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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 32 — Nov. 10, 2009
  • pp: 6178–6187

Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application

Vladimir V. Berdnik and Valery A. Loiko  »View Author Affiliations

Applied Optics, Vol. 48, Issue 32, pp. 6178-6187 (2009)

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A method to retrieve the radius and the relative refractive index of spherical homogeneous nonabsorbing particles by multiangle scattering is proposed. It is based on the formation of noise-resistant functionals of the scattered intensity, which are invariant with respect to the linear homogeneous transformations of an intensity-based signal and approximation of the retrieved parameters’ dependence on the functionals by a feed-forward neural network. The neural network was trained by minimization of the mean squared relative error in the range of particle radii from 0.6 mkm up to 13.6 mkm and relative refractive index from 1.015 up to 1.28. In comparison with training on a minimum of the mean squared error, this method enables one to increase the accuracy of the radius retrieval in the range of radii from 0.6 to 2 μm and refractive index in the range from 1.015 to 1.1. The values of intensity of light scattered in the interval of angles 10 ° 60 ° are used as input data. If the measurement error is 20%, the mean errors of the radius and relative refractive index are 0.8% and 7%, respectively. The results obtained by the proposed method and by the trial and error method with published experimental data (measured with a scanning flow cytometer) are compared. The maximal difference in the retrieval results of radius and the relative refractive index of particles obtained by both methods is under 5%.

© 2009 Optical Society of America

OCIS Codes
(160.2100) Materials : Electro-optical materials
(160.3710) Materials : Liquid crystals
(310.6860) Thin films : Thin films, optical properties
(290.5855) Scattering : Scattering, polarization

ToC Category:

Original Manuscript: March 19, 2009
Revised Manuscript: October 15, 2009
Manuscript Accepted: October 19, 2009
Published: November 2, 2009

Vladimir V. Berdnik and Valery A. Loiko, "Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application," Appl. Opt. 48, 6178-6187 (2009)

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  1. R. Xu, Particle Characterization: Light Scattering Methods (Kluwer, 2000).
  2. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, 1977).
  3. A. N. Tichonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, 1977).
  4. E. Kissa, Dispersions: Characterization, Testing, and Measurement, Vol. 84 of Surfactant Science Series (Marcel Dekker, 1999).
  5. M. A. van Dilla, P. N. Dean, O. D. Laerum, and M. R. Melamed, Flowcytometry: Instrumentation and Data Analysis (Academic, 1985).
  6. M. Bartholdi, G. C. Salzman, R. D. Hielbert, and M. Kerker, “Differential light scattering photometer for rapid analysis of single particles in flow,” Appl. Opt. 19, 1573-1581 (1980). [CrossRef]
  7. V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243-255 (2000). [CrossRef]
  8. F. Girosi, M. Jones, and T. Poggio, “Regularization theory and neural networks architectutes,” Neural Comput. 7, 219-296(1995). [CrossRef]
  9. C. M. Bishop, “Training with noise is equivalent to Tikhonov regularization,” Neural Comput. 7, 108-116 (1995). [CrossRef]
  10. K. Ludlow and J. Everitt, “Inverse Mie problem,” J. Opt. Soc. Am. A 17, 2229-2235 (2000). [CrossRef]
  11. D. H. Tycko, M. H. Metz, E. A. Epstein, and A. Grinbaum, “Flow-cytometric light scattering measurement of red blood cell volume and hemoglobin concentration,” Appl. Opt. 24, 1355-1365 (1985). [CrossRef]
  12. S. Zakovic, Z. J. Ulanowski, and M. C. Bartholomew-Biggs, “Application of global optimization to particle identification using light scattering,” Inverse Prob. 14, 1053-1067(1998).
  13. S. Zakovic, Z. J. Ulanowski, and M. C. Bartholomew-Biggs, “Using global optimization for a microparticle identification problem with noise data,” J. Global Optimization 32, 325-347(2005).
  14. S. Min and A. Gomez, “High-resolutionsize measurement if single spherical particles with a fast Fourier transform of the angular scattering intensity,” Appl. Opt. 35, 4919-4926(1996). [CrossRef]
  15. K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004). [CrossRef]
  16. www.nvidia.com
  17. S. Haykin, Neural Networks--A Comprehensive Foundation (Prentice-Hall, 1999).
  18. C. Lee Giles and T. Maxwell, “Learning, invariance, and generalization in high-order neural networks,” Appl. Opt. 26, 4972-4978 (1987). [CrossRef]
  19. Z. Ulanowski, Z. Wang, P. H. Kaye, and I. K. Ludlow, “Application of neural networks to the inverse light-scattering problem for spheres,” Appl. Opt. 37, 4027-4033 (1998). [CrossRef]
  20. Z. Wang, Z. Ulanowski, and P. H. Kaye, “On solving the inverse scattering problem with RBF neural networks: noise-free case,” Neural Comput. Applic. 8, 177-186 (1999).
  21. V. V. Berdnik, R. D. Mukhamedjarov, and V. A. Loiko, “Application of the neural network method for determining the characteristics of homogeneous spherical particles,” Opt. Spectrosc. 96, 285-291 (2004). [CrossRef]
  22. V. V. Berdnik, R. D. Mukhamedjarov, and V. A. Loiko, “Characterization of optically soft spheroidal particles by multiangle light-scattering data by use of the neural-networks method,” Opt. Lett. 29, 1019-1021 (2004). [CrossRef]
  23. V. V. Berdnik, K. Gilev, A. Shvalov, V. P. Maltsev, and V. A. Loiko, “Characterization of spherical particles using high-order neural networks and scanning flow cytometry,” J. Quant. Spectrosc. Radiative Transf. 102, 62-72(2006).
  24. V. V. Berdnik and V. A. Loiko, “Retrieval of particle characteristics with high-order neural networks: application to scanning flow cytometry,” Proc. SPIE 6734 (2007).
  25. A. Ishimaru, R. J. Marks, L. Tsang, C. M. Lam, D. C. Park, and S. Kitamura, “Particle-size distribution determination using optical sensing and neural networks,” Opt. Lett. 15, 1221-1223 (1990). [CrossRef]
  26. A. O. Nascimento, R. Guardani, and M. Giulietti, “Use of neural networks in the analysis of particle size distributions by laser diffraction,” Powd. Technol. 90, 89-94 (1997).
  27. P. G. Hull and Quinby-Hunt, “A neural-network to extract size parameter from light-scattering data,” Proc. SPIE 2963, 448-453 (1997).
  28. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  29. D. Dejrmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, 1969).
  30. V. A. Babenko, L. A. Astafyeva, and V. N. Kuzmin, Electromagnetic Scattering in Disperse Media (Springer, , 2003).
  31. X.-P. Zhang, “Space--scale adaptive noise reduction in images based on thresholding neural network,” Mathematical Programming B 45, 503-528 (1989).
  32. D. Liu and J. Nocedal, “On the limited memory BFGS method for large scale optimization,” Mathematical Programming B 45, 503-528 (1989).
  33. V. P. Maltsev and K. A. Semyanov, Characterization of Bio-Particles from Light Scattering (VSP, 2004).

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