Monte Carlo Method for Solving Inverse Problems of Radiation Transfer

Abstract

Monte Carlo modifications for solving problems of radiation transfer: elements of using the Monte Carlo method in radiation transfer computation the conjugate computation scheme use of the importance function method of mathematical expectation for plane slab model improvement of the method of mathematical expectation modification of the distribution of particle path length modification of the trajectory angular distribution modification of radiation transfer modelling in spherical atmosphere (statement of the problem computational algorithm). Generalized transport equation with highly peaked phase function: generalized transport equation approximation of highly peaked phase function transformation of standard transport equation optimizing procedures for modelling and calculations (modification of the estimate modification of trajectory modelling modifications of the calculation of the radiation flux) radiation transfer in broken clouds (free path density in the layer of broken clouds results of numerical experiments) conclusions. Calculation of the correlation characteristics of radiation field in the stochastic medium by the Monte Carlo method: problem statement computation of derivatives of a field of brightness by the Monte Carlo method dispersions of the derivatives DjI estimator. Identification of the phase function: statement of the problem method of successive approximations (additive method multiplicative method) estimating the intensity of scattered radiation (on the use of the plane atmosphere model local estimate of intensity) numerical results study of convergence. Regularization in solving inverse problems of atmosphere optics: recovery of altitudinal variations of the scattering coefficient analytical regularization regularization in estimating the phase function statistical regularization application of statistically orthogonal expansions. Direct and inverse problems of radiation transfer in a plant canopy plant canopy model transport equation for a plant canopy Markov chain modelling taking into account the hot spot effect statement of the inverse problem and an algorithm of its solution evaluation of derivatives by the Monte Carlo method on estimating the leaf-normal distribution for a plant canopy (iterative method on calculating the integrals A, B and C) numerical results synopsis. X-ray tomography in scattering media: mathematical background the general scheme of the method (design and arrangement of the detectors step 1 - reconstruction of the extinction coefficient distribution step 2 - reconstruction of the scattering coefficients step 3 - reconstruction of the absorption coefficient distribution) numerical results (computing the jumps of the first and second kind scattering effect on body image reconstruction) conclusions.