基于主成分分析的白光干涉微观形貌测量算法 -

姓名
邮箱
手机号码
标题
留言内容
验证码

基于主成分分析的白光干涉微观形貌测量算法

doi:10.37188/CO.2022-0172

陈浩博^{1, 2,},
张力伟^{1, 2,},
孙文卿^{1, 2,,},
陈宝华^{1, 2,},
曹召良^{1, 2,},
吴泉英^{1, 2,}

1.
苏州科技大学物理科学与技术学院, 江苏苏州 215009
2.
江苏省微纳热流技术与能源应用重点实验室, 江苏苏州 215009

基金项目:国家自然科学基金（No. 61875145，No. 11804243）；“十四五”江苏省重点学科资助（No. 2021135）；苏州市科技计划前瞻性应用研究项目（No. SYG202013）

详细信息

作者简介:
陈浩博（1997—），男，江苏启东人，硕士研究生，2019年于金陵科技学院获得学士学位，主要从事光学干涉计量与测试方面的研究。E-mail：1103321006@qq.com
张力伟（1997—），男，江苏苏州人，硕士研究生，主要从事光学干涉计量与测试方面的研究。E-mail：20865288@qq.com
孙文卿（1984—），男，江苏南京人，博士，副教授，硕士生导师，主要从事光学计量测试与图像处理方面的研究。E-mail：sunwenqing@mail.usts.edu.cn
陈宝华（1990—），男，江苏泰州人，实验师，主要从事光学仪器加工与检测方面的研究。E-mail：1192166284@qq.com
曹召良（1974—），男，博士，教授，硕士生导师，主要从事光电仪器设备及其应用研究。E-mail：caozl@usts.edu.cn
吴泉英（1965—），女，江苏苏州人，博士，教授，博士生导师，主要从事光学仪器设计与信息处理方面的研究工作。E-mail：wqycyh@mail.usts.edu.cn

中图分类号:P164
计量
- 文章访问数:380
- HTML全文浏览量:258
- PDF下载量:316
- 被引次数:0
出版历程
- 收稿日期:2022-07-26
- 录用日期:2022-09-09
- 修回日期:2022-08-18
- 网络出版日期:2022-09-28

White light interferometry micro measurement algorithm based on principal component analysis

CHEN Hao-bo^{1, 2,},
ZHANG Li-wei^{1, 2,},
SUN Wen-qing^{1, 2,,},
CHEN Bao-hua^{1, 2,},
CAO Zhao-liang^{1, 2,},
WU Quan-ying^{1, 2,}

1.
School of Physical Science and Technology, Suzhou University of Science and Technology, Suzhou 215009, China
2.
Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, Suzhou 215009, China

Funds:Supported by National Natural Science Foundation of China (No. 61875145, No. 11804243); China Jiangsu Key Disciplines of the fourteenth Five-Year Plan (No. 2021135); the Prospective Application Research Project of Suzhou Science and Technology Plan (No. SYG202013)

More Information

Corresponding author:sunwenqing@mail.usts.edu.cn

摘要

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。
- 光学测量/
- 白光干涉/
- 主成分分析/
- 微观形貌测量
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.
- optical testing/
- white light interferometry/
- principal component analysis/
- micro topography measurement

HTML全文

图 1白光显微干涉测量系统示意图

Figure 1.Schematic diagram of white light microscopic interferometry

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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)

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

图 7不同方法轮廓线对比结果

Figure 7.The results of contour comparison by different methods

下载: 全尺寸图片幻灯片

图 8表面粗糙度样块及白光干涉图

Figure 8.Surface roughness specimen and white light interferogram

下载: 全尺寸图片幻灯片

表 1PCA-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

下载: 导出CSV

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

下载: 导出CSV

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

下载: 导出CSV

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
算法	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

下载: 导出CSV

参考文献 (19)

