Transition radiation (TR) and diffraction radiation (DR) appearing as a result of dynamic polarization of medium has widely been used for electron beam diagnostics during the last few years. A lot of techniques for electron beam diagnostics imply description of these phenomena assuming that the radiated area of the target is negligibly small in comparison with the radiation spot in the detector plane (far-field approximation). However, for high-energy electrons this area may reach a macroscopic dimension. In this Letter the general theory in the pre-wave zone is presented. Two new approaches for rejecting the pre-wave zone effect are described and analyzed. By installing a thin lens in the optical path of the measurement system or by developing a concave target, the pre-wave zone effect can be reduced or even rejected.