基于散射光信号分形的亚微米及纳米颗粒测量技术研究
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摘要
具有表面效应、小尺寸效应和宏观量子隧道效应的亚微米及纳米颗粒表现出电、磁、光、声、热等方面的特性,在化工、医学、国防等领域被广泛应用,因而亚微米及纳米颗粒的测量具有重要的意义。目前,广泛使用的测量纳米颗粒的方法是光子相关光谱颗粒测量技术,该技术对实验条件要求较高、相应的测量仪器价格昂贵,一般用于研究领域。在亚微米及纳米材料制备行业,迫切需要一种低成本、测量方法简洁的快速颗粒测量方法。本文针对这一需求,进行了基于散射光信号分形的亚微米及纳米颗粒测量技术研究,主要研究工作如下:
一、基于颗粒测量的光散射理论分析了颗粒散射光的波动特征,研究了颗粒散射光信号的分形表征。
二、基于对测量装置结构参数的分析,研制了基于散射光信号分形的颗粒测量装置,并针对该测量方法对温度恒定性的特殊要求,研制了样品池温度控制器。
三、分别在18、20、22、24、26、28、30℃温度下,对60、90、200、300、450nm标准聚苯乙烯颗粒进行了实验,计算了颗粒散射光信号的分形维数,研究了温度对分形维数的影响。研究结果表明,分形维数不但与颗粒粒径有关,而且与温度有关。颗粒粒径相同时,温度越高,分形维数越大。
四、对不同温度下颗粒散射光信号的分形维数进行拟合,得到了在18℃到30℃(间隔0.1℃)温度下标准聚苯乙烯颗粒(粒径从50nm到480nm,间隔1nm)粒径与分形维数的对应关系。
五、在26℃温度下,分别取采样点个数为512、1024、2048、4096、8192、16384、32768、65536,对60、90、200、300、450nm颗粒进行了测量。测量结果表明,当采样点数不小于16384时,颗粒测量结果的重复性和相对误差满足小于2%的要求。
六、利用该测量方法,分别在18、20、22、24、26、28、30℃温度下,对60、90、200、300、450nm颗粒进行了实测,对测量结果的重复性和相对误差进行了分析,并就测量方法的特点与光子相关光谱颗粒测量方法进行了比较。
与光子相关光谱颗粒测量技术相比,基于散射光信号分形的亚微米及纳米颗粒测量技术具有测量装置成本低、所需的采样数据量小、数据处理方法简洁且易于实现在线测量等优点。
With the special characters in electrics, magnetic, photics and acoustics, submicron and nanometer particle has wide applications in many fields such as chemical, medicine, national defense, etc, so the measurement is very important. Currently, the Photon Correlation Spectroscopy (PCS) is the widely used measurement, but the equipment is expensive, and it is used in research generally. In the industry of the preparation of nanometer particle, the measurement is the urgent needed which is low-cost, simple and speeded. This dissertation studied on the measurement of submicron and nanometer particle based on the fractal of scattering light signal, the main researches are as following:
1. Based on light scattering theory, the fluctuation of the scattered light was analyzed and the fractal characterization of the scattering light signal was investigated.
2. Based on the analysis of structural parameters, a particle sizing apparatus was developed, and a temperature control device was designed to meet constant temperature requirement of the sample cell.
3. Experiments with particles of different diameters were carried out under 18,20,22,24,26,28,30℃, the fractal dimensions of scattering light signal were computed, and the influences of temperature were researched. Conclusion can be obtained that the higher the temperature, the bigger the fractal dimensions for particles of the same diameter.
4. The corresponding relationship of diameters from 50nm to 480nm and fractal dimension under temperatures from 18℃to 30℃was acquired.
5. When the temperature was 26℃, particles with different diameters were measured with sampling points of 512,1024,2048,4096,8192,16384,32768,65536. And the results indicated that when the sampling points are more than 16384, the repeatability and relative error of the results were smaller than 2%.
6. Particles with different diameters were measured when the temperature were 18、20、22、24、26、28、30℃, the repeatability and relative error of the results were analyzed. And finally this measuring method was compared with the PCS.
Compared with PCS, the measurement which this dissertation studied is low-cost, its amount of sample data is small, the data processing method is simple, and it is easy to realize on-line measurement.
