Integral form of the radiative transfer equation inside refractive cylindrical media

We consider the time-independent radiative transfer process inside cylindrical refractive semitransparent media with an internal space-dependent energy source, anisotropic scattering function, and specular reflecting boundary conditions. The integral form of the radiative transfer equation with any spatially continuous refractive index is worked out from its integro-differential form. To this end, the method of characteristics is used to solve the optical problem and, combined with a ray tracing technique, to integrate the radiative transfer equation along the curved light paths.