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Applied Optics

Applied Optics


  • Vol. 40, Iss. 9 — Mar. 20, 2001
  • pp: 1525–1531

Light-transmittance predictions under multiple-light-scattering conditions. II. Inverse problem: particle size determination

Marek Czerwiński, Janusz Mroczka, Thiery Girasole, Gérard Gouesbet, and Gérard Gréhan  »View Author Affiliations

Applied Optics, Vol. 40, Issue 9, pp. 1525-1531 (2001)

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Our aim is to present the application of the hybrid method presented in part I to an inverse procedure to determine particle size and concentration under multiple-scattering conditions. The hybrid method is introduced as a combination of the four-flux method with coefficients obtained from Monte Carlo statistical simulations to take into account the actual three-dimensional geometry. Then an inversion scheme is expanded to enable the application of the hybrid method to particle size and concentration determination. We present the inversion method as well as exemplifying results of spectrum inversions.

© 2001 Optical Society of America

OCIS Codes
(290.0290) Scattering : Scattering
(290.4210) Scattering : Multiple scattering
(290.5850) Scattering : Scattering, particles

Original Manuscript: December 23, 1999
Revised Manuscript: December 8, 2000
Published: March 20, 2001

Marek Czerwiński, Janusz Mroczka, Thiery Girasole, Gérard Gouesbet, and Gérard Gréhan, "Light-transmittance predictions under multiple-light-scattering conditions. II. Inverse problem: particle size determination," Appl. Opt. 40, 1525-1531 (2001)

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  1. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier Scientific, Amsterdam, 1977).
  2. G. Backus, F. Gilbert, “Uniqueness in the inversion of gross earth data,” Philos. Trans. R. Soc. London Ser. A 266, 123–192 (1970). [CrossRef]
  3. M. Czerwiński, J. Mroczka, D. Wysoczański, “Inverse problem in multiple light scattering—hybrid method application,” in Proceedings of MUSCLE, the 10 Tenth International Workshop on Multiple Scattering Lidar Experiments, P. Bruscaglioni, ed. (Department of Physics, University of Florence, Italy, 1999), pp. 257–263.
  4. M. Czerwiński, “Modélisation de la turbidité spectrale d’un milieu multidiffusif et son application au problème inverse,” Ph.D. dissertation (Université de Rouen, Rouen, France, 1998).
  5. R. P. Brend, Algorithms for Minimisation without Derivatives, Prentice-Hall, Englewood Cliffs, N.J., 1973) Chaps. 3 and 4.
  6. G. E. Forsythe, M. A. Malcolm, B. C. Moler, Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J., 1977), Chap. 7.2.

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