一、基于颗粒测量的光散射理论分析了颗粒散射光的波动特征,研究了颗粒散射光信号的分形表征。
二、基于对测量装置结构参数的分析,研制了基于散射光信号分形的颗粒测量装置,并针对该测量方法对温度恒定性的特殊要求,研制了样品池温度控制器。
三、分别在18、20、22、24、26、28、30℃温度下,对60、90、200、300、450nm标准聚苯乙烯颗粒进行了实验,计算了颗粒散射光信号的分形维数,研究了温度对分形维数的影响。研究结果表明,分形维数不但与颗粒粒径有关,而且与温度有关。颗粒粒径相同时,温度越高,分形维数越大。
四、对不同温度下颗粒散射光信号的分形维数进行拟合,得到了在18℃到30℃(间隔0.1℃)温度下标准聚苯乙烯颗粒(粒径从50nm到480nm,间隔1nm)粒径与分形维数的对应关系。
五、在26℃温度下,分别取采样点个数为512、1024、2048、4096、8192、16384、32768、65536,对60、90、200、300、450nm颗粒进行了测量。测量结果表明,当采样点数不小于16384时,颗粒测量结果的重复性和相对误差满足小于2%的要求。
六、利用该测量方法,分别在18、20、22、24、26、28、30℃温度下,对60、90、200、300、450nm颗粒进行了实测,对测量结果的重复性和相对误差进行了分析,并就测量方法的特点与光子相关光谱颗粒测量方法进行了比较。
与光子相关光谱颗粒测量技术相比,基于散射光信号分形的亚微米及纳米颗粒测量技术具有测量装置成本低、所需的采样数据量小、数据处理方法简洁且易于实现在线测量等优点。
With the special characters in electrics, magnetic, photics and acoustics, submicron and nanometer particle has wide applications in many fields such as chemical, medicine, national defense, etc, so the measurement is very important. Currently, the Photon Correlation Spectroscopy (PCS) is the widely used measurement, but the equipment is expensive, and it is used in research generally. In the industry of the preparation of nanometer particle, the measurement is the urgent needed which is low-cost, simple and speeded. This dissertation studied on the measurement of submicron and nanometer particle based on the fractal of scattering light signal, the main researches are as following:
1. Based on light scattering theory, the fluctuation of the scattered light was analyzed and the fractal characterization of the scattering light signal was investigated.
2. Based on the analysis of structural parameters, a particle sizing apparatus was developed, and a temperature control device was designed to meet constant temperature requirement of the sample cell.
3. Experiments with particles of different diameters were carried out under 18,20,22,24,26,28,30℃, the fractal dimensions of scattering light signal were computed, and the influences of temperature were researched. Conclusion can be obtained that the higher the temperature, the bigger the fractal dimensions for particles of the same diameter.
4. The corresponding relationship of diameters from 50nm to 480nm and fractal dimension under temperatures from 18℃to 30℃was acquired.
5. When the temperature was 26℃, particles with different diameters were measured with sampling points of 512,1024,2048,4096,8192,16384,32768,65536. And the results indicated that when the sampling points are more than 16384, the repeatability and relative error of the results were smaller than 2%.
6. Particles with different diameters were measured when the temperature were 18、20、22、24、26、28、30℃, the repeatability and relative error of the results were analyzed. And finally this measuring method was compared with the PCS.
Compared with PCS, the measurement which this dissertation studied is low-cost, its amount of sample data is small, the data processing method is simple, and it is easy to realize on-line measurement.
