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宽分布和双峰分布颗粒的准确反演是动态光散射技术至今未能有效解决的难题，尤其峰值位置比小于2：1且含有大粒径颗粒（350 nm）的双峰分布.造成这一难题的主要原因包括：1）单角度测量数据的粒度信息含量不足；2）常规反演方法对测量数据的噪声抑制以及粒度信息利用缺乏针对性.对测量数据（即光强自相关函数）的研究发现，数据噪声主要分布在长延迟时段，而粒度信息集中分布在衰减延迟时段.基于此，本文提出了采用粒度信息分布为底数、调节参数为指数的权重系数对自相关函数进行加权反演的约束正则化方法.由于采用了与粒度信息分布一致的权重系数，该方法既充分利用了衰减延迟时段的粒度信息，又有效地抑制了长延迟时段的数据噪声.不同噪声水平下，宽分布和双峰分布颗粒体系的反演结果表明，与常规反演方法相比，这一方法可以获得更为准确的宽分布和近双峰分布的反演结果.In particle sizing with dynamic light scattering (DLS) technique, the determination of particle size distribution (PSD), via inversing the autocorrelation function (ACF) of scattering light, is usually limited by the inherently low particle size information in ACF data and, the lack of targeted inversion on the noise restriction and the particle size information utilization. For the ACF data in DLS measurement, most of particle size information is centrally contained in the decay section and the larger noise is contained in the larger delay section. However, no consideration of the particle size information distribution in the ACF data for the routine inversion method increases the difficulty of the accurate PSD inversion, especially the broad and bimodal PSDs. Until now, it is still a difficult problem to obtain an accurate recovery of the broad and bimodal PSDs, specifically the bimodal PSD with a peak position ratio less than 2:1 and containing large particles (350 nm). In this paper, a character-weighted constrained regularization (CW-CR) method is proposed, in which, the particle size information distribution in the ACF as the base and the adjustment parameter as the exponent are used to weight the ACF. By using the weighting coefficients corresponding to the particle size information distribution along the delay time in ACF, the CW-CR method can enhance the utilization of the particle size information in ACF data, and effectively weaken the effect of noise at large delay time. With this method, the closely spaced bimodal PSD (with nominal diameters of m 350 nm:500 nm in simulation, m 300 nm:502 nm in experiment) is recovered successfully at a high noise level of 0.01. It shows that the CW-CR method, combined with the multiangle DLS (MDLS) measurement, can effectively make the best use of the particle size information hiding in the noisy ACF data, and improve the resolution of bimodal PSD as well as the capability of noise suppression. So it can make the advantages of MDLS more highlighted than the routine method in the recovery of the broad and bimodal PSDs.
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Keywords:
- dynamic light scattering /
- particle size distribution /
- inversion problem /
- constrained regularization
[1] Pecora R 1985 Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (New York: Plenum) pp1-6
[2] Goll J H, Stock G B 1977 Biophys. J. 19 265
[3] Gulari E, Gulari E, Tsunashima Y, Chu B 1979 J. Chem. Phys. 70 3965
[4] Cummins P G, Staples E J 1987 Langmuir 3 1109
[5] Bryant G, Thomas J C 1995 Langmuir 11 2480
[6] Vega J R, Gugliotta L M, Gonzalez V D G, Meira G R 2003 J. Colloid Interf. Sci. 261 74
[7] Liu X, Shen J, Thomas J C, Shi S, Sun X, Liu W 2012 Appl. Opt. 51 846
[8] Buttgereit R, Roths T, Honerkamp J, Aberle L B 2001 Phys. Rev. E 64 1515
[9] Gugliotta L M, Vega J R, Meira G R 2000 J. Colloid Interf. Sci. 228 14
[10] Clementi L A, Vega J R, Gugliotta L M, Orlande H R B 2011 Chemometr. Intell. Lab. 107 165
[11] Naiim M, Boualem A, Ferre C, Jabloun M, Jalocha A, Ravier P 2015 Soft Matter 11 28
[12] Gugliotta L M, Stegmayer G S, Clementi L A, Gonzalez V D G, Minari R J, Leiza J R, Vega J R 2009 Part. Part. Syst. Char. 26 41
[13] Liu X, Shen J, Thomas J C, Clementi L A, Sun X 2012 J. Quant. Spectrosc. Ra. 113 489
[14] Zhu X, Shen J, Song L 2015 IEEE Photon. Tech. L. 28 311
[15] Xu M, Shen J, Thomas J C, Huang Y, Zhu X L, Clementi A, Vega J R 2018 Opt. Express 26 15
[16] Mie G 1908 Ann. Phys. New York 25 377
[17] Wiscombe W J 1980 Appl. Opt. 19 1505
[18] Frisken B J 2001 Appl. Opt. 40 4087
[19] Mailer A G, Clegg P S, Pusey P N 2015 J. Phys.: Condens. Matter 27 145102
[20] Hansen P C, O'Leary D P 1993 SIAM J. Sci. Comput. 14 1487
[21] Rezghi M, Hosseini S M 2009 J. Comput. Appl. Math. 231 914
[22] Thomas J C 1987 J. Colloid Interf. Sci. 117 187
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[1] Pecora R 1985 Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (New York: Plenum) pp1-6
[2] Goll J H, Stock G B 1977 Biophys. J. 19 265
[3] Gulari E, Gulari E, Tsunashima Y, Chu B 1979 J. Chem. Phys. 70 3965
[4] Cummins P G, Staples E J 1987 Langmuir 3 1109
[5] Bryant G, Thomas J C 1995 Langmuir 11 2480
[6] Vega J R, Gugliotta L M, Gonzalez V D G, Meira G R 2003 J. Colloid Interf. Sci. 261 74
[7] Liu X, Shen J, Thomas J C, Shi S, Sun X, Liu W 2012 Appl. Opt. 51 846
[8] Buttgereit R, Roths T, Honerkamp J, Aberle L B 2001 Phys. Rev. E 64 1515
[9] Gugliotta L M, Vega J R, Meira G R 2000 J. Colloid Interf. Sci. 228 14
[10] Clementi L A, Vega J R, Gugliotta L M, Orlande H R B 2011 Chemometr. Intell. Lab. 107 165
[11] Naiim M, Boualem A, Ferre C, Jabloun M, Jalocha A, Ravier P 2015 Soft Matter 11 28
[12] Gugliotta L M, Stegmayer G S, Clementi L A, Gonzalez V D G, Minari R J, Leiza J R, Vega J R 2009 Part. Part. Syst. Char. 26 41
[13] Liu X, Shen J, Thomas J C, Clementi L A, Sun X 2012 J. Quant. Spectrosc. Ra. 113 489
[14] Zhu X, Shen J, Song L 2015 IEEE Photon. Tech. L. 28 311
[15] Xu M, Shen J, Thomas J C, Huang Y, Zhu X L, Clementi A, Vega J R 2018 Opt. Express 26 15
[16] Mie G 1908 Ann. Phys. New York 25 377
[17] Wiscombe W J 1980 Appl. Opt. 19 1505
[18] Frisken B J 2001 Appl. Opt. 40 4087
[19] Mailer A G, Clegg P S, Pusey P N 2015 J. Phys.: Condens. Matter 27 145102
[20] Hansen P C, O'Leary D P 1993 SIAM J. Sci. Comput. 14 1487
[21] Rezghi M, Hosseini S M 2009 J. Comput. Appl. Math. 231 914
[22] Thomas J C 1987 J. Colloid Interf. Sci. 117 187
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