[1]	SAFRANI A, ABDULHALIM I. Real-time phase shift interference microscopy[J].Optics Letters, 2014, 39(17): 5220-5223.doi:10.1364/OL.39.005220
[2]	LEACH R.Optical Measurement of Surface Topography[M]. Berlin: Springer, 2011.
[3]	张磊, 吴金灵, 刘仁虎, 等. 光学自由曲面自适应干涉检测研究新进展[J]. 中国光学,2021,14(2):227-244.doi:10.37188/CO.2020-0126 ZHANG L, WU J L, LIU R H,et al. Research advances in adaptive interferometry for optical freeform surfaces[J].Chinese Optics, 2021, 14(2): 227-244. (in Chinese)doi:10.37188/CO.2020-0126
[4]	梁子健, 杨甬英, 赵宏洋, 等. 非球面光学元件面型检测技术研究进展与最新应用[J]. 中国光学,2022,15(2):161-186. LIANG Z J, YANG Y Y, ZHAO H Y,et al. Advances in research and applications of optical aspheric surface metrology[J].Chinese Opticals, 2022, 15(2): 161-186. (in Chinese)
[5]	VARGAS J, QUIROGA J A, BELENGUER T. Phase-shifting interferometry based on principal component analysis[J].Optics Letters, 2011, 36(8): 1326-1328.doi:10.1364/OL.36.001326
[6]	WYANT J C. White light interferometry[J].Proceedings of SPIE, 2002, 4737: 98-107.doi:10.1117/12.474947
[7]	SCHMIT J, CREATH K, WYANT J C.Surface Profilers, Multiple Wavelength, and White Light Intereferometry[M]//MALACARA D. Optical Shop Testing. 3rd ed. Hoboken: John Wiley & Sons, Inc. , 2006: 667-755.
[8]	马龙. 白光扫描干涉测量方法与系统的研究[D]. 天津: 天津大学, 2011. MA L. Study on white light scanning interferometry: measurement method and system[D]. Tianjin: Tianjin University, 2011. (in Chinese)
[9]	SANDOZ P. An algorithm for profilometry by white-light phase-shifting interferometry[J].Journal of Modern Optics, 1996, 43(8): 1545-1554.
[10]	LARKIN K G. Efficient nonlinear algorithm for envelope detection in white light interferometry[J].Journal of the Optical Society of America A, 1996, 13(4): 832-843.doi:10.1364/JOSAA.13.000832
[11]	HARASAKI A, SCHMIT J, WYANT J C. Improved vertical-scanning interferometry[J].Applied Optics, 2000, 39(13): 2107-2115.doi:10.1364/AO.39.002107
[12]	韩志刚, 陈磊. 对包络变化及移相误差不敏感的宽带光八步移相算法[J]. 红外与工程,2015,44(4):1236-1242.doi:10.3969/j.issn.1007-2276.2015.04.022 HAN ZH G, CHEN L. Eight-step phase shifting algorithm for broadband light interferometry insensitive to envelop variation and phase shifting error[J].Infrared and Laser Engineering, 2015, 44(4): 1236-1242. (in Chinese)doi:10.3969/j.issn.1007-2276.2015.04.022
[13]	李慧鹏, 谭朦曦, 朱伟伟, 等. 基于白光干涉测试技术的改进Carré相移算法[J]. 光子学报,2016,45(6):0612001.doi:10.3788/gzxb20164506.0612001 LI H P, TAN M X, ZHU W W,et al. Improved Carré phase shifting algorithm based on white light interferometry[J].Acta Photonica Sinica, 2016, 45(6): 0612001. (in Chinese)doi:10.3788/gzxb20164506.0612001
[14]	贾竣. 应用于白光轮廓仪的白光相移干涉算法研究[D]. 天津: 中国民航大学, 2020. JIA J. Research on white light phase-shifting algorithm for white light profiler[D]. Tianjin: Civil Aviation University of China, 2020. (in Chinese)
[15]	陆冬筱, 房文汇, 李玉瑶, 等. 光学相干层析成像技术原理及研究进展[J]. 中国光学,2020,13(5):919-935.doi:10.37188/CO.2020-0037 LU D X, FANG W H, LI Y Y,et al. Optical coherence tomography: principles and recent developments[J].Chinese Optics, 2020, 13(5): 919-935. (in Chinese)doi:10.37188/CO.2020-0037
[16]	XIN L, LIU X, YANG ZH M,et al. Three-dimensional reconstruction of super-resolved white-light interferograms based on deep learning[J].Optics and Lasers in Engineering, 2021, 145: 106663.doi:10.1016/j.optlaseng.2021.106663
[17]	张超, 袁群, 张佳乐, 等. 白光显微干涉三维形貌测量中的移相误差校正方法[J]. 红外与工程,2022,51(7):20220050. ZHANG CH, YUAN Q, ZHANG J L,et al. Calibration method of the phase-shifting error for the topography measurement utilizing white light interferometric microscopy[J].Infrared and Laser Engineering, 2022, 51(7): 20220050. (in Chinese)
[18]	WANG ZH Y, HAN B. Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms[J].Optics Letters, 2004, 29(14): 1671-1673.doi:10.1364/OL.29.001671
[19]	LEI Z L, LIU X J, CHEN L ZH,et al. A novel surface recovery algorithm in white light interferometry[J].Measurement, 2016, 80: 1-11.doi:10.1016/j.measurement.2015.11.019