引文
[1] 张立德. 纳米材料的主要应用领域[J]. 中国科技月报,2001,(1):7-9
[2] 管映亭,金志浩,董政娥. 纳米材料及其在纺织等领域中的应用[J]. 纺织学报,2004,25(3):116-118
[3] 马建中,储芸,高党鸽. 我国纳米生物技术的医学应用及研究进展[J]. 中国医学科学院学报,2006,28(4):579-582
[4] 王学船,任龙芳,强涛涛. 纳米材料在化妆品中的应用[J]. 日用化学品科学,2006,29(4):15-18
[5] 赵树朋,杨玉瑛,屈平,张世芳,李久熙,高喜银. 纳米技术在农业工程中的应用[J]. 农机化研究,2006,(2):119-120
[6] http://www.ocn.com.cn/reports/2006082nami.htm
[7] 张立德. 我国纳米产业面临的新转折和挑战[J]. 新材料产业,2005,(10):48-51
[8] 王乃宁. 颗粒粒径的光学测量技术及应用[M]. 北京:原子能出版社,2000 年
[9] 王书运. 纳米颗粒的测量与表征[J]. 微纳电子技术,2005,(01)
[10] http://erran.blogerhome.com/135461.shtml
[11] http://www.bak.com.cn/cn/xinxi-bakyuekan-xiangxi.asp?id=365
[12] Krishnomurti, P. Studies in X-Ray Diffraction. Part1: The Structure of Amorphous Scattering. Part2: Colloidal Solutions and Liquid Mixtures [J]. Indian J. Phys., 1930, (5): 473-500
[13] Warren, B. E. X-Ray Diffraction Study of Carbon Black [J]. Chem. Phys. 1934, (2): 551-555
[14] Kratky, O., & Porod, G. Diffuse Small-Angle Scattering of X-Rays in Colloid Systems[J]. Colloid Sci., 1949, (4): 35-70
[15] Guinier, A. Study of Catalysts by Scattering of X-Rays at Small Angles[J]. Discussions Faraday Soc., 1950, (8): 344-347
[16] Guinier, A. & Fournet G. Small-Angle Scattering of X-Rays[M]. New York: John Wiley, 1955
[17] Hosemann, R., & Bagchi, S. N. The Interference Theory of Ideal Paracrystals[J]. Acta Cryst.,1952 ,(5):612-614
[18] Debye, P. & Bueche, A. M. Scattering by an Inhomogeneous Solid[J]. Appl. Phys., 1949, (20):518-525
[19] Porod, G. X-Ray and Light Scattering by Chain Molecules in Solution[J]. Polemer Sci.,1953, (10): 157-166
[20] R. Pecora. Doppler Shifts in Light Scattering from Pure Liquids and Polymer Solutions[J]. Chem. Phys., 1964, 40:1604
[21] R. Foord, E. Jakeman, C. Oliver. Determination of Diffusion Coefficients of Haemocyanin at Low Concentration by Intensity Fluctuation Spectroscopy of Scattered Laser Light[J]. Nature, 1970,227:242-245
[22] S. P. Lee, W. Tscharnuter, B. Chu, Calibration of an optical self-beating spectrometer by polystyrene latex spheres and confirmation of the Stokes-Einstein formula[J]. Polym. Sci. Phys., 1972, 10:2453-2459)
[23] S. P. Lee, W. Tscharnuter, B. Chu, Calibration of an optical self-beating spectrometer by polystyrene latex spheres and confirmation of the Stokes-Einstein formula[J]. Polym. Sci. Phys., 1972, 10:2453-2459)
[24] T. Provder. Challenges in particle size distribution measurement past, present and for the 21st century[J]. Progress inorganic Coatings, 1997, 32:143-153
[25] S. W. Provencher, J. Hendrix, L. Maryer etc. Direct determination of molecular weight distributions of polystyrene in cyclochexane with photon correlation spectroscopy[J]. Chem. Phys., 1978, 69:4273-427
[26] S. W. Provencher. A constrained regularization method for inverting data represented by linear algebraic or integral equation[J]. Comput. Phy. Commun. 1982,27: 213-227
[27] S. W. Provencher. CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[J]. Comput. Phy. Commun. 1982,27: 229-242
[28] J. G. McWhirter. A stabilized model-fitting approach to the processing of laser anemometry and other photon-correlation data[J]. Optica Acta, 1980, 27:83-105
