Задачи рентгеновской и оптической томографии [Итоговый научный отчет по междисциплинарному интеграционному проекту СО РАН: “Разработка теории и вычислительной технологии решения обратных и экстремальных задач с приложением в математической физике и гравимагниторазведке”]

The problems of X-ray and optical tomography have been considered in the review. A method for determination of a substance chemical composition based on the use of X-ray irradiation results has been proposed. The solution uniqueness for the problem of the attenuation coefficient determination for the vector transfer equation under a special external radiation source has been shown. The problems of determination of the refraction indices and optical thicknesses for a layered medium have been studied. A computer verification of the proposed numerical algorithms has been carried out.