Null-collision meshless Monte Carlo - A new reverse Monte Carlo algorithm designed for laser-source emission in absorbing/scattering inhomogeneous media

Sans, M. ; El Hafi, M. ; Eymet, V. ; Forest, V. ; Fournier, R. ; Villefranque, Najda

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<p align=justify>Over recent decades, numerous studies in a myriad of research fields have improved the efficiency of the Monte Carlo method to solve radiative transfers in heterogeneous media. The formalization of the concept of path integral formulation on which the construction of the random trajectories is based has made it possible to lay down a convenient framework to investigate sampling strategies and to design adapted low-variance algorithms. Our study focuses on the particular case of laser emission, which corresponds to a spatially-localized source emitting in a low solid angle, which partially illuminates the environment. In this case, the intrinsic characteristics of the laser emission cause problems of convergence with a Monte Carlo method due to the difficulty in statistically linking sensors (probe points) to sources. This paper proposes, using integral formulation and a Null-Collision Algorithm (NCA), a practicable and simply implementable method to avoid such constraints. The intensity is broken down into a direct and a scattered term (local estimate technique). Then, a reworking of the various integral terms makes it possible to propose a complete algorithm adapted to a collimated source partially illuminating the studied scene. Non-zero contributions are brought more continuously to the Monte Carlo weight and variance is strongly reduced. The entire methodology, from integral formulation to algorithmic interpretation, is presented step by step. For validation purposes, a new reverse and optimized Monte Carlo algorithm is compared with an analogous Monte Carlo for estimation of flux absorbed by a wall in an academic configuration, which ensures benchmark results. As the current proposed algorithm is highly suitable for building computer-generated images (probe calculation), the propagation of light due to laser emission through inhomogeneous environments is then illustrated by the construction of such images. This new tool provides useful support for experimental characterization of the radiative behaviour of particles.</p>
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