[29] N. Ostrowsky, D. Sornette. Exponential sampling method for light scattering polydispersity analysis[J]. Optica Acta, 1981,28: 1050-1070
[30] M. Bertero, P. Boccacci, E. R. Pike. On the recovery and resolution of exponential relaxation rates from exponential data: a singular value analysis of the Laplace transform inversion in the presence of noise[J]. Proc. R. Soc. London, 1982, A383:15-29
[31] T. G.. Braginskaya, P. D. Dobichin, M. I. Ivanova et al. Analysis of the polydispersity by photon correlation spectroscopy[J]. Regularization procedure. Phys. Scr.,1983, 28:73-79
[32] G. C. Fletcher, D. J. Ramsay. Photon correlation spectroscopy of polydisperse samples Ⅰ. Histogram method with exponential sampling[J]. Optica Acta, 1983, 30: 1183-1196
[33] G. C. Fletcher, D. J. Ramsay. Photon correlation spectroscopy of polydisperse samples Ⅱ. Optimal choice of histogram parameters with exponential sampling[J]. Optica Acta, 1986, 33: 1253-1262
[34] M. Bertero, P. Brianzi, E. R. Pike et al. Light scattering polydispersity analysis of molecular diffusion by Laplace transform inversion in weighted space[J]. Chem. Phys. 1985,82:1551-1554
[35] H. S. Dhadwal. Regularized inversion of the Laplace integral equation- polydispersity analysis in photon correlation spectroscopy[J]. Part. Part. Syst. Charact., 1989, 6:28-33
[36] D. A. Ross, T. H. Nguyen. Spectral properties of the regularized inversion of the Laplace transform[J]. Part. Part. Syst. Charact., 1990, 7:80-86
[37] H. S. Dhadwal, K. Suh, D. A. Ross. A direct method of particle sizing based on the statistical processing of scattered photons from particles executing Brownian motion[J]. Applied Physics, 1996, B62:575-581
[38] A. J. Adorjan, J. A. Lock, T. W. Taylor et al. Particle sizing in strongly turbid suspensions with the one-beam cross-correlation dynamic light-scattering technique[J]. Appl. Opt., 1999, 38: 3409-3416
[39] B. J. Frisken. Revisiting the method of cumulants for the analysis of dynamic light-scattering data[J]. Appl. Opt., 2001, 40:4087-4091
[40] P. Bowen. Particle size distribution measurement from millimeters to nanometers and from rods to platelets[J]. Journal of Dispersion Science and Technology, 2002, 23 : 631-662
[41] H. Ruf, B. J. Gould, W. Haase. Effect of nonrandom errors on the results from regularized inversions of dynamic light scattering data[J]. Langmuir, 2000, 16: 471-480
[42] J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez et al. Latex particle size distribution by dynamic light scattering: Novel data processing for multiangle measurements[J]. Journal of Colloid and Interface Science, 2003, 261: 74-81
[43] H. Ruf. Treatment of contributions of dust to dynamic light scattering data[J]. Langmuir 2002, 18: 3804-3814
[44] J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez et al. Latex particle size distribution by dynamic light scattering: Novel data processing for multiangle measurements[J]. Journal of Colloid and Interface Science, 2003, 261: 74-81
[45] Barbara J.Frisken. Revisiting the method of cumulantsfor the analysis of dynamic light scattering data[J], Appl. Opt., 2001,40:4087-4089
