光学三维形貌测量中的时频分析技术研究
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摘要
很多物理量可以被物体表面形貌的变化所反映。光学三维形貌测量技术具有非接触性、高精度、高速性和自动化程度高等特点,在形貌测量领域得到了广泛的应用。而傅里叶变换轮廓术作为一种主动光学三维形貌测量技术,因其只需要一幅变形光栅图样来做全场分析的优点,而受到人们广泛关注。但是,传统的傅里叶变换是一种全局频谱分析法,不适用于对复杂物面调制的非平稳变形光栅条纹信号的分析,而且对噪声敏感。
本文不但回顾了傅里叶变换轮廓术中算法存在的缺点,而且研究了一类为了改进傅里叶变换轮廓术中算法缺陷的非平稳信号时频分析算法,如窗口傅里叶变换法、伸缩窗口傅里叶变换法和多尺度窗口傅里叶变换法。随后提出了窗口尺度选取改进算法,该算法通过小波脊来提取信号的瞬时频率,然后控制逐点分析窗口的宽度来保证窗口内信号的准平稳性。该算法在信号的频率分辨率和空间(时间)分辨率之间达到一种更佳的调和,即使条纹信号被噪声污染时,仍然可以得到很好的物面重建效果。
其次,研究了窗口尺度选取改进算法在非平稳信号时频表示当中的有效性,并与现有的各种在时频表示中常用的时频分析算法相比较。比较结果表明,该算法在运算复杂度与时频局域化能力综合考虑的前提下具有优势。
再次,研究了热门的经验模态分解方法在光学三维形貌测量当中的除噪应用,光学三维形貌测量易受高频的背景噪声和CCD噪声的干扰。实验结果显示,使用经验模态分解方法在去除噪声,提高信噪比方面具有优越性。
Many physical quantity of an object can be reflected by changes of its shape. Optical 3-D shape measurement technology has been widely used in shape measurement because of its characteristics of non-contact, high accuracy, high speed and high automation. The Fourier transform profilometry as an active optical 3D shape measurement technology has been widely concerned because it need only one deformed grating image to make full-field analysis. However, conventional Fourier transform method is a global spectrum analytical method which is unsuitable to analyze non-stationary fringe signal that modulated by complex shape, and it is sensitive to noise.
This paper not only review the shortcoming of the algorithm of Fourier transform profilometry, but also a class of time-frequency analysis algorithms for non-stationary signal has been researched. These methods are aim to improve the algorithm of Fourier transform profilometry, such as windowed Fourier transform, dilating Gabor transform and multiscale windowed Fourier transform. Then an improved window scale selection algorithm is proposed, the instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform, and the pointwise analytical window width is controlled to keep the inside signal quasi-stationary. There is a better harmonization between the frequency resolution and space (time) resolution which make it more accurate to the fundamental frequency spectrum extraction. Even if the fringe signal is polluted by noise pollution, it still gets a good reconstruction results.
Secondly, the application of improved window scale selection algorithm in time-frequency representation of non-stationary signal is researched and compared with existing time-frequency analysis algorithm applied in time-frequency representation. The result proved that the algorithm is at an advantage considering about both computational complexity and time-frequency concentration capability.
At last, the application of popular empirical mode decomposition method in denoising of optical 3-D shape measurement is researched. Optical 3-D shape measurement is vulnerable to high-frequency background noise and CCD noise. Simulation result shows that the empirical mode decomposition method is at an advantage when denoising and improving SNR.
