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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 12 — Apr. 20, 2013
  • pp: 2792–2799

Inversion of photon correlation spectroscopy based on truncated singular value decomposition and cascadic multigrid technology

Yajing Wang, Jin Shen, Liu Wei, Zhenhai Dou, and Shanshan Gao  »View Author Affiliations


Applied Optics, Vol. 52, Issue 12, pp. 2792-2799 (2013)
http://dx.doi.org/10.1364/AO.52.002792


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Abstract

For the low accuracy of single-scale inversion method in photon correlation spectroscopy technology, a cascadic multigrid (CMG)- truncated singular value decomposition (TSVD) inversion method that combines the TSVD regularization with CMG technology is proposed. This method decomposes the original problem into several subproblems in different scale grid space. According to the particle sizes inverted from the coarsest scale to the finest scale, the solution of an original inversion problem can be obtained. For the inversion of each subproblem, TSVD method is used. The simulation and experimental data were respectively inverted by TSVD and CMG-TSVD methods. The inversion results demonstrate that the CMG-TSVD method has higher accuracy, more strong noise immunity and better smoothness than the TSVD method.

© 2013 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:
Scattering

History
Original Manuscript: November 2, 2012
Manuscript Accepted: December 3, 2012
Published: April 17, 2013

Citation
Yajing Wang, Jin Shen, Liu Wei, Zhenhai Dou, and Shanshan Gao, "Inversion of photon correlation spectroscopy based on truncated singular value decomposition and cascadic multigrid technology," Appl. Opt. 52, 2792-2799 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-12-2792


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References

  1. B. Chu and T. Liu, “Characterization of nanoparticles by scattering techniques,” J. Nanopart. Res. 2, 29–41 (2000). [CrossRef]
  2. R. S. Dias, J. Innerlohinger, and O. Glatter, “Coil-globule transition of DNA molecules induced by cationic surfactants: a dynamic light scattering study,” J. Phys. Chem. B 109, 10458–10463 (2005). [CrossRef]
  3. M. Alexander and D. G. Dalgleish, “Dynamic light scattering techniques and their applications in food science,” Food Biophys. 1, 2–13 (2006). [CrossRef]
  4. F. Krahl, V. Boyko, and K. F. Arndt, “Characterization of spatial inhomogeneities and dynamic properties of random cross-linked polystyrene networks by dynamic light scattering,” Polymer 51, 2576–2584 (2010). [CrossRef]
  5. D. E. Kopple, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972). [CrossRef]
  6. 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).
  7. S. W. Provencher, “CONTIN: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229–242 (1982). [CrossRef]
  8. B. E. Dahneke, Measurement of Suspended Particles by Quasi-Elastic Light Scattering (Wiley Interscience, 1983).
  9. I. D. Morrison and E. F. Grabowski, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1, 496–501 (1985). [CrossRef]
  10. J. G. McWhirter and E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” Phys. A 11, 1729–1745 (1978). [CrossRef]
  11. L. M. Gugliotta, G. S. Stegmayer, and L. A. Clementi, “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]
  12. S. Li, “Inversion of particle size distribution from dynamic light scattering data with gray-code genetic algorithm,” Chin. J. Comput. Phys. 25, 323–329 (2008).
  13. X. J. Zhu, J. Shen, W. Liu, X. M. Sun, and Y. J. Wang, “Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data,” Appl. Opt. 49, 6591–6596 (2010). [CrossRef]
  14. K. Stuben, “A review of algebraic multigrid,” J. Comput. Appl. Math. 128, 281–309 (2001). [CrossRef]
  15. F. A. Bornemann and P. Deuflhard, “The cascadic multigrid method for elliptic problems,” Numer. Math. 42, 917–924 (1996).
  16. F. A. Bornemann and R. Krause, “Classical and cascadic multigrid-A methodogical comparison,” Proceedings of the 9th International Conference on Domain Decomposition (Wiley, 1998), pp. 64–71.
  17. F. Bornemann and P. Deuflhard, “The cascadic multi-grid method,” The Eighth International Conference on Domain Decomposition Method for Partial Differential Equations(Wiley, 1997), pp. 205–212.
  18. P. C. Hansen, “Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algorithms 6, 1–35 (1994). [CrossRef]
  19. P. C. Hansen, “Analysis of discrete ill-posed problems by means of the l-curve,” SIAM Rev. 34, 561–580 (1992). [CrossRef]
  20. K. Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52–74 (1970). [CrossRef]
  21. A. B. Yu and N. Standish, “A study of particle size distribution,” Power Technol. 62, 101–118 (1990). [CrossRef]
  22. T. F. Coleman and Y. Li, “An interior trust region approach for nonlinear minimization subject to bounds,” SIAM J. Optim. 6, 418–445 (1996). [CrossRef]
  23. J. Wu, M. Li, and T. Yu, “Ill matrix and regularization method in surveying data processing,” J. Geodesy Geodyn. 30, 102–105 (2010).
  24. 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.
  25. 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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