21 June 2015 Simulating the coherent light propagation in a random scattering materials using the perturbation expansion
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Multiple scattering of a coherent light plays important role in the optical metrology. Probably the most important phenomenon caused by multiple scattering are the speckle patterns present in every optical imaging method based on coherent or partially coherent light illumination. In many cases the speckle patterns are considered as an undesired noise. However, they were found useful in various subsurface imaging methods such as laser speckle imaging (LSI) or optical coherence tomography (OCT). All features of the speckle patterns and their connection with microstructure of scattering materials was not fully exploited. Further research on this topic may lead to a simple and inexpensive optical diagnostic methods. Theoretical and numerical research could greatly facilitate development of such methods. However, this requires simulations of coherent light propagation through a random scattering media of a length larger than few hundreds of a light wavelength. During such propagation the light can be scattered by many tens of thousands of scattering particles. The numerical methods, such as the radiative transfer theory and the Monte Carlo methods, allows to simulate propagation of the incoherent light in such a media but they do not consider the coherence properties of light. Moreover, they consider only average realization of the scattering medium and therefore does not allow to predict properties of any random fluctuations of the scattered light, such as a speckle patterns. Direct solvers of Maxwell or Helmholtz equations, such as finite-difference or finite-element methods could solve this problem but their computational complexity limits their application to media no longer than about 10 to 20 wavelengths of the light. Here we show an alternative approach based on solving the integral form of the Helmholtz equation written as a so called perturbation expansion. We show the numerical algorithm for solving this equation. The presented algorithm allows to simulate light scattering with accuracy similar to the finite difference methods but with much lower computational complexity. This can make it an useful tool in research on coherent light propagating through the random media.
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Maciej Kraszewski, Maciej Kraszewski, Michal Trojanowski, Michal Trojanowski, Marcin R. Strąkowski, Marcin R. Strąkowski, Jerzy Pluciński, Jerzy Pluciński, } "Simulating the coherent light propagation in a random scattering materials using the perturbation expansion", Proc. SPIE 9526, Modeling Aspects in Optical Metrology V, 95260M (21 June 2015); doi: 10.1117/12.2184870; https://doi.org/10.1117/12.2184870

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