[46] Leksey Lomakin. Fitting the correlation function[J]. Appl. Opt., 2001, 40: 4079～4086
[47] Okabe Satoshi, Karino Takeshi, Shibayama Mitsuhiro. Distribution analyses of multi-modal dynamic light scattering data[J]. Polymer Preprints, 55th SPSJ Symposium on Macromolecules, 2006, 55: 3218-3219
[48] G. W. Mulholand, M. K. Donnelly, C. R. Hogwood et al. Measurement of 100 nm and 60 nm particle standards by differential mobility analysis[J]. Journal of Research of the National Institute of Standards and Technology, 2006, 111: 257-312
[49] 周祖康. 动态光散射[J].化学通报,1986,(10):34～39
[50] 郑容,吴佩强. 激光光散射谱仪的数据采集与处理系统[J]. 计算机与应用化学,1998,15(2):89-94
[51] 郑容. 线性积分方程反演软件-CONTIN 的求解方法与使用[J]. 计算机与应用化学,2000,17(4):363-370
[52] 周俊虎.PCS 超细颗粒测量技术的理论及其应用研究[D].博士学位论文,上海机械学院,1990
[53] 周俊虎,王乃宁. 光子相关光谱法测量超细颗粒的理论研究[J]. 上海机械学院学报,1990,12(3):39-52
[54] 周俊虎,王乃宁. 用累积法确定光子相关光谱测量中的超细颗粒粒度[J]. 上海机械学院学报,1992,14(1):1-14
[55] 杨建文,李峰,田维坚等. 分段自相关动态光散射测量亚微米粒度[J]. 光学学报,1998,18(5):602-606
[56] 叶子,陆祖康. 小粒子动态光散射信号的计算机模拟及分析[J]. 光学学报,1996, 16(6):755-758
[57] 王少清,娄本浊,陶冶薇,任中京. 动态光散射中光子相关谱测量系统的空间相干性问题[J]. 应用激光 , 2004, (05)
[58] 申晋,郑刚,庄松林等.基于动态光散射信号分形的颗粒测量技术研究[J]. 仪器仪表学报,2004,25(4)
[59] 岳成凤,杨冠玲,何振江. 动态光散射光强自相关函数与颗粒分布关系及算法比较[J]. 光电子技术与信息 , 2004, (01)
[60] 刘桂强,杨冠玲,何振江,韩鹏,岳成凤,李丰果,彭力,喻雷寿,李仪芳. 动态光散射在颗粒检测中的应用[J]. 中国粉体技术 , 2005, (03)
[61] 郭永彩,王远,高潮,邓冬梅. 基于动态光散射法的亚微米级微粒粒度测量[J]. 重庆大学学报(自然科学版) , 2006, (02)
[62] 张济忠. 分形[M].北京:清华大学出版社,1995 年
[63] Kerker M. The scattering of light and other Electromagnetic Radiation[M]. New York: Acadmic Press, 1969
[64] Van de Hulst H C. The scattering by small Particles [M]. London: Chapman and Hall, 1957
[65] A. Einstein. Investigation of Theory of the Brownian Movement [M]. Dover Publications, 1956
[66] M. J. Perrin. Brownian Movement and Molecular Reality[M], Taylor and Francis, London, 1910
[67] S. Papoulis. Probability Random Variables, and Stochastic Processes, Chap 15, McGraw-Hill Book Company, First Edition, 1965
[68] 叶子,陆祖康. 小粒子动态光散射信号的计算机模拟及分析. 光学学报,1996, 16(6):755-758
[69] 刘衡郁. 我国股市分形特征研究[D].武汉:武汉大学管理系
[70] Mandelbrot.B. The Fractal Geometry of Nature[M] . New York: W. h. Freeman. 1982
[71] 沙震,阮火军编著. 分形与拟合[M].杭州:浙江大学出版社,2005, 25-26
[72] 李水根编著. 分形[M].北京:高等教育出版社,2004, 6-7
[73] 孙霞等. 分形原理及其应用[M].合肥:中国科技技术大学出版社,2003
[74] R. G. W. Brown, A. E. Smart. Practical considerations in photon correlation experiments[J]. Appl. Opt., 1997, 36:7480-7492
[75] H. Z. Cummins, E. R. Pike. Photon Correlation and Light Beating Spectroscopy[M]. Plenum Press, N.Y., 1974
[76] 激光编写组.激光[M].上海:上海人民教育出版社,1971
[77] J.W.顾得门著.秦克诚、刘培森、曹其智等译。统计光学[M].北京:科学出版社,1992
[78] R. Foord, R. Jones, C. J. Oliver et al. The use of photomultiplier tubes for photon counting[J]. Appl. Opt., 1969, 8:1975-1989
[79] 周仁忠,阎吉祥. 光电统计理论与技术[M]. 北京:北京理工大学出版社,1989
[80] [80] Hamamatu. Photomultipiler Tubes
[81] SIDE-ON PMT PHOTO COUNING HEADS H6240 Series INSTRUCTION MANUAL Vol.3.1. Hamamatsu. Photonics K. K. ELECTRON TUBE CENTER. 1998.9
[82] M8784 Photon Counting Board Instruction Manual, Hamamatsu
[83] 杜广生. 工程流体力学[M].北京:中国电力出版社,2004
[84] Particle size analysis-Photon correlation spectroscopy. ISO 13321:1996E
