Monte Carlo Method for Solving Inverse Problems of Radiation Transfer

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 local 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.