Two-dimensional radiative transfer due to curved Dirac delta line sources

In this article, the two-dimensional radiative transport equation is considered for the curved Dirac delta line source. In order to account this source type, Green's function of the radiative transport equation for the half-plane is derived in parts of the ballistic and diffuse contribution as well as under consideration of the Fresnel reflection at the boundary. The final results are verified with the Monte Carlo method for different collimated beams and several curved sources such as the elliptic and logarithmic spiral line source.