基于奇异值分解的光子相关光谱滤波方法研究
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摘要
针对光子相关光谱颗粒测量法在测量超细纳米颗粒时,容易受噪声影响,导致拟合误差较大的问题,提出了一种基于奇异值分解的光子相关光谱滤波方法。其处理步骤为:利用颗粒系的光强自相关函数数据构造Hankel矩阵H;对矩阵进行奇异值分解;根据奇异值的大小分布,确定噪声级别和重建参数r;从重建矩阵H1中提取经滤波后的光强自相数据,再通过传统方法进行拟合,得到颗粒的粒径分布。实验中采用30nm标准乳胶球单分散颗粒系,以及30nm和100nm标准乳胶球双分散颗粒系进行实验对比。结果证明:基于奇异值分解的光子相关光谱滤波法有效地提高了测量准确性。
During the measurement of the ultrafine nanoparticles' s size with the method of PCS(Photon Correlation Spectroscopy),the fitting results are always susceptible to the noise and have quite large errors.To solve the problem, the filtering algorithm of photon correlation spectroscopy based on singular value decomposition is proposed.Its procedure is:the Hankel matrix H with the intensity autocorrelation data is constructed;the singular value decomposition of His calculated;the reconstruction parameters r with the singular value of H are determined;the filtered light intensity autocorrelation data from the reconstruction matrix H1 are extrac-ted,and fitting with the traditional method,and then the particle size distribution is obtained.The experiment is carried out in two different particle dispersions,one is 30nm standard monodisperse latex particle dispersion,and another is 30nm and 100nm standard double dispersion latex particle dispersion.The results show that,the filtering algorithm of photon correlation spectroscopy based on singular value decomposition can improve the measurement accuracy effectively.
During the measurement of the ultrafine nanoparticles' s size with the method of PCS(Photon Correlation Spectroscopy),the fitting results are always susceptible to the noise and have quite large errors.To solve the problem, the filtering algorithm of photon correlation spectroscopy based on singular value decomposition is proposed.Its procedure is:the Hankel matrix H with the intensity autocorrelation data is constructed;the singular value decomposition of His calculated;the reconstruction parameters r with the singular value of H are determined;the filtered light intensity autocorrelation data from the reconstruction matrix H1 are extrac-ted,and fitting with the traditional method,and then the particle size distribution is obtained.The experiment is carried out in two different particle dispersions,one is 30nm standard monodisperse latex particle dispersion,and another is 30nm and 100nm standard double dispersion latex particle dispersion.The results show that,the filtering algorithm of photon correlation spectroscopy based on singular value decomposition can improve the measurement accuracy effectively.
引文
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[10]叶天语.基于方差的奇异值分解域鲁棒零水印算法[J].光子学报,2011,40(6):961—966.Ye T Y.A Robust zero-watermarking algorithm using variance in singular value decomposition domain[J].Acta Photonica Sinica,2011,40(6):961—966.
[11]梁毅雄,龚卫国,潘英俊,等.基于奇异值分解的人脸识别方法[J].光学精密工程,2004,12(5):543—549.Liang Y X,Gong W G,Pan Y J,et al.Singular value decomposition-based approach for face recognition[J].Optics and Precision Engineering,2004,12(5):543—549.
[12]Hall P,Marshall D,Martin R.Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition[J].Image and Vision Computing,2002,20(13):1009—1016.
[13]Graves E E,Culver J P,Ripoll J,et al.Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography[J].Journal of Optical Society of America,2004,21(2):231—241.
[14]Berenguer L,Dufaud T,Tromeur-Dervout D.Aitken’s acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems[J].Computers&Fluids,2013,80(10):320—326.
[15]Brookhaven Instruments Corporation.Instruction manual for BI-9000AT digital autocorrelator[R].New York:Holtsville,1998:IX12—IX16.
[2]Berne B J,Pecora R.Dynamic light scattering with applications to chemistry[J].Biology and Physics,Willey-Interscience,New York,1976.
[3]Yang H,Zheng G,Li M C,et al.A discussion of noise in dynamic light scattering for particle sizing[J].Part.Part.Syst.Charact.,2009,25(5-6):406—413.
[4]杨晖,郑刚,张荣福,等.基于偏振门的动态光散射颗粒测量法的研究[J].光学技术,2010,36(3):415—419.Yang H,Zheng G,Zhang R F,et al.Study on the method of particle sizing by dynamic light scattering based on polarization gating[J].Optical Technique,2010,36(3):415—419.
[5]Scheffold F,Cerbino R.New trends in light scattering[J].Current Opinion in Colloid&Interface Science,2007,12:50—57.
[6]杨晖,郑刚,张荣福,等.用LabVIEW实现基于光子计数的动态光散射系统[J].光子学报,2007,36(1):170—173.Yang H,Zheng G,Zhang R F,et al.Dynamic light scattering system based on photon counting developed by LabVIEW[J].Acta Photonica Sinica,2007,36(1):170—173.
[7]程坤,赵军普,胡东霞,等.基于光限幅效应时域滤波的分析[J].激光与光电子学进展,2011,48:101901.1—101901.7.Cheng K,Zhao J P,Hu D X,et al.Analysis of time domain filtering based on optical limiting effect[J].Laster&Optoelectronics Progress,2011,48:101901.1—101901.7.
[8]何宇航,曹益平,钟立俊,等.采用频域滤波提高数字相位测量轮廓术的测量精度[J].中国激光,2010,37(1):220—224.He Y H,Cao Y P,Zhong L J,et al.Improvement on measuring accuracy of digital phase measuring profilometry by frequency filtering[J].Chinese Journal of Lasers,2010,37(1):220—224.
[9]罗胜恩,罗来源,苑小华,等.频域滤波算法的幅相失真分析及抑制方法[J].数据采集与处理,2010,25(S):51—55.Luo S E,Luo L Y,Yuan X H,et al.Analysis and suppression of amplitude-phase distortion for frequency domain filtering algorithm[J].Journal of Data Acquisition and Processing,2010,25(S):51—55.
[10]叶天语.基于方差的奇异值分解域鲁棒零水印算法[J].光子学报,2011,40(6):961—966.Ye T Y.A Robust zero-watermarking algorithm using variance in singular value decomposition domain[J].Acta Photonica Sinica,2011,40(6):961—966.
[11]梁毅雄,龚卫国,潘英俊,等.基于奇异值分解的人脸识别方法[J].光学精密工程,2004,12(5):543—549.Liang Y X,Gong W G,Pan Y J,et al.Singular value decomposition-based approach for face recognition[J].Optics and Precision Engineering,2004,12(5):543—549.
[12]Hall P,Marshall D,Martin R.Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition[J].Image and Vision Computing,2002,20(13):1009—1016.
[13]Graves E E,Culver J P,Ripoll J,et al.Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography[J].Journal of Optical Society of America,2004,21(2):231—241.
[14]Berenguer L,Dufaud T,Tromeur-Dervout D.Aitken’s acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems[J].Computers&Fluids,2013,80(10):320—326.
[15]Brookhaven Instruments Corporation.Instruction manual for BI-9000AT digital autocorrelator[R].New York:Holtsville,1998:IX12—IX16.