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Application of the Tikhonov and the modified Twomey methods to calculate narrow microparticle size distributions by the laser diffraction technique

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Języki publikacji
EN
Abstrakty
EN
New ways of calculating narrow microparticle size distributions based on using the Tikhonov and the modified Twomey methods for the laser diffraction technique are presented. These allow to have reduced the broadening (over-smoothing) of the result occurring in these methods for narrow distributions both singular and their sum. The calculated singular distributions and their distribution sum were then approximated by a Gaussian function and a bimodal Gaussian function, respectively, using the Levenberg- Marquardt method. The angular distribution of scattering power was measured for polystyrene particles with radii of 0.676 μm and 1.573 μm, and for their sum. The tests were carried out for linearly polarized He-Ne laser light scattered by a dilute aqueous suspension of these particles. The results obtained were compared with those obtained with the nanoDS instrument (CILAS). It turned out that using the way based on the Twomey method, the parameters of the narrow distribution sought could be determined quite well.
Rocznik
Strony
art. no. e145497
Opis fizyczny
Bibliogr. 22 poz., rys., wykr.
Twórcy
  • Institute of Optoelectronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland
  • Institute of Optoelectronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland
Bibliografia
  • [1] Tikhonov, A. N., Goncharsky, A. V., Stepanov, V. V. & Yagola, A. G. Numerical Methods for The Solution of Ill-Posed Problems. (Kluwer Academic Publishers, Dordrecht 1995).
  • [2] Groetsch, C. W. The Theory of Tikhonov Regularization for Fredholm Equations of The First Kind. (Boston-London-New York, Pitman Publishing 1984).
  • [3] Igushi, T. & Yoshida, H. Investigation of low-angle laser light scattering patterns using the modified twomey iterative method for particle sizing. Rev. Sci. Instrum. 82, 015111 (2011). https://doi.org/10.1063/1.3520136
  • [4] Igushi, T. & Yoshida, H. Influence of the number of detectors by laser scattering method for estimation of particle size. Rev. Sci. Instrum. 83, 055103 (2012). https://doi.org/10.1063/1.4709493
  • [5] Twomey, S. Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions. J. Comput. Phys. 18, 188-200 (1975). https://doi.org/10.1016/0021-9991(75)90028-5
  • [6] Twomey, S., Herman, B. & Rabinoff, R. An extension to the Chahine method of inverting the radiative transfer equation. J. Atmos. Sci. 34, 1085-1090 (1977). https://doi.org/10.1175/1520-0469(1977)034<1085:AETTCM>2.0.CO;2
  • [7] Markowski, G. R. Improving Twomey’s algorithm for inversion of aerosol measurement data. Aerosol Sci. Technol. 7, 127-141 (1987). https://doi.org/10.1080/02786828708959153
  • [8] Marquardt, D. W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math. 11, 431-441 (1963). https://doi.org/10.1137/0111030
  • [9] Madsen, K., Nielsen, H. B. & Tingleff, O. Methods for Non-Linear Least Squares Problems 2nd edition (Technical University of Denmark, 2004). http://www2.imm.dtu.dk/pubdb/edoc/imm3215.pdf
  • [10] Weiner, I., Rust, M. & Donelly, T. D. Particle size determination: an undergraduate lab in Mie scattering. Am. J. Phys. 69, 129-136 (2001). https://doi.org/10.1119/1.1311785
  • [11] van de Hulst, H. C. Light Scattering by Small Particles. (Dover Publications, New York, 1981).
  • [12] Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles. (Wiley, New York, 1983).
  • [13] Kandlikar, M. & Ramachandran, G. Inverse methods for analysing aerosol spectrometer measurements: A critical review. J. Aerosol Sci. 30, 413-437 (1998). https://doi.org/10.1016/S0021-8502(98)00066-4
  • [14] Wiscombe, W. Mie Scattering Calculations: Advances in Technique and Fast Vector-Speed Computer Code. (NCAR, 1996).
  • [15] Hansen, P. C. The L-Curve and its Use in The Numerical Treatment of Inverse Problems (Technical University of Denmark, 2000).
  • [16] Hansen, P. C., Jensen, T. K. & Rodriguez, G. An adaptative pruning algorithm for the discrete l-curve criterion. J. Comput. Appl. Math. 198, 483–492 (2005). https://doi.org/10.1016/j.cam.2005.09.026
  • [17] Castellanos, J. L., Gomez, S. & Guerra, V. The triangle method for finding the corner of the L-curve. Appl. Numer. Math. 43, 359-373 (2002). https://doi.org/10.1016/S0168-9274(01)00179-9
  • [18] Pawlata, A. Examination of smooth surfaces roughness using angle scatterometer, part.1. The method of measurement. The measure-ment instrument. Bulletin of Military University of Technology 64, 47-58 (2015). https://doi.org/10.5604/12345865.1145426
  • [19] Particle size analysis - Laser diffraction methods. ISO 13320 (2009). https://www.iso.org/standard/44929.html
  • [20] Hale, G. M. & Querry, M. R. Optical constants of water in the 200nm to 200μm wavelength region. Appl. Opt. 12, 555-563 (1973). https://doi.org/10.1364/AO.12.000555
  • [21] Ma, X. et al. Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm. Phys. Med. Biol. 48, 4165-4172 (2003). https://doi.org/10.1088/0031-9155/48/24/013
  • [22] Xu, R. Particle Characterization. (Kluwer Academic Publishers, Dordrecht, 2000)
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ac1444a3-e1ba-4e68-bbad-71786f7fa7aa
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