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Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations

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Języki publikacji
EN
Abstrakty
EN
The light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present the implementation of this algorithm for one and three-dimensional light scattering computations and discuss its applicability in this field. We show that the Monte Carlo algorithm can provide valid and accurate results but, due to its convergence properties, it might be difficult to apply for problems with large volumes or refractive indices of scattering objects.
Słowa kluczowe
Czasopismo
Rocznik
Strony
17--35
Opis fizyczny
Bibliogr. 23 poz., rys.
Twórcy
  • Department of Metrology and Optoelectronics, Faculty of Electronics, Telecommunications and Engineering, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
  • Department of Metrology and Optoelectronics, Faculty of Electronics, Telecommunications and Engineering, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
Bibliografia
  • [1] TAFLOVE A., HAGNESS S.C., Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Norwood, MA, 2005.
  • [2] LAKHTAKIA A., Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields, International Journal of Modern Physics C 3(3), 1992, pp. 583–603, DOI:10.1142/S0129183192000385.
  • [3] YURKIN M.A., HOEKSTRA A.G., The discrete dipole approximation: an overview and recent developments, Journal of Quantitative Spectroscopy and Radiative Transfer 106(1–3), 2007, pp. 558–589, DOI:10.1016/j.jqsrt.2007.01.034.
  • [4] MISHCHENKO M.I., Electromagnetic Scattering by Particles and Particle Groups: An Introduction, Cambridge University Press, Cambridge, 2014.
  • [5] DRAINE B.T., FLATAU P.J., Discrete-dipole approximation for scattering calculations, Journal of the Optical Society of America A 11(4), 1994, pp. 1491–1499, DOI:10.1364/JOSAA.11.001491.
  • [6] MISCHCHENKO M.I., TRAVIS L.D., MACKOWSKI D.W., T-matrix computations of light scattering by nonspherical particles: a review, Journal of Quantitative Spectroscopy and Radiative Transfer 55(5), 1996, pp. 535–575, DOI:10.1016/0022-4073(96)00002-7.
  • [7] MARTELLI G.Z.F., DEL BAINCO S., ISMAELLI A., Light Propagation Through Biological Tissue and Other Diffusive Media: Theory, Solutions and Software, SPIE Press Monograph, Vol. PM193, Bellingham, 2010.
  • [8] WANG L., JACQUES S.L., ZHENG L., MCML – Monte Carlo modeling of light transport in multi-layered tissues, Computer Methods and Programs in Biomedicine 47(2), 1995, pp. 131–146, DOI:10.1016/0169-2607(95)01640-F.
  • [9] DORONIN A., RADOSEVICH A.J., BACKMAN V., MEGLINSKI I., Two electric field Monte Carlo models of coherent backscattering of polarized light, Journal of the Optical Society of America A 31(11), 2014, pp. 2394–2400, DOI:10.1364/JOSAA.31.002394.
  • [10] SMITHIES D.J., LINDMO T., CHEN Z., NELSON J.S., MILNER T.E., Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation, Physics in Medicine and Biology 43(10), 1998, pp. 3025–3044, DOI:10.1088/0031-9155/43/10/024.
  • [11] PLUCIŃSKI J., FRYDRYCHOWSKI A.F., New aspects in assessment of changes in width of subarachnoid space with near-infrared transillumination/backscattering sounding, part 1: Monte Carlo numerical modeling, Journal of Biomedical Optics 12(4), 2007, article 044015, DOI:10.1117/1.2757603.
  • [12] PLUCIŃSKI J., FRYDRYCHOWSKI A.F., Influence of pulse waves on the transmission of near-infrared radiation in outer-head tissue layers, Frontiers of Optoelectronics 10(3), 2017, pp. 287–291, DOI:10.1007/s12200-017-0723-7.
  • [13] KRASZEWSKI M., PLUCIŃSKI J., Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations, Optica Applicata 50(1), 2020, pp. 1–15, DOI:10.37190/oa200101.
  • [14] XIONG G., XUE P., WU J., MIAO Q., WANG R., JI L., Particle-fixed Monte Carlo model for optical coherence tomography, Optics Express 13(6), 2005, pp. 2182–2195, DOI:10.1364/OPEX.13.002182.
  • [15] DARIA V.R., SALOMA C., KAWATA S., Excitation with a focused, pulsed optical beam in scattering media: diffraction effects, Applied Optics 39(28), 2000, pp. 5244–5255, DOI:10.1364/AO.39.005244.
  • [16] DEVANEY A.J., Mathematical Foundations of Imaging, Tomography and Wavefield Inversion, Cambridge University Press, Cambridge, 2012.
  • [17] DUNN W.L., SHULTIS J.K., Exploring Monte Carlo Methods, Elsevier Science, Amsterdam, 2011.
  • [18] DOUCET A., JOHANSEN A.M., TADIĆ V.B., On solving integral equations using Markov chain Monte Carlo methods, Applied Mathematics and Computation 216(10), 2010, pp. 2869–2880, DOI:10.1016/j.amc.2010.03.138.
  • [19] PEREIRA P.F., SHERIF S.S., Simulation of the interaction of light and tissue in a large volume usinga Markov chain Monte Carlo method, Proceedings of SPIE 8412, 2012, article 841218, DOI:10.1117/12.2001455.
  • [20] KRASZEWSKI M., PLUCIŃSKI J., Coherent-wave Monte Carlo method for simulating light propagationin tissue, Proceedings of SPIE 9706, 2016, article 970611, DOI:10.1117/12.2213213.
  • [21] BORN M., WOLF E., Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th Ed., Cambridge University Press, New York, 2013.
  • [22] AKKERMANS E., MONTAMBAUX G., Mesoscopic Physics of Electrons and Photons, Cambridge University Press, Cambridge, 2007.
  • [23] SAAD Y., Iterative methods for sparse linear systems, 2nd Ed., Society for Industrial and AppliedMathematics, Philadelphia, 2003.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-05eb0198-4c40-4539-8b09-a2a0b072b2be
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