An extremum problem for the radiation transfer equation

Abstract

In the present work, we treat a coated-optics problem in which it is required to choose an optimal refractive index of intermediate layer in a threelayer medium providing for maximum transmission of radiation through the medium. The extremum problem is considered as a formulation of the inverse problem for the stationary radiation transfer equation with generalized matching conditions for the Fresnel reflection-refraction at the interfaces between the media. Some analytical solutions are obtained.

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

“…in C b (Γ + ) since if f + is known then we can find the solution to (10) using the explicit formula (11). Since for λ > λ − we have…”

“…In the theory of boundary value problems for the stationary transfer equation with generalized matching conditions at the interface between the media [9][10][11][12][13] it is known that the conditions B ≤ 1 and Λ < 1 ensure the unique solvability of the stationary boundary value problem. It follows from (34) that if B ≤ 1 then the stabilization of nonstationary solution requires that…”

“…The articles [9][10][11][12][13] are devoted to studying boundary value problems for the stationary radiation transfer equation with generalized matching conditions at the interface between the media. Continuing the research in this article, we consider the case of nonstationary equation in a medium with plane-parallel geometry.…”

“…The concrete form of the matching operator B is determined by the characteristics of radiation and interfaces. The most widespread matching conditions in radiation transfer theory are those corresponding to the continuous "gluing" of the solution [1,2] as well as Fresnel and diffusion type conditions [9][10][11][12][13]. Note that we do not exclude the case of a breeding medium and its boundaries, and thus, do not impose the restrictions Λ ≤ 1 and B ≤ 1 typical for the solvability of the stationary boundary value problem [9][10][11][12][13].…”

Определение Показателей Преломления Слоистой Среды При Импульсном Режиме Облучения

“…В рамках этой модели авторами исследованы обратные и экстремальные задачи для стационарного уравнения переноса неполяризованного излучения [20][21][22][23]. Содержание обратных задач заключалось в нахождения показателей преломления слоистой среды, а постановки экстремальных задач имели цель определения оптимальных параметров иммерсионной жидкости при оптическом просветлении биологических тканей.…”