Flow chart sketching the steps of the numerical procedure of the relativistic ray tracing method (see Sect. A.5). As a first step the geometrical setup, the emitting surface, is defined by a mesh of triangular surface elements. Additionally an interpolation table has to be provided, which contains information of possible photon trajectories. Based on these inputs the main step, the projection onto the observer sky, can be performed. In this step the two solutions for trajectories are determined and saved if valid for each phase ϕ and for each surface element n. In an optional step (dashed arrows) overlapping projections are filtered. In the end the given specific intensity is applied to the valid projections of each individual surface element and the resulting overall observed flux is determined.