电子散斑干涉条纹图和相位图滤波方法的应用研究
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摘要
电子散斑干涉测量(Electronic speckle pattern interferometery简写为ESPI)是一种全场非破坏性光学测量技术,广泛应用于光学粗糙表面的变形测量和无损检测。准确地提取相位在应用ESPI获得物体变形位移信息中起着非常重要的作用。然而,通常实验获得的相位图在很大程度上受到噪声的影响,所以滤波方法的研究就变得很重要了。本文针对电子散斑条纹图和相位图的滤波方法进行了研究。
首先本文将改进的偏微分方程滤波方法应用在电子散斑条纹图上。然后,根据电子散斑相位图的特性,在滤波的过程既要去除噪声又要保持相位跳变信息,本文将偏微分方程滤波方法与正余弦滤波法相结合,应用于电子散斑相位图去噪。
本文把最小二乘拟合的思想加入到相位图滤波上,提出了一种有效的滤波方法:切线方向的最小二乘相位图滤波法。改进的相位图滤波方法具有以下几个优点:第一,本算法适用性强,可以应用在由各种方法得到的散斑相位图噪声去除上;第二,本算法可以根据图像噪声大小的情况进行迭代次数的选择;第三,根据相位条纹图的条纹形状,本算法中滤波窗口可以选取竖直方向的矩形窗口或正方形窗口。为了达到更好的滤波效果,对于条纹比较稠密的相位图,可以在沿条纹切线方向的窗口中进行平滑处理,可以有效的避免条纹模糊现象的发生。而对于条纹稀疏的相位图,可以在计算过程中采取串行计算:对于一幅图像,逐个像素点进行运算,得到滤波后的相位值,并立即更新原图像当前点的相位值,这样可以提高算法的平滑效率。本算法是一种行之有效的相位图滤波算法,具有较高的实用价值。
Electronic speckle pattern interferometry (ESPI) is a nondestructive, whole-field optical measurement technique. It is a well-known technique for deformed and nondestructive measurement of optical coarse surface. Accurate extraction of phase value is of fundamental importance for the successful application of ESPI in obtaining of the displacement. However, generally the resulting phase patterns are very noisy. Therefore, the phase pattern filtering method is very important to obtain precisely displacement information. In this paper, we put emphasis on discussing the filtering algorithm for fringes patterns and phase patterns.
First, we apply the improved PDE image filtering methods to the ESPI fringe patterns. Then, according to the property of ESPI phase fringe pattern, we should reduce noise as well as preserve the phase jump in the filtering process. We apply the improved PDE image filtering methods to the ESPI phase patterns combined with the sine/cosine filtering method.
The idea of Least-squares fitting is added to filtering method for phase pattern, and an effective filtering method is presented- The tangent Least-squares fitting filtering method. The improved filtering method has three advantages. First, this method has good applicability, it is suitable for all phase maps obtained by any technique; Second, this method can be repeated according to the noise level; Third, according to the shape of fringes, the small filtering window can be either rectangle or square along vertical direction. To obtaining better filtering effect, we establish filtering windows along the tangent direction of phase fringe pattern for dense fringes. For the phase patterns with sparse fringes, serial processing can be taken: for a picture of image, the calculation is carried out pixel-by-pixel, and the phase value of current pixel in original image renew immediately. The adoption of serial processing can improve the smoothing efficiency. The validity of the method is demonstrated and it is valuable for ESPI phase patterns.
首先本文将改进的偏微分方程滤波方法应用在电子散斑条纹图上。然后,根据电子散斑相位图的特性,在滤波的过程既要去除噪声又要保持相位跳变信息,本文将偏微分方程滤波方法与正余弦滤波法相结合,应用于电子散斑相位图去噪。
本文把最小二乘拟合的思想加入到相位图滤波上,提出了一种有效的滤波方法:切线方向的最小二乘相位图滤波法。改进的相位图滤波方法具有以下几个优点:第一,本算法适用性强,可以应用在由各种方法得到的散斑相位图噪声去除上;第二,本算法可以根据图像噪声大小的情况进行迭代次数的选择;第三,根据相位条纹图的条纹形状,本算法中滤波窗口可以选取竖直方向的矩形窗口或正方形窗口。为了达到更好的滤波效果,对于条纹比较稠密的相位图,可以在沿条纹切线方向的窗口中进行平滑处理,可以有效的避免条纹模糊现象的发生。而对于条纹稀疏的相位图,可以在计算过程中采取串行计算:对于一幅图像,逐个像素点进行运算,得到滤波后的相位值,并立即更新原图像当前点的相位值,这样可以提高算法的平滑效率。本算法是一种行之有效的相位图滤波算法,具有较高的实用价值。
Electronic speckle pattern interferometry (ESPI) is a nondestructive, whole-field optical measurement technique. It is a well-known technique for deformed and nondestructive measurement of optical coarse surface. Accurate extraction of phase value is of fundamental importance for the successful application of ESPI in obtaining of the displacement. However, generally the resulting phase patterns are very noisy. Therefore, the phase pattern filtering method is very important to obtain precisely displacement information. In this paper, we put emphasis on discussing the filtering algorithm for fringes patterns and phase patterns.