[85] 粒度分析～光子相关光谱法. GB/T 19627-2005
[2] 管映亭,金志浩,董政娥. 纳米材料及其在纺织等领域中的应用[J]. 纺织学报,2004,25(3):116-118
[3] 马建中,储芸,高党鸽. 我国纳米生物技术的医学应用及研究进展[J]. 中国医学科学院学报,2006,28(4):579-582
[4] 王学船,任龙芳,强涛涛. 纳米材料在化妆品中的应用[J]. 日用化学品科学,2006,29(4):15-18
[5] 赵树朋,杨玉瑛,屈平,张世芳,李久熙,高喜银. 纳米技术在农业工程中的应用[J]. 农机化研究,2006,(2):119-120
[6] http://www.ocn.com.cn/reports/2006082nami.htm
[7] 张立德. 我国纳米产业面临的新转折和挑战[J]. 新材料产业,2005,(10):48-51
[8] 王乃宁. 颗粒粒径的光学测量技术及应用[M]. 北京:原子能出版社,2000 年
[9] 王书运. 纳米颗粒的测量与表征[J]. 微纳电子技术,2005,(01)
[10] http://erran.blogerhome.com/135461.shtml
[11] http://www.bak.com.cn/cn/xinxi-bakyuekan-xiangxi.asp?id=365
[12] Krishnomurti, P. Studies in X-Ray Diffraction. Part1: The Structure of Amorphous Scattering. Part2: Colloidal Solutions and Liquid Mixtures [J]. Indian J. Phys., 1930, (5): 473-500
[13] Warren, B. E. X-Ray Diffraction Study of Carbon Black [J]. Chem. Phys. 1934, (2): 551-555
[14] Kratky, O., & Porod, G. Diffuse Small-Angle Scattering of X-Rays in Colloid Systems[J]. Colloid Sci., 1949, (4): 35-70
[15] Guinier, A. Study of Catalysts by Scattering of X-Rays at Small Angles[J]. Discussions Faraday Soc., 1950, (8): 344-347
[16] Guinier, A. & Fournet G. Small-Angle Scattering of X-Rays[M]. New York: John Wiley, 1955
[17] Hosemann, R., & Bagchi, S. N. The Interference Theory of Ideal Paracrystals[J]. Acta Cryst.,1952 ,(5):612-614
[18] Debye, P. & Bueche, A. M. Scattering by an Inhomogeneous Solid[J]. Appl. Phys., 1949, (20):518-525
[19] Porod, G. X-Ray and Light Scattering by Chain Molecules in Solution[J]. Polemer Sci.,1953, (10): 157-166
[20] R. Pecora. Doppler Shifts in Light Scattering from Pure Liquids and Polymer Solutions[J]. Chem. Phys., 1964, 40:1604
[21] R. Foord, E. Jakeman, C. Oliver. Determination of Diffusion Coefficients of Haemocyanin at Low Concentration by Intensity Fluctuation Spectroscopy of Scattered Laser Light[J]. Nature, 1970,227:242-245
[22] S. P. Lee, W. Tscharnuter, B. Chu, Calibration of an optical self-beating spectrometer by polystyrene latex spheres and confirmation of the Stokes-Einstein formula[J]. Polym. Sci. Phys., 1972, 10:2453-2459)
[23] S. P. Lee, W. Tscharnuter, B. Chu, Calibration of an optical self-beating spectrometer by polystyrene latex spheres and confirmation of the Stokes-Einstein formula[J]. Polym. Sci. Phys., 1972, 10:2453-2459)
[24] T. Provder. Challenges in particle size distribution measurement past, present and for the 21st century[J]. Progress inorganic Coatings, 1997, 32:143-153
[25] S. W. Provencher, J. Hendrix, L. Maryer etc. Direct determination of molecular weight distributions of polystyrene in cyclochexane with photon correlation spectroscopy[J]. Chem. Phys., 1978, 69:4273-427
[26] S. W. Provencher. A constrained regularization method for inverting data represented by linear algebraic or integral equation[J]. Comput. Phy. Commun. 1982,27: 213-227
[27] S. W. Provencher. CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[J]. Comput. Phy. Commun. 1982,27: 229-242
[28] J. G. McWhirter. A stabilized model-fitting approach to the processing of laser anemometry and other photon-correlation data[J]. Optica Acta, 1980, 27:83-105
