基于小波阈值去噪的偏振模色散测量
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摘要
针对固定分析仪法在测量光纤偏振模色散时会引入误差、降低测量精度这一问题,提出了一种基于小波阈值的去噪方案,以提升固定分析仪法的测量精度。给出了算法的具体流程,并详细讨论了小波阈值、阈值函数、基函数以及分解层数的选取原则及方案。搭建了实验平台并进行测定,将测定结果与常用的傅里叶变换法及商用的偏振模色散测量仪的测量结果进行对比。实验结果表明,所提出的小波阈值去噪方案能够有效地降低噪声对测量结果的影响,且对于不同类型、不同长度的测试光纤样本均适用。以商用仪器的测量结果为参考,本方案测量结果的最大误差为2.27%,该数据表明本方案显著提升了固定分析仪法测量偏振模色散的精度。
The fixed analyzer method commonly used for measuring the polarization mode dispersion of optical fibers can introduce errors and reduce measurement accuracy, and thus a novel scheme based on wavelet threshold denoising is proposed to further improve the measurement accuracy. The specific workflow of the scheme is presented and the selection principle and scheme of wavelet threshold, threshold function, mother wavelet and wavelet decomposition layer number are discussed in detail. An experimental platform is built and the measurement is conducted. The measurement results are compared with those by the commonly used Fourier transform method and commercial polarization mode dispersion measurement instruments. The experimental results show that the proposed wavelet threshold denoising scheme can be used to effectively reduce the impact of noises on the measurement results and is also suitable for different types and lengths of test fiber samples. If the measurement results by commercial instruments are taken as the reference standard, the maximum error by the proposed scheme is 2.27%, which indicates the polarization mode dispersion measurement accuracy by the fixed analyzer method is significantly enhanced.
The fixed analyzer method commonly used for measuring the polarization mode dispersion of optical fibers can introduce errors and reduce measurement accuracy, and thus a novel scheme based on wavelet threshold denoising is proposed to further improve the measurement accuracy. The specific workflow of the scheme is presented and the selection principle and scheme of wavelet threshold, threshold function, mother wavelet and wavelet decomposition layer number are discussed in detail. An experimental platform is built and the measurement is conducted. The measurement results are compared with those by the commonly used Fourier transform method and commercial polarization mode dispersion measurement instruments. The experimental results show that the proposed wavelet threshold denoising scheme can be used to effectively reduce the impact of noises on the measurement results and is also suitable for different types and lengths of test fiber samples. If the measurement results by commercial instruments are taken as the reference standard, the maximum error by the proposed scheme is 2.27%, which indicates the polarization mode dispersion measurement accuracy by the fixed analyzer method is significantly enhanced.
引文
[1] Zhang X G. Polarization mode dispersion in fiber principle, measurement, and adaptive compensation[M]. Beijing: Beijing University of Posts and Telecommunications Press, 2017. 张晓光. 光纤偏振模色散原理、测量与自适应补偿技术[M]. 北京: 北京邮电大学出版社, 2017.
[2] Gordon J P, Kogelnik H. PMD fundamentals: polarization mode dispersion in optical fibers[J]. Proceedings of the National Academy of Sciences of the United States of America, 2000, 97(9): 4541-4550.
[3] Pan P, Xi L X, Zhang X G, et al. Experimental research on polarization mode dispersion measurement based on empirical mode decomposition[J]. Chinese Journal of Lasers, 2018, 45(1): 0106002. 潘潘, 席丽霞, 张晓光, 等. 基于经验模态分解的偏振模色散测量实验研究[J]. 中国激光, 2018, 45(1): 0106002.
[4] Xu H Y, Zhang X G, Tang X F, et al. Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second order for flexible receivers[J]. IEEE Photonics Journal, 2017, 9(6): 1-15.
[5] Donoho D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3): 613-627.
[6] Hui R, O′Sullivan M S. Fiber optic measurement techniques[M]. Netherlands: Academic Press/Elsevier, 2009: 495-510.
[7] Xi L X, Zhang X G, Yu L, et al. Techniques of adaptive compensation for two-second polarization mode dispersion[J]. Journal of Optoelectronics·Laser, 2004, 15(8): 924-928. 席丽霞, 张晓光, 于丽, 等. 二阶偏振模色散自适应补偿的关键技术[J]. 光电子·激光, 2004, 15(8): 924-928.
[8] Tian F, Xi L X, Zhang X F, et al. An experiment of PMD compensation in 40-Gb/s PSBT transmission system[J]. Chinese Optics Letters, 2010, 8(9): 816-818.
[9] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients[J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3445-3462.
[10] Liu L, Yu M, Yang R J, et al. Wavelet denoising applied in optical fiber Raman temperature sensor system[J]. Chinese Journal of Lasers, 2013, 40(6): 0605005. 刘磊, 于淼, 杨瑞娟, 等. 小波去噪用于光纤拉曼温度传感系统[J]. 中国激光, 2013, 40(6): 0605005.
[11] Song X D, Zhou C K, Hepburn D M, et al. Second generation wavelet transform for data denoising in PD measurement[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2007, 14(6): 1531-1537.