本文不但回顾了傅里叶变换轮廓术中算法存在的缺点,而且研究了一类为了改进傅里叶变换轮廓术中算法缺陷的非平稳信号时频分析算法,如窗口傅里叶变换法、伸缩窗口傅里叶变换法和多尺度窗口傅里叶变换法。随后提出了窗口尺度选取改进算法,该算法通过小波脊来提取信号的瞬时频率,然后控制逐点分析窗口的宽度来保证窗口内信号的准平稳性。该算法在信号的频率分辨率和空间(时间)分辨率之间达到一种更佳的调和,即使条纹信号被噪声污染时,仍然可以得到很好的物面重建效果。
其次,研究了窗口尺度选取改进算法在非平稳信号时频表示当中的有效性,并与现有的各种在时频表示中常用的时频分析算法相比较。比较结果表明,该算法在运算复杂度与时频局域化能力综合考虑的前提下具有优势。
再次,研究了热门的经验模态分解方法在光学三维形貌测量当中的除噪应用,光学三维形貌测量易受高频的背景噪声和CCD噪声的干扰。实验结果显示,使用经验模态分解方法在去除噪声,提高信噪比方面具有优越性。
Many physical quantity of an object can be reflected by changes of its shape. Optical 3-D shape measurement technology has been widely used in shape measurement because of its characteristics of non-contact, high accuracy, high speed and high automation. The Fourier transform profilometry as an active optical 3D shape measurement technology has been widely concerned because it need only one deformed grating image to make full-field analysis. However, conventional Fourier transform method is a global spectrum analytical method which is unsuitable to analyze non-stationary fringe signal that modulated by complex shape, and it is sensitive to noise.
This paper not only review the shortcoming of the algorithm of Fourier transform profilometry, but also a class of time-frequency analysis algorithms for non-stationary signal has been researched. These methods are aim to improve the algorithm of Fourier transform profilometry, such as windowed Fourier transform, dilating Gabor transform and multiscale windowed Fourier transform. Then an improved window scale selection algorithm is proposed, the instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform, and the pointwise analytical window width is controlled to keep the inside signal quasi-stationary. There is a better harmonization between the frequency resolution and space (time) resolution which make it more accurate to the fundamental frequency spectrum extraction. Even if the fringe signal is polluted by noise pollution, it still gets a good reconstruction results.
Secondly, the application of improved window scale selection algorithm in time-frequency representation of non-stationary signal is researched and compared with existing time-frequency analysis algorithm applied in time-frequency representation. The result proved that the algorithm is at an advantage considering about both computational complexity and time-frequency concentration capability.
At last, the application of popular empirical mode decomposition method in denoising of optical 3-D shape measurement is researched. Optical 3-D shape measurement is vulnerable to high-frequency background noise and CCD noise. Simulation result shows that the empirical mode decomposition method is at an advantage when denoising and improving SNR.
引文
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[2]苏显渝,李继陶.信息光学[M].北京：科学出版社.1999.
[3]F. Chen, G. M. Brown, M. Song. Overview of three-dimensional shape measurement using optical methods[J]. Opt. Eng.,2000,39(l):10-22.
[4]苏显渝,李继陶.三维面形测量技术的新进展.物理,1996,25(10)：614-620.
[5]李永怀,马其波.光学三维轮廓测量技术进展.激光与红外,2005,35(3)：143-147.
[6]J. Schwider, O. Fallkenstorfer, H. Schreiber, A. Zoller, N. Streibl. New compensating four-phase algorithm for phase-shift interferometry[J]. Opt. Eng., 1993,32(8):1883-1885.
[7]Jingang Zhong, Jin Zhao. Three-dimensional shape measurement system with digitallight projector[J]. Proc SPIE,2002,4778:95-104.
[8]杜芳,查选平,李世恒.一种非接触式三维形貌测量系统的设计与应用[J].测量与设备,2005,4：12-14.
[9]钱克矛,缪泓,伍小平.一种用于动态过程测量的实时偏振相移方法[J].光学学报,2001,21(1)：64-67.
[10]J. Schmit, K. Greth. Windows function influences on phase error in phase shifting algorithm[J]. App.Opt.,1966,35(28):5462-5649.
[11]S. H. Tang, Y. Y. Huang. Fast profilometer for the automatic measurement of 3D object shapes[J]. App. Opt.,1990,29(20):3012-3018.
[12]康新,何小元.两步相移实现投影栅相位测量轮廓术.光学学报,2003,23(1)：75-79.
[13]M. Takeda, K. Mutoh. Fourier transform profilometry for the automatic measurement of 3-D object shapes[J]. App. Opt.,1983,22:3977-3982.
[14]M. Takeda. Spatial carrier fringe pattern analysis and its applications to precision interferometry and profilometry:an overview[J]. Indust Metrol,1990,1:79-99
[15]翁嘉文,钟金钢.加窗傅里叶变换在三维形貌测量中的应用[J].光子学报,2003,32(3)：993-996.
