Transition radiation in the pre-wave zone for an oblique incidence of a particle on the flat target

Backward transition radiation of an electron with an arbitrary energy is studied when an ideally-conducting target is flat and its normal is not collinear with the particle velocity (oblique incidence). A model for radiation registered with a small flat detector placed at a finite distance (including the radiation in the pre-wave zone) in the vicinity of specular reflection direction is developed. Characteristics of the radiation in the far-field zone are in complete agreement with well-known results. The calculations for pre-wave zone show that the angular distribution of the radiation intensity is distorted compared to the far-field case, and the radiation asymmetry (having a place in the far-field for moderately relativistic energies) is also preserved in the pre-wave zone. Some numerical estimations of the radiation asymmetry at a finite distance are also given. The technique developed may be used for estimations of coherent transition radiation intensity in the mm-wavelength range.