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。在一组干涉图中，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包裹相位分布。实验结果表明，本文所提方法对于标定高度为956.05 nm的台阶测量结果为953.66 nm，且可以获得与迭代算法近似的解，而本文所提方法与迭代算法相比，处理速度提高了2个数量级。利用本文方法分析了表面粗糙度为0.025 µm样块的干涉条纹。结果显示：计算得到的表面粗糙度均值为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:A white light interferometry micro measurement algorithm based on principal component analysis is proposed to solve the problem of the phase solution in white light interferometry and realize the height measurement of micro morphology. The 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 a matrix operation. Finally, the phase distribution is calculated by the arctangent function. Experimental results indicate that the measurement result of a standard step height of 956.05 nm by the proposed method is about 953.66 nm and the solution is approximately consistent with the iterative algorithm. In comparison to the iterative algorithm, the processing speed of the proposed method is 2 orders of magnitude faster. The interference fringes with surface roughness of 0.025 μm is analyzed, the mean of the surface roughness calculated by the proposed method is 24.83 nm, and the sample’s standard deviation is 0.3831 nm. The proposed method improves the deficiency of monochromatic interferometry and has the advantages of high speed, low computational requirements and high accuracy.
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图 1 白光显微干涉测量系统示意图
Figure 1. Schematic diagram of white light microscopic interferometry
图 2 白光干涉光强与光程差的关系
Figure 2. Relationship between white light interference intensity and optical path difference
图 3 （a）第一帧和（b）第二帧白光干涉图
Figure 3. (a) The first and (b) the second white light phase shifting interferograms
图 4 理想台阶高度与真实台阶高度计算结果比较
Figure 4. Comparison of calculation results of ideal height of step and real height of step
图 5 台阶白光相移干涉图（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 （a）PCA-WLI和（b）AIA的台阶高度计算结果
Figure 6. The heights of step caculated by (a) PCA-WLI algorithm and (b) AIA algorithm
表 1 PCA-WLI和AIA算法结果对比
Table 1. Comparison of PCA-WLI and AIA algorithms
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 不同算法的台阶测量结果
Table 2. Measurement results of step by different algorithms
Algorithm Times PCA-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 specimen
Times Ra 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 两种算法对不同分辨率干涉图序列所用时间对比
Table 4. Comparison of consuming times of interferogram sequence with different resolutions processed by the two algorithms (s)
算法 分辨率 200×200 400×400 800×800 PCA-WLI算法 0.0168 0.0358 0.1226 AIA算法 2.8852 10.0738 38.8263
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