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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 34 — Dec. 1, 2010
  • pp: 6591–6596

Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data

Xinjun Zhu, Jin Shen, Wei Liu, Xianming Sun, and Yajing Wang  »View Author Affiliations

Applied Optics, Vol. 49, Issue 34, pp. 6591-6596 (2010)

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The weak symmetry relationship between the relative error and solution norm holds in our developed nonnegative least-squares truncated singular value decomposition method. By using this relationship to specify the optimal regularization parameters, we applied the proposed algorithm to recover particle size distribution from dynamic light scattering (DLS) data. Simulated results and experimental validity demonstrate that the proposed method, which compliments the CONTIN algorithm, might serve as a powerful and simple approach to the inverse problem in DLS.

© 2010 Optical Society of America

OCIS Codes
(290.3200) Scattering : Inverse scattering
(290.3700) Scattering : Linewidth
(290.5820) Scattering : Scattering measurements
(290.5850) Scattering : Scattering, particles
(300.6170) Spectroscopy : Spectra

ToC Category:

Original Manuscript: June 21, 2010
Revised Manuscript: October 5, 2010
Manuscript Accepted: October 11, 2010
Published: November 23, 2010

Xinjun Zhu, Jin Shen, Wei Liu, Xianming Sun, and Yajing Wang, "Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data," Appl. Opt. 49, 6591-6596 (2010)

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  1. R. Pecora, Dynamic Light Scattering: Application of Photon Correlation Spectroscopy (Plenum, 1985).
  2. L. Gugliotta, J. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228, 14–17 (2000). [CrossRef] [PubMed]
  3. F. Scheffold, A. Shalkevich, R. Vavrin, J. Crassous, and P. Schurtenberger, PCS Particle Sizing in Turbid Suspensions: Scope and Limitations (American Chemical Society, 2004).
  4. K. Otsuka, K. Abe, N. Sano, S. Sudo, and J. Y. Ko, “Two-channel self-mixing laser Doppler measurement with carrier-frequency-division multiplexing,” Appl. Opt. 44, 1709–1714 (2005). [CrossRef] [PubMed]
  5. C. Zakian, M. Dickinson, and T. King, “Dynamic light scattering by using self-mixing interferometry with a laser diode,” Appl. Opt. 45, 2240–2245 (2006). [CrossRef] [PubMed]
  6. H. S. Dhadwal, K. Suh, and D. A. Ross, “A direct method of particle sizing based on the statistical processing of scattered photons from particles executing Brownian motion,” Appl. Phys. B 62, 575–581 (1996). [CrossRef]
  7. J. Shen, G. Zheng, G. Sun, and Q. Tu, “Fractal character of dynamic light scattering of particles,” Part. Part. Syst. Charact. 21, 411–414 (2004). [CrossRef]
  8. D. E. Kopple, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972). [CrossRef]
  9. J. G. McWhirter and E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A Math. Theor. 11, 1729–1745(1978). [CrossRef]
  10. N. Ostrowsky, D. Sornette, P. Parker, and E. R. Pike, “Exponential sampling method for light scattering polydispersity analysis,” J. Mod. Opt. 28, 1059–1070 (1981). [CrossRef]
  11. S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations,” Commun. Comput. Phys. 27, 213–227(1982). [CrossRef]
  12. I. D. Morrison and E. F. Grabowski, “Improved techniques for particle size determination for quasi-elastic light scattering,” Langmuir 1, 496–501 (1985). [CrossRef]
  13. M. Iqbal, “On photon correlation measurements of colloidal size distributions using Bayesian strategies,” J. Comput. Appl. Math. 126, 77–89 (2000). [CrossRef]
  14. J. V. Ubera, J. F. Aguilar, and D. M. Gale, “Reconstruction of particle-size distributions from light-scattering patterns using three inversion methods,” Appl. Opt. 46, 124–132(2007). [CrossRef]
  15. B. J. Frisken, “Revisiting the method of cumulants for analysis of dynamic light-scattering data,” Appl. Opt. 40, 4087–4091(2001). [CrossRef]
  16. P. A. Hassan and S. K. Kulshreshtha, “Modification to the cumulant analysis of polydispersity in quasi-elastic light scattering data,” J. Colloid. Interface Sci. 300, 744–748(2006). [CrossRef] [PubMed]
  17. A. R. Roig and J. L. Alessandrini, “Particle size distribution from static light scattering with regularized non-negative least squares constraints,” Part. Part. Syst. Charact. 23, 431–437 (2006). [CrossRef]
  18. M. L. Arias and G. L. Frontini, “Particle size distribution retrieval from elastic light scattering measurement by a modified regularization method,” Part. Part. Syst. Charact. 23, 374–380 (2006). [CrossRef]
  19. D. A. Ligon, T. W. Chen, and J. B. Gillespie, “Determination of aerosol parameters light-scattering data using an inverse Monte Carlo technique,” Appl. Opt. 35, 4297–4303 (1996). [CrossRef] [PubMed]
  20. M. Ye, S. Wang, and Y. Lu, “Inversion of particle-size distribution from angular light-scattering data with genetic algorithms,” Appl. Opt. 38, 2677–2685 (1999). [CrossRef]
  21. L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, and V. D. G. Gonzalez, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26, 41–52 (2009). [CrossRef]
  22. P. C. Hansen, “The truncated SVD as a method for regularization,” BIT (Nord. Tidskr. Inf.-Behandl.) 27, 534–553(1987). [CrossRef]
  23. P. C. Hansen and D. P. O’Leary, “The use of L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993). [CrossRef]
  24. D. Krawczyk-Stando and M. Rudnicki, “Regularization parameter selection in discrete ill-posed problems—the use of the U-curve,” Int. J. Appl. Math. Comput. Sci. 17, 157–164(2007). [CrossRef]
  25. A. B. Yu and N. Standish, “A study of particle size distribution,” Powder Technol. 62, 101–118 (1990). [CrossRef]
  26. T. F. Coleman and Y. Li, “A reflective Newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996). [CrossRef]
  27. R. Finsy, L. Deriemaeker, N. De Jaeger, R. Sneyers, J. Vanderdeelen, P. Van der Meeren, H. Demeyere, J. Stone-Masui, A. Haestier, J. Clauwaert, W. De Wispelaere, P. Gillioen, S. Steyfkens, and E. Gelade, “Particle sizing by photon correlation spectroscopy. Part IV: resolution of bimodals and comparison with other particle sizing methods,” Part. Part. Syst. Charact. 10, 118–128 (1993). [CrossRef]
  28. W. Liu, J. Shen, and X. Sun, “Design of multiple-tau photon correlation system implemented by FPGA,” in Proceedings of The International Conference on Embedded Software and Systems (IEEE, 2008), pp. 410–414. [CrossRef]
  29. W. Liu, J. Shen, Y. Cheng, and W. Chen, “Novel photon correlator with less hardware resource,” Proc. SPIE 7283, 72833B (2009). [CrossRef]

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