[29] N. Ostrowsky, D. Sornette. Exponential sampling method for light scattering polydispersity analysis[J]. Optica Acta, 1981,28: 1050-1070
[30] M. Bertero, P. Boccacci, E. R. Pike. On the recovery and resolution of exponential relaxation rates from exponential data: a singular value analysis of the Laplace transform inversion in the presence of noise[J]. Proc. R. Soc. London, 1982, A383:15-29
[31] T. G.. Braginskaya, P. D. Dobichin, M. I. Ivanova et al. Analysis of the polydispersity by photon correlation spectroscopy[J]. Regularization procedure. Phys. Scr.,1983, 28:73-79
[32] G. C. Fletcher, D. J. Ramsay. Photon correlation spectroscopy of polydisperse samples Ⅰ. Histogram method with exponential sampling[J]. Optica Acta, 1983, 30: 1183-1196
[33] G. C. Fletcher, D. J. Ramsay. Photon correlation spectroscopy of polydisperse samples Ⅱ. Optimal choice of histogram parameters with exponential sampling[J]. Optica Acta, 1986, 33: 1253-1262
[34] M. Bertero, P. Brianzi, E. R. Pike et al. Light scattering polydispersity analysis of molecular diffusion by Laplace transform inversion in weighted space[J]. Chem. Phys. 1985,82:1551-1554
[35] H. S. Dhadwal. Regularized inversion of the Laplace integral equation- polydispersity analysis in photon correlation spectroscopy[J]. Part. Part. Syst. Charact., 1989, 6:28-33
[36] D. A. Ross, T. H. Nguyen. Spectral properties of the regularized inversion of the Laplace transform[J]. Part. Part. Syst. Charact., 1990, 7:80-86
[37] H. S. Dhadwal, K. Suh, D. A. Ross. A direct method of particle sizing based on the statistical processing of scattered photons from particles executing Brownian motion[J]. Applied Physics, 1996, B62:575-581
[38] A. J. Adorjan, J. A. Lock, T. W. Taylor et al. Particle sizing in strongly turbid suspensions with the one-beam cross-correlation dynamic light-scattering technique[J]. Appl. Opt., 1999, 38: 3409-3416
[39] B. J. Frisken. Revisiting the method of cumulants for the analysis of dynamic light-scattering data[J]. Appl. Opt., 2001, 40:4087-4091
[40] P. Bowen. Particle size distribution measurement from millimeters to nanometers and from rods to platelets[J]. Journal of Dispersion Science and Technology, 2002, 23 : 631-662
[41] H. Ruf, B. J. Gould, W. Haase. Effect of nonrandom errors on the results from regularized inversions of dynamic light scattering data[J]. Langmuir, 2000, 16: 471-480
[42] J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez et al. Latex particle size distribution by dynamic light scattering: Novel data processing for multiangle measurements[J]. Journal of Colloid and Interface Science, 2003, 261: 74-81
[43] H. Ruf. Treatment of contributions of dust to dynamic light scattering data[J]. Langmuir 2002, 18: 3804-3814
[44] J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez et al. Latex particle size distribution by dynamic light scattering: Novel data processing for multiangle measurements[J]. Journal of Colloid and Interface Science, 2003, 261: 74-81
[45] Barbara J.Frisken. Revisiting the method of cumulantsfor the analysis of dynamic light scattering data[J], Appl. Opt., 2001,40:4087-4089
