A problem of surface imaging and parameter determination in an antenna far-field range by scanning the electromagnetic field intensity distribution in a plane combined with the imagined position of a test antenna aperture is considered. The signal at the receiver output is formed as a result of superposition in the antenna of the direct and reflected waves from the range surface. Exact and approximate mathematical models for description of an "Antenna - Range" system are offered and analysed. Model parameters are determining by statistical regression method. The system parameter dependence on model parameters is obtained. The offered method allows determining both the path length and direction of the reflected waves, the sites of the antenna range essential in reflection, as well as all system parameters, including the module of reflection coefficient. Processing of both modeled and measured signals, as well as surface imaging of a virtual and the real antenna ranges are carried out. The results may be used during operation of any existing antenna range, as well as in their design.