Polyhedral sampling structures for phaseless spherical near-field antenna measurements

The reconstruction of radiation patterns from phaseless near-field antenna measurements has been investigated using different methods like two-sphere techniques, indirect holography, or the use of different probes. Recent research on two-sphere techniques introduces algorithms originally developed for phase retrieval, e.g., PhaseLift and Wirtinger-Flow - applied to Spherical Near-Field (SNF) measurements, phase retrieval corresponds to obtaining the phase of the Spherical Mode Coefficients (SMCs) from amplitude Near-Field (NF) measurements only. It has been shown that Wirtinger-Flow benefits in this case from sample points distributed over distinct structures (two spheres of different size or a sphere and a plane), decreasing the redundancy. Furthermore, it has been shown that increasing the distance between both structures improves the reconstruction of the Far Field (FF). With this work we aim at deepening the above knowledge in the context of spherical wave expansions. From a mathematical point of view, planes can be seen as spheres of infinite radius, i.e., a plane combined with a sphere may be interpreted as a special case of combining two spheres. This interpretation goes hand in hand with the observation that an increased radius difference between two spheres leads to better reconstruction performance. Consequently, we analyze different polyhedral sampling structures composed of planes (such as octahedrons or cubes), mimicking several spheres of infinite radius in different spatial directions. For the mathematical analysis of non-spherical structures in the basis of spherical waves, pointwise probe correction is used. In experiments the polyhedron approach is less influenced by the choice of radii of the single structures compared to the standard two-spheres/sphere-plane sampling.