract:in order to save the problem of the phase solution in white light interferometry and realize the height measurement of micro morphology, white light interferometry micro measurement algorithm based on principal component analysis was proposed. White light microscopic interference system is used to collect multiple interferograms and reconstruct them into vector form. From a set of interferograms, the background illumination can be estimated by a temporal average, eliminating background light components. Then, the eigenvalues and eigenvectors representing the original data are obtained by matrix operation. Finally, the phase distribution is calculated by arctangent function. Experimental results indicate that the measurement result of standard step height of 956.05 nm by the proposed method is about 953.66 nm, the solution is approximately consistent with the iterative algorithm, in comparison to the iterative algorithm, the average time of the proposed method is 2 orders of magnitude faster. The interference fringes with surface roughness of 0.025 μm were analyzed, the mean of surface roughness calculated by the proposed method was 24.83 nm, and the sample standard deviation is 0.3831 nm. The proposed method improves the deficiency of monochromatic interferometry and has advantages of low computational requirements, fast and high accuracy.
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图 3 前两帧白光干涉图
Figure 3. The first and the second white light phase shifting interferogram
图 4 理想台阶高度与真实台阶高度计算结果
Figure 4. Calculation results of ideal height of step and real height of step
图 5 台阶白光干涉图（红线代表的长度为0.2 mm）
Figure 5. White light phase-shifting interferogram of step (The red line represents an actual physical length of 0.2 mm)
图 6 PCA-WLA和AIA的台阶计算结果
Figure 6. The results of step determined by PCA-WLI algorithm and AIA algorithm
表 1 PCA-WLI和AIA算法结果对比
Table 1. The result of PCA-WLI is compared with AIA algorithm
算法 PV误差（%） RMS误差（%） 计算时间（s） PCA-WLI算法 0.452 0.035 0.026 AIA算法 0.443 0.034 5.2465 
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表 2 不同算法对台阶的测量
Table 2. The measurement of step based on different algorithms
Algorithm
TimesPCA-WLI AIA 1 958.35 955.09 2 949.59 948.38 3 947.80 960.16 4 955.29 959.11 5 957.46 960.65 6 949.70 958.31 7 951.09 944.28 8 954.79 956.26 9 956.99 949.77 10 955.56 956.58 Mean value/nm 953.66 954.87
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表 3 表面粗糙度测量结果
Table 3. Measurement results of surface roughness pieces
Roughness/nm
TimesRa 1 24.9 2 25.3 3 24.7 4 24.6 5 25.1 6 24.8 7 24.2 8 24.6 9 25.5 10 24.6 Mean value/nm 24.83 Standard deviation/nm 0.3831
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表 4 对干涉图序列分辨率不同的算法所用时间的结果对比
Table 4. Comparison of the results of the algorithms with different resolution of interferogram sequence
分辨率
算法200*200 400*400 800*800 PCA-WLI算法 0.0168 s 0.0358 s 0.1226 s AIA算法 2.8852 s 10.0738 s 38.8263 s
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