[16]付艳华,陈文静,苏显渝.窗口傅里叶变换的三维面形测量[J].激光杂志,2006,27(1)：39-41.
[17]翁嘉文,钟金钢.伸缩窗口傅里叶变换在三维形貌测量中的应用[J].光学学报,2004,24(6)：725-729.
[18]曾惠萍.基于小波脊的条纹分析技术及应用研究[D].广州：暨南大学光电工程系,2007.
[19]Jingang Zhong, Huiping Zeng. Multiscale windowed Fourier transform for phase extraction of fringe patterns[J]. Appl. Opt.,2007,46(14):2670-2675.
[20]S. G. Mallat, A Wavelet Tour of Signal Processing. Academic Press,1998.
[21]L. J. November, G. W. Simon. Precise proper-motion measurement of solar granulation[J]. Astrophysical Journal, Part 1,1988,333:427-442.
[22]J. R. Carson, T. C. Fry. Variable frequency electric circuit theory with application to the theory of frequency modulation[J]. Bell Sys. Tech. J.,1937,16:513-540.
[23]D. Gabor. Theory of communication[J]. J. IEE,1946,93:429-457.
[24]J. Ville. Theorie et applications de la notion de signal analytique[J]. Cables et Transmission,1948,2A:61-74.
[25]E. C. Titchmarsh. Introduction to the theory of Fourier integrals[M]. Oxford University Press,1948.
[26]B. A. Telfer, H. H. Szu. New Wavelet transform normalization to remove frequency bias[J]. Optical Engineering,1992,31(9):1830-1834.
[27]R. A. Carmona, W. L. Hwang, B. Torresani. Characterization of signals by the ridge of their Wavelet transforms [J]. IEEE Trans. Signal Processing,1997,45: 2586-2590.
[28]N. Delprat, B. Escudie, P. Guillemain, R. Kronland-Martinet, P. Tchamitchian, B. Torresani. Asymptotic Wavelet and Gabor analysis:extraction of instantaneous frequencies[J]. IEEE Trans. Inf. Theory,1992,38:644-664.
[29]钱云襄,刘渝.调频连续波雷达信号调制方式识别算法研究[J].数据采集与处理,2005,20(3)：272-276.
[30]周浩,文必洋,吴世才,马志刚.基于时频分析的高频雷达目标检测与定向[J].电子学报,2005,33(12)：2265-226.
[31]孔凡让,朱忠奎,羊拯民,赵吉文,李晓峰,王建平.信号的小波尺度——频率表示及在机械故障诊断中的应用[J].振动与冲击,2003,22(4)：20-24.
[32]胡劲松,杨世锡,吴昭同,严拱标.旋转机械振动信号基于EMD的HT和STFT时频分析比较[J].汽轮机技术,2002,44(6)：336-338.
[33]张细致.一种新的基于时频分析扩频通信去干扰技术[J].湖南工程学院学报,2004,14(4)：50-54.
[34]茹乐,杜兴民,毕笃彦.STFT与SOPC技术相结合实现高速跳频图案的识别与跟踪[J].电讯技术,2005,1：40-44.
[35]J. Gutierrez, R. Alcantara, V. Medina. Analysis and localization of epileptic events using Wavelet packets[J]. Med. Eng. Phys.,2001,23:623-631.
[36]朱冰莲,杨磊.心音信号的短时傅立叶变换分析[J].重庆大学学报,2004,27(8)：83-85.
[37]M. Portnoff. Time-frequency representation digital signals and systems based on short-time Fourier analysis[J]. IEEE Trans. Acoustics, Speech and Signal Processing,1980,28:55-69.
[38]M. Portnoff. Short-time Fourier analysis of sampled speech[J]. IEEE Trans. Acoustics, Speech and Signal Processing,1981,29:364-373.
[39]I. Daubechies. The Wavelet transform, time-frequency localization and signal analysis[J]. IEEE Trans. Inf. Theory,1990,36:961-1005.
[40]T. A. C. M. Claasen, W. F. G. Mecklenbrauker. The Wigner distribution-a tool for time-frequency signal analysis, Part Ⅰ:Continuous-time signals[J]. Philip J. Res., 1980,35(3):217-250.
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