Optical tomography problems at layered media

Abstract

In the present work, problems of optical diagnostics for inhomogeneous layered media are studied by the methods of the radiation transfer theory. A method for finding the relative refraction indices and optical layers thickness based on the results of tomography transmission measurements under a special type of external radiation source is proposed.

Solvability of the initial-boundary value problem for an integrodifferential equation

“…Inserting the resulting estimate into (20), we see that (13) holds in this case as well. By (13), we deduce from (11) that…”

“…The applications of radiation transfer theory [1,19,20] commonly deal with both the inhomogeneity of the equation itself and some inhomogeneous boundary conditions. For instance, this happens when the medium contains interior radiation sources Φ and the radiation h on the medium is specified on the outer nonreflecting boundary Γ − ext .…”

Studying the problem of acoustic sounding of the seabed using methods of radiative transfer theory

“…It is caused by the smallness of the ratio of the reflected sig nal to the total signal In our opinion, the field of developing methods based on analysis of the quali tative properties of the solution to the transfer equa tion is promising. These methods make it possible to effectively solve inverse problems for the radiative transfer equation in the case of strongly scattering media [19][20][21][22].…”

Initial-boundary value problem for a radiative transfer equation with generalized matching conditions

“…The rapid development of computational methods over the last decades allows for solving genuinely timeconsuming computational problems of the radiation transfer theory. In turn, new sophisticated models, new statements of the direct, inverse, and the extremal problems require both the theoretical justification and the development of numerical methods for its solving [6][7][8][9][10][11][12][13][14][15][16][17][18].…”