[12] Wang H Y, Lang Y, Han H H, et al. Denoising algorithm of express way floating car data based on wavelet threshold[J]. Transactions of Beijing Institute of Technology, 2017, 37(7): 717-720, 770. 汪宏宇, 郎莹, 韩海花, 等. 基于小波阈值的浮动车数据消噪算法[J]. 北京理工大学学报, 2017, 37(7): 717-720, 770.
[13] Hou H H, Gui Z G. Denoising processing of ECG signal based on wavelet entropy[J]. Chinese Journal of Biomedical Engineering, 2010, 29(1): 22-28, 34. 侯宏花, 桂志国. 基于小波熵的心电信号去噪处理[J]. 中国生物医学工程学报, 2010, 29(1): 22-28, 34.
[14] Daamouche A, Hamami L, Alajlan N, et al. A wavelet optimization approach for ECG signal classification[J]. Biomedical Signal Processing and Control, 2012, 7(4): 342-349.
[15] Sun Z, Chang C C. Structural damage assessment based on wavelet packet transform[J]. Journal of Structural Engineering, 2002, 128(10): 1354-1361.
[16] Xu K, Xie S Z. PMD in high bitrate optical fiber communications and its compensation technology[J]. Semiconductor Optoelectronics, 2000, 21(1): 1-5. 徐坤, 谢世钟. 高速光纤通信中的偏振模色散及其补偿技术[J]. 半导体光电, 2000, 21(1): 1-5.
[2] Gordon J P, Kogelnik H. PMD fundamentals: polarization mode dispersion in optical fibers[J]. Proceedings of the National Academy of Sciences of the United States of America, 2000, 97(9): 4541-4550.
[3] Pan P, Xi L X, Zhang X G, et al. Experimental research on polarization mode dispersion measurement based on empirical mode decomposition[J]. Chinese Journal of Lasers, 2018, 45(1): 0106002. 潘潘, 席丽霞, 张晓光, 等. 基于经验模态分解的偏振模色散测量实验研究[J]. 中国激光, 2018, 45(1): 0106002.
[4] Xu H Y, Zhang X G, Tang X F, et al. Joint scheme of dynamic polarization demultiplexing and PMD compensation up to second order for flexible receivers[J]. IEEE Photonics Journal, 2017, 9(6): 1-15.
[5] Donoho D L. De-noising by soft-thresholding[J]. IEEE Transactions on Information Theory, 1995, 41(3): 613-627.
[6] Hui R, O′Sullivan M S. Fiber optic measurement techniques[M]. Netherlands: Academic Press/Elsevier, 2009: 495-510.
[7] Xi L X, Zhang X G, Yu L, et al. Techniques of adaptive compensation for two-second polarization mode dispersion[J]. Journal of Optoelectronics·Laser, 2004, 15(8): 924-928. 席丽霞, 张晓光, 于丽, 等. 二阶偏振模色散自适应补偿的关键技术[J]. 光电子·激光, 2004, 15(8): 924-928.
[8] Tian F, Xi L X, Zhang X F, et al. An experiment of PMD compensation in 40-Gb/s PSBT transmission system[J]. Chinese Optics Letters, 2010, 8(9): 816-818.
[9] Shapiro J M. Embedded image coding using zerotrees of wavelet coefficients[J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3445-3462.
[10] Liu L, Yu M, Yang R J, et al. Wavelet denoising applied in optical fiber Raman temperature sensor system[J]. Chinese Journal of Lasers, 2013, 40(6): 0605005. 刘磊, 于淼, 杨瑞娟, 等. 小波去噪用于光纤拉曼温度传感系统[J]. 中国激光, 2013, 40(6): 0605005.
[11] Song X D, Zhou C K, Hepburn D M, et al. Second generation wavelet transform for data denoising in PD measurement[J]. IEEE Transactions on Dielectrics and Electrical Insulation, 2007, 14(6): 1531-1537.
[12] Wang H Y, Lang Y, Han H H, et al. Denoising algorithm of express way floating car data based on wavelet threshold[J]. Transactions of Beijing Institute of Technology, 2017, 37(7): 717-720, 770. 汪宏宇, 郎莹, 韩海花, 等. 基于小波阈值的浮动车数据消噪算法[J]. 北京理工大学学报, 2017, 37(7): 717-720, 770.
[13] Hou H H, Gui Z G. Denoising processing of ECG signal based on wavelet entropy[J]. Chinese Journal of Biomedical Engineering, 2010, 29(1): 22-28, 34. 侯宏花, 桂志国. 基于小波熵的心电信号去噪处理[J]. 中国生物医学工程学报, 2010, 29(1): 22-28, 34.
[14] Daamouche A, Hamami L, Alajlan N, et al. A wavelet optimization approach for ECG signal classification[J]. Biomedical Signal Processing and Control, 2012, 7(4): 342-349.
[15] Sun Z, Chang C C. Structural damage assessment based on wavelet packet transform[J]. Journal of Structural Engineering, 2002, 128(10): 1354-1361.
[16] Xu K, Xie S Z. PMD in high bitrate optical fiber communications and its compensation technology[J]. Semiconductor Optoelectronics, 2000, 21(1): 1-5. 徐坤, 谢世钟. 高速光纤通信中的偏振模色散及其补偿技术[J]. 半导体光电, 2000, 21(1): 1-5.