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Abstract:

We consider the problem of inversion of elastic light scattering (ELS) measurements from polymeric emulsions, to obtain its particle size distribution (PSD) and its refractive index. The mathematical formulation results in a nonlinear inverse problem. A Fredholm integral equation of the first kind appears with an unknown parameter in its kernel. We discuss the existence, uniqueness, and stability of the generalized solutions of the problem when it is stated as a minimization problem with a least square functional. First, we assume that the PSD is known, and for this case we prove that the solution exists and is unique as long as the relation between the measurements and the parameter is by an injective function. Then, we use this result to state sufficient conditions for the complete problem. The analysis of existence and uniqueness of the solution for the problem in hand is supported by numerical simulation. The Phillips-Tikhonov regularization method is proposed to stabilize the problem when noisy-data is available.

Registro:

Documento: Artículo
Título:Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
Autor:Frontini, G.L.; Berdaguer, E.M.F.
Filiación:Instituto de Investigación en Ciencia y Tecnología de Materiales (INTEMA), Univ. Nac. de Mar del Plata, Mar del Plata, Argentina
Instituto de Cálculo FCEyN, Fac. Ingeniería, Univ. Nac. de Buenos Aires, Argentina
Año:2007
Volumen:15
Número:2
Página de inicio:123
Página de fin:135
DOI: http://dx.doi.org/10.1080/17415970600573940
Título revista:Inverse Problems in Science and Engineering
Título revista abreviado:Inverse Probl. Sci. Eng.
ISSN:17415977
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17415977_v15_n2_p123_Frontini

Referencias:

  • Mie, G., Beitrage zur Optic truber Medien speziell kolloidaler Metallosungen (1908) Annals of Physics (Leipzig), 25, pp. 377-445
  • Glatter, O., Holer, M., Interpretation of elastic light scattering data III. Determination of size distributions of polydisperse systems (1988) Journal of Colloid and Interface Science, 2 (122), pp. 496-506
  • Wyatt, P.J., Some chemical, physical and optical properties of fly ash particles (1980) Applied Optics, 19, pp. 975-983
  • Frontini, G.L., Elicabe, G.E., A novel methodology to estimate the particle size distribution of latex using relative measurements of elastic light scattering and turbidimetry (2000) Journal of Chemometrics, 14, pp. 51-61
  • Ludlow, I.K., Everitt, J., Inverse Mie problem (2000) J. Opt. Soc. Am. A, 17 (12), pp. 2229-2235
  • Zakovic, S., Ulanowsdki, Z., Bartholomew-Biggs, M.C., Application of global optimization to particle identification using light scattering (1998) Inverse Problems, 14, pp. 1053-1067
  • Hodgson, R.J.W., Genetic algorithm approach to particle identification by light scattering (2000) Journal of Colloid and Interface Science, 229, pp. 399-406
  • Glatter, O., Siebere, J., Schnablegger, H., A comparative study on different scattering techniques and data evaluation methods for sizing of colloidal systems using light scattering (1991) Particles and Particle System Characterization, 8, pp. 274-281
  • Schnablegger, H., Glatter, O., Simultaneous determination of size distribution and refractive index of colloidal particles from static light-scattering experiments (1993) Journal of Colloid and Interface Science, 158, pp. 228-242
  • Jones, M.R., Curry, B.P., Brewster, M.Q., Leong, K.H., Inversion of light-scattering measurements for particle size and optical constants: Theoretical study (1994) Applied Optics, 33, p. 18
  • Frontini, G.L., Fernández Berdaguer, E.M., Inversion of elastic light scattering measurements to determine refractive index and particle size distribution of polymeric emulsions (2003) Inverse Problems in Engineering, 11 (4), pp. 329-340
  • Bohren, C., Huffman, D., (1983) Absorption and Scattering of Light by Small Particles, , New York: Wiley
  • Devon, M.J., Rudin, A., A simple technique for measuring the refractive index of polymer latexes at various wavelengths (1987) Journal of Applied Polymer Science, 34, pp. 469-476
  • Khairullina, A.Y., Makarevich, S.A., Klyubin, V.V., Determination of the imaginary part of complex refractive index and other optical parameters of a latex suspension in water in the visible spectral range (1998) Optics and Spectroscopy, 85 (1), pp. 95-98
  • Barber, O.W., Hill, S.C., (1990) Computational Light Scattering, , Singapore: World Scientific
  • Groetsch, C.W., (1993) Inverse Problems in the Mathematical Sciences, , V. Verlag Ed, Wiesbaden, Germany: Vieweg
  • Tikhonov, A.N., Arsenin, V., (1977) Solution of Ill-posed Problems, , New York: Wiley
  • Phillips, D.L., A technique for the numerical solution of certain integral equations of the first kind (1962) Journal of AMC, 9, pp. 84-91
  • Golub, G.H., Heath, M., Wahba, G., Generalized cross validation as a method for choosing a good parameter (1979) Technometrics, 21, p. 215
  • Neubauer, A., An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error (1988) Applied Numerical Mathematics, 4, pp. 507-519
  • Hansen, P.C., (1998) Rank-deficient and Discrete Ill-posed Problems, Numerical Aspects of Linear Inversion, , Philadelphia: Siam

Citas:

---------- APA ----------
Frontini, G.L. & Berdaguer, E.M.F. (2007) . Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions. Inverse Problems in Science and Engineering, 15(2), 123-135.
http://dx.doi.org/10.1080/17415970600573940
---------- CHICAGO ----------
Frontini, G.L., Berdaguer, E.M.F. "Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions" . Inverse Problems in Science and Engineering 15, no. 2 (2007) : 123-135.
http://dx.doi.org/10.1080/17415970600573940
---------- MLA ----------
Frontini, G.L., Berdaguer, E.M.F. "Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions" . Inverse Problems in Science and Engineering, vol. 15, no. 2, 2007, pp. 123-135.
http://dx.doi.org/10.1080/17415970600573940
---------- VANCOUVER ----------
Frontini, G.L., Berdaguer, E.M.F. Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions. Inverse Probl. Sci. Eng. 2007;15(2):123-135.
http://dx.doi.org/10.1080/17415970600573940