提高S变换轮廓术测量精度的方法

谌秋菊; 陈文静; 钟敏; 苏显渝

doi:doi:10.3788/aos201333.0612009

光学学报, 2013, 33 (6): 0612009, 网络出版: 2013-05-14

提高S变换轮廓术测量精度的方法

Method for Improving the Accuracy of S-Transform Profilometry

论文大纲

谌秋菊 ^*陈文静钟敏苏显渝

作者单位

四川大学电子信息学院光电科学技术系, 四川成都 610064

测量 S变换条纹分析泰勒展开三维面形重建 measurement S transform fringe pattern analysis Taylor expansion 3D reconstruction

摘要

S变换结合了短时傅里叶变换和小波变换的优点，是一种无损可逆的非平稳信号时频分析方法，具有线性、多分辨率、逆变换唯一，且与傅里叶变换保持着直接联系等特点。针对基于“脊”分析原理的S变换轮廓术中，相位采用一阶泰勒展开描述时存在的不足，提出了更为精确的二阶泰勒展式的相位描述方法。通过严格的理论分析，得到了更准确的相位场的计算公式，弥补了采用一阶泰勒展式描述相位的不足，大大提高了Ｓ变换“脊”方法重建三维面形的精度。完成了相应的计算机模拟和实验验证，并将S变换三维重建效果与以前的基于相位一阶展式的结果进行了对比。

Abstract

S Transform combines the advantages of the windowed Fourier transform and the wavelet transform. It is a kind of nondestructive and reversible time-frequency analysis method for the non-stationary signals with the characteristics of the linearity, multi-resolution and the only one inverse transformation existing. In addition, it has direct relationship with Fourier transform. Due to the shortage of the phase description based on the 1st-order Taylor expansion in the S transform “ridge” method, a more accuracy phase expression based on the 2nd-order Taylor expansion is proposed. According to the strictly theoretical analysis, a more accuracy calculation expression formula of the phase field is gotten and corresponding computer simulation and experiment are finished, which enriches the theory of S transform and improves the measurement accuracy of S transform. The three-dimensional (3D) reconstruction results based on the 1st-order Taylor expansion are also compared with that based on our method in S transform “ridge” method. The simulations and experiments show that the reconstruction of the surface from the 2nd-order Taylor expansion has higher measurement precision.

参考文献

[1] 苏显渝, 李继陶. 信息光学[M]. 北京: 科学出版社, 1999. 306～338

Su Xianyu, Li Jitao. Information Optics [M]. Beijing: Science Press, 1999. 306～338

[2] Frank Chen, Gordon M. Brown, Mumin Song. Overview of three dimensional shape measurement using optical methods [J]. Opt. Eng., 2000, 39(1): 10～22

[3] 金国藩, 李景镇. 激光测量学[M]. 北京: 科学出版社, 1998, 337

Jin Guofan, Li Jingzhen. Laser Metrology [M]. Beijing: Science Press, 1998. 337

[4] V. Srinivasan, H. C. Liu, M. Halioua. Automated phase-measuring profilometry of 3-D diffuse objects [J]. Appl. Opt., 1984, 23(18): 3105～3108

[5] M. Takeda, K. Mutoh. Fourier transform profilometry for the automatic measurement of 3-D object shapes [J]. Appl. Opt., 1983, 22(24): 3977～3982

[6] Kemao Qian, Haixia Wang, Wenjing Gao. Windowed Fourier transform for fringe pattern analysis: theoretical analyses [J]. Appl. Opt., 2008, 47(29): 5408～5419

[7] Kemao Qian. Windowed Fourier transform for fringe pattern analysis [J]. Appl. Opt., 2004, 43(13): 2695～2702

[8] 翁嘉文, 钟金钢. 小波变换在载频条纹相位分析法中的应用研究[J]. 光学学报, 2005, 25(4): 454～459

Weng Jiawen, Zhong Jingang. Apply wavelet transform to phase analysis of spatial carrier-fringe pattern [J]. Acta Optica Sinica, 2005, 25(4): 454～459

[9] 孙娟, 陈文静, 苏显渝等. 小波变换轮廓术的测量范围研究[J]. 光学学报, 2007, 27(4): 647～653

Sun Juan, Chen Wenjing, Su Xianyu et al.. Study the measurement range of wavelet transform profilometry [J]. Acta Optica Sinica, 2007, 27(4): 647～653

[10] R. G. Stockwell, L. Mansinha, R. P. Lowe. Localization of the complex spectrum: the S-transform [J]. IEEE Transactions on Signal Processing, 1996, 44(4): 998～1001

[11] 蒋模华, 陈文静, 郑志平. 基于S变换的解相技术研究[J]. 光学学报, 2011, 31(4): 0412001

Jiang Mohua, Chen Wenjing, Zheng Zhiping. Research of phase demodulation technique based on S-transform [J]. Acta Optica Sinica, 2011, 31(4): 0412001

[12] 钟敏, 陈文静, 蒋模华. S变换轮廓术中消除条纹非线性影响的方法[J]. 光学学报, 2011, 31(11): 1112003

Zhong Min, Chen Wenjing, Jiang Mohua. S-transform profilometry eliminates nonlinear error in deformed fringe pattern [J]. Acta Optica Sinica, 2011, 31(11): 1112003

[13] L. Mansinha, R. G. Stoekwell, R. P. Lowe. Pattern analysis with two-dimensional spectral localization: applications of two-dimensional S transforms [J]. Physica A: Statistical Mechanics and Its Applications, 1997, 239(1-3): 286～295

[14] 董富强, 达飞鹏, 黄昊. 基于S变换的改进窗口傅里叶三维测量法[J]. 光学学报, 2012, 32(5): 0512008

Dong Fuqiang, Da Feipeng, Huang Hao. Windowed Fourier transform profilometry based on advanced S-transform [J]. Acta Optica Sinica, 2012, 32(5): 0512008

[15] Huang Lei, Kemao Qian, Pan Bing et al.. Comparison of Fourier transform,windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry [J]. Opt. & Lasers in Eng., 2010, 48(2): 141～148

[16] 苏显渝, 谭松新, 向立群等. 基于傅里叶变换轮廓术方法的复杂物体三维面形测量[J]. 光学学报, 1998, 18(9): 1228～1233

Su Xianyu, Tan Songxin, Xiang Liqun et al.. Complex object shape measurement using FTP method [J]. Acta Optica Sinica, 1998, 18(9): 1228～1233

谌秋菊, 陈文静, 钟敏, 苏显渝. 提高S变换轮廓术测量精度的方法[J]. 光学学报, 2013, 33(6): 0612009. Shen Qiuju, Chen Wenjing, Zhong Min, Su Xianyu. Method for Improving the Accuracy of S-Transform Profilometry[J]. Acta Optica Sinica, 2013, 33(6): 0612009.

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