X-ray transition radiation detectors (TRDs) are used for particle identification in both high energy physics and astroparticle physics. In most of the detectors, emission of the X-ray transition radiation (TR) starts at Lorentz factors above γ∼500 and reaches saturation at γ∼2÷3⋅103 . However, many experiments require particle identification up to γ∼105 , which is very difficult to achieve with conventional detectors. Semiconductor pixel detectors offer a unique opportunity for precise simultaneous measurements of spectral and angular parameters of TR photons. Test beam studies of the energy and the angular distributions of TR photons emitted by electrons and muons of different momenta crossing several types of radiators were performed at the CERN SPS with a 480 μ m thick silicon detector bonded to a Timepix3 chip. High resolution images of the energy−angle phase space of the TR produced by different radiators were obtained and compared with MC simulations. The characteristic interference patterns are in agreement with the theoretical models with an unprecedented level of details. The studies presented in this paper also show that simultaneous measurements of both the energy and the emission angles of the TR X-rays could be used to enhance the particle identification performances of TRDs.