Non-redundant representation of the field radiated in the Fraunhofer region by a parabolic reflector

In this work, a non-redundant and efficient representation of the electromagnetic field, radiated in the far-field region by a centered parabolic antenna fed at the focus, is developed. This result is a consequence of a proper choice of the source modelling, which fixes the optimal phase factor to extract from the field expression and the optimal coordinates to use for parameterizing the observation domain. In fact, by using the minimal convex domain enclosing the antenna, the number of needed field samples can be significantly reduced as compared with the spherical modelling of the source. A precise, fast and stable sampling algorithm of central type is developed to interpolate efficiently the antenna far-field samples. Some reconstruction examples, assessing the effectiveness of the algorithm, complete the paper