Numerical statistical modeling of optical radiation transfer in random crystal media

The problem of numerical Monte Carlo simulation of the process of optical radiation transfer in scattering media, the scattering elements of which are transparent or semitransparent crystal particles, is considered. Among a large number of applications that require solving the equation for the transfer of electromagnetic radiation in the optical wavelength range in crystal media, the main attention is paid to solving one of the most important problems in atmospheric optics - the study of solar radiation transfer in cirrus clouds consisting of ice crystal particles. The main goal of such a study is to construct an adequate radiation model of crystal clouds, taking into account multiple scattering. In this paper, we consider two algorithms for numerical simulation of radiation transfer based on the Monte Carlo method and ray tracing. The first algorithm can be called traditional. It is well known and widely used by many authors for estimating linear functionals of the solution of the optical radiation transfer equation in isotropic media, in which the scattering phase functions do not depend on the direction of motion of photon, but are functions of the scattering angles. Such a model works well for media such as atmospheric aerosol or liquid drop clouds, in which scattering occurs on particles of spherical shape. In this context, this algorithm is adapted to the problems of radiation transfer in anisotropic crystal media. Its application to crystal media requires obtaining and storing a significant amount of initial data on the primary optical characteristics (attenuation coefficients and volume phase functions (second-rank tensors) of radiation scattering) necessary for modeling scattering processes. This volume especially increases for inhomogeneous stochastic scattering media, in which the shape, size, and orientation of particles are random functions of spatial coordinates. The key idea of the second, alternative algorithm is that in the process of modeling photon trajectories, the direction of scattering of a photon after a collision with a crystal is calculated using ray tracing, provided that the shape, size, and orientation of the particle are previously randomly selected from some random distribution that specifies the composition of the scattering environment. In this algorithm, there is no need for preliminary calculations of a large array of data on the primary optical characteristics of scattering media. The algorithm has a limitation on the size of crystal particles: their linear size must significantly exceed the radiation wavelength, since the laws of geometric optics are used in modeling the scattering angles and wave effects are not taken into account.