Application of reflection on curved surfaces and roughness on surface in ray tracing for tunnel propagation

In ray tracing simulations, curved surfaces and edges are difficult to handle. The approximation of dividing the curved surface into smaller flat plates is not so accurate as the size of smaller plates may not satisfy geometrical optics assumption, and the reflection point which satisfies Fermat's principle may not exist. In this work, a new ray tracing method which models the reflection on the curved surface was implemented. Path gain simulation results are then compared with measurements made inside an arched tunnel. Next, the effect of rough surface is introduced in the ray tracing simulation, and simulation results are compared with measurement data.