Ray-tube integration in shooting and bouncing ray method revisited

The method of shooting and bouncing rays (SBR) was originally developed for radar cross section (RCS) analysis of aircraft engines, but is today widely used in many applications requiring high-frequency approximations. A dense grid of ray-tubes are launched from the source and traced by the laws of geometrical optics (GO) until they reach a defined exit aperture, from which the far field contribution of the ray-tube is obtained by surface integration. Two alternatives have been suggested on where to perform the surface integration, namely (1) on the ray-tube cross-section or (2) on the exit aperture. The first option is convenient as the electrical field is assumed constant in the ray-tube surface and has been suggested for complex scattering problems. In this paper, it is demonstrated that the surface integration over the ray-tube area can cause a ripple anomaly. It is illustrated that the ripple is caused by omitting parts of the integration surface from which there are no power flow. It is concluded that exit aperture integration should be selected in SBR analysis.