[46] Leksey Lomakin. Fitting the correlation function[J]. Appl. Opt., 2001, 40: 4079～4086
[47] Okabe Satoshi, Karino Takeshi, Shibayama Mitsuhiro. Distribution analyses of multi-modal dynamic light scattering data[J]. Polymer Preprints, 55th SPSJ Symposium on Macromolecules, 2006, 55: 3218-3219
[48] G. W. Mulholand, M. K. Donnelly, C. R. Hogwood et al. Measurement of 100 nm and 60 nm particle standards by differential mobility analysis[J]. Journal of Research of the National Institute of Standards and Technology, 2006, 111: 257-312
[49] 周祖康. 动态光散射[J].化学通报,1986,(10):34～39
[50] 郑容,吴佩强. 激光光散射谱仪的数据采集与处理系统[J]. 计算机与应用化学,1998,15(2):89-94
[51] 郑容. 线性积分方程反演软件-CONTIN 的求解方法与使用[J]. 计算机与应用化学,2000,17(4):363-370
[52] 周俊虎.PCS 超细颗粒测量技术的理论及其应用研究[D].博士学位论文,上海机械学院,1990
[53] 周俊虎,王乃宁. 光子相关光谱法测量超细颗粒的理论研究[J]. 上海机械学院学报,1990,12(3):39-52
[54] 周俊虎,王乃宁. 用累积法确定光子相关光谱测量中的超细颗粒粒度[J]. 上海机械学院学报,1992,14(1):1-14
[55] 杨建文,李峰,田维坚等. 分段自相关动态光散射测量亚微米粒度[J]. 光学学报,1998,18(5):602-606
[56] 叶子,陆祖康. 小粒子动态光散射信号的计算机模拟及分析[J]. 光学学报,1996, 16(6):755-758
[57] 王少清,娄本浊,陶冶薇,任中京. 动态光散射中光子相关谱测量系统的空间相干性问题[J]. 应用激光 , 2004, (05)
[58] 申晋,郑刚,庄松林等.基于动态光散射信号分形的颗粒测量技术研究[J]. 仪器仪表学报,2004,25(4)
[59] 岳成凤,杨冠玲,何振江. 动态光散射光强自相关函数与颗粒分布关系及算法比较[J]. 光电子技术与信息 , 2004, (01)
[60] 刘桂强,杨冠玲,何振江,韩鹏,岳成凤,李丰果,彭力,喻雷寿,李仪芳. 动态光散射在颗粒检测中的应用[J]. 中国粉体技术 , 2005, (03)
[61] 郭永彩,王远,高潮,邓冬梅. 基于动态光散射法的亚微米级微粒粒度测量[J]. 重庆大学学报(自然科学版) , 2006, (02)
[62] 张济忠. 分形[M].北京:清华大学出版社,1995 年
[63] Kerker M. The scattering of light and other Electromagnetic Radiation[M]. New York: Acadmic Press, 1969
[64] Van de Hulst H C. The scattering by small Particles [M]. London: Chapman and Hall, 1957
[65] A. Einstein. Investigation of Theory of the Brownian Movement [M]. Dover Publications, 1956
[66] M. J. Perrin. Brownian Movement and Molecular Reality[M], Taylor and Francis, London, 1910
[67] S. Papoulis. Probability Random Variables, and Stochastic Processes, Chap 15, McGraw-Hill Book Company, First Edition, 1965
[68] 叶子,陆祖康. 小粒子动态光散射信号的计算机模拟及分析. 光学学报,1996, 16(6):755-758
[69] 刘衡郁. 我国股市分形特征研究[D].武汉:武汉大学管理系
[70] Mandelbrot.B. The Fractal Geometry of Nature[M] . New York: W. h. Freeman. 1982
[71] 沙震,阮火军编著. 分形与拟合[M].杭州:浙江大学出版社,2005, 25-26
[72] 李水根编著. 分形[M].北京:高等教育出版社,2004, 6-7
[73] 孙霞等. 分形原理及其应用[M].合肥:中国科技技术大学出版社,2003
[74] R. G. W. Brown, A. E. Smart. Practical considerations in photon correlation experiments[J]. Appl. Opt., 1997, 36:7480-7492
[75] H. Z. Cummins, E. R. Pike. Photon Correlation and Light Beating Spectroscopy[M]. Plenum Press, N.Y., 1974
[76] 激光编写组.激光[M].上海:上海人民教育出版社,1971
[77] J.W.顾得门著.秦克诚、刘培森、曹其智等译。统计光学[M].北京:科学出版社,1992
[78] R. Foord, R. Jones, C. J. Oliver et al. The use of photomultiplier tubes for photon counting[J]. Appl. Opt., 1969, 8:1975-1989
[79] 周仁忠,阎吉祥. 光电统计理论与技术[M]. 北京:北京理工大学出版社,1989
[80] [80] Hamamatu. Photomultipiler Tubes
[81] SIDE-ON PMT PHOTO COUNING HEADS H6240 Series INSTRUCTION MANUAL Vol.3.1. Hamamatsu. Photonics K. K. ELECTRON TUBE CENTER. 1998.9
[82] M8784 Photon Counting Board Instruction Manual, Hamamatsu
[83] 杜广生. 工程流体力学[M].北京:中国电力出版社,2004
[84] Particle size analysis-Photon correlation spectroscopy. ISO 13321:1996E
[85] 粒度分析～光子相关光谱法. GB/T 19627-2005