First, we apply the improved PDE image filtering methods to the ESPI fringe patterns. Then, according to the property of ESPI phase fringe pattern, we should reduce noise as well as preserve the phase jump in the filtering process. We apply the improved PDE image filtering methods to the ESPI phase patterns combined with the sine/cosine filtering method.
The idea of Least-squares fitting is added to filtering method for phase pattern, and an effective filtering method is presented- The tangent Least-squares fitting filtering method. The improved filtering method has three advantages. First, this method has good applicability, it is suitable for all phase maps obtained by any technique; Second, this method can be repeated according to the noise level; Third, according to the shape of fringes, the small filtering window can be either rectangle or square along vertical direction. To obtaining better filtering effect, we establish filtering windows along the tangent direction of phase fringe pattern for dense fringes. For the phase patterns with sparse fringes, serial processing can be taken: for a picture of image, the calculation is carried out pixel-by-pixel, and the phase value of current pixel in original image renew immediately. The adoption of serial processing can improve the smoothing efficiency. The validity of the method is demonstrated and it is valuable for ESPI phase patterns.
引文
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[5] S.H. Baik, S.K. Park, C.J. Kim, et al, Two-channel spatial phase shifting electronic speckle pattern interferometer, Opt. Commun., 2001, 192:205~211
[6] C.J. Tay, C. Quan, L. Chen, et al, Phase extraction from electronic speckle patterns by statistical analysis, Opt. Commun., 2004, 236:259~269
[7] M. Takeda, H. Ina, and S. Kobayashi, Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry, J. Opt. Soc. Am.,1982, 72: 156~160
[8] T. Kreis, Digital holographic interference-phase measurement using the Fourier-transform method, J. Opt. Soc. Am. A, 1986, 3: 847~855
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[10] K.H. Womack, Interferometric phase measurement using spatial synchronous detection, Opt. Eng., 1984, 23: 391~395
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[12] M. Servin, J.L. Marroquin and F.J. Cuevas, Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms, J. Opt. Soc. Am. A, 2001, 18: 689~695
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[17] Su X Y, Bally G V, Vakicevic D, Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation, Opt. Common., 1993, 98: 141~150
[18] Aoki T, Sotomaru T., Two-dimension phase unwrapping by direct elimination of rotational vector fields from phase gradient, obtained by heterodyne techniques, Pro. SPIE, 1998, 3 478: 162~169
[19] 惠梅,邓年茂,王东生等,基于跳变线估测的相位包裹去除法,光电子·激光,2003,14 (7): 745~748
[20] 刘晓军,章明,高永生等.基于图像分析技术的实用相位恢复去包裹技术,光学技术,2000, 26 (4): 358~360
[21] 贾书海,姜虹,乐开端等,一种去包裹误差校正法及其在ESPI中的应用,半导体光电,2000, 21 (1): 20~23
[22] 康新,何小元,Quan C.,基于正弦条纹投影的三维传感及其去包裹处理,光学学报,200l, 21 (12): 1444~1447
[23] 陶 刚,李喜德,时间序列散斑干涉场中相位函数的计算,光学学报,2001,21 (10): l203~1207
[24] C. K. Hong, H. S. Ryu, and H. C. Lim, Least-squares fitting of the phase map obtained in phase-shifting electronic speckle pattern interferometry, Opt. Lett., 1995, 20: 931~933
[25] H.S. Ryu and C.K. Hong, Maximum-likelihood phase estimation in phase-shifting electronic speckle pattern interferometry, J. Opt. Soc. Am. A, 1997, 14: 1051~1057
[26] H.Y. Yun, C.K. Hong, and S.W. Chang, Least-squares phase estimation with multiple parameters in phase-shifting electronic speckle pattern interferometry, J. Opt. Soc. Am. A, 2003, 20: 240~247
[27] Wang Feng, Prinet Veronique, and Ma Sonede, A vector filtering technique for SAR interferometric phase image, The IASTED International Symposia on Applied Informatics: Artificial Intelligence and Application, Advances in Computer Applications, 2001, 566~570
[28] H. A. Aebischer and S. Waldner, A simple and effective method for filtering speckle-interferometric phase fringe patterns, Opt. Commun., 1999, 162: 205~210
[29] D. Gabor, Information theory in electron microscopy, Lab. Invest., 1965, 14:801~807
[30] J.J. Koenderink, The structure of images, Biol. Cyber., 1984, 50: 363~370
[31] A. P. Witkin, Scale-space filtering, Proceedings of the International Joint Conference on Artificial Intelligence, ACM Inc. 1983, 1019~1021
[32] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE TPAMI., 1990, 12: 629~639
[33] F. Catté, P.-L. Lions, J.-M. Morel, et al, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 1992, 29: 182~193
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[35] L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 1992, 60: 259 ~268
[36] M. Lysaker, A. Lundervold and X.-C. Tai., Noise removal using a fourth-order PDE with application to MRI in space and time, IEEE Transactions on image processing, 2003, 12: 1579~1590
[37] Y.-L. You and M. Kaveh, Fourth-order partial differential equation for noise removal, IEEE Transactions on Image Processing, 2000, 9: 1723~1730
[38] T. Chan, A. Marquina and P. Mulet, High-order total variation-based image restoration, SIAM Journal on Scientific Computing, 2000, 22: 503 ~516
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