On the Interpolation of Electromagnetic Near Field Without Prior Knowledge of the Radiating Source

A method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available. In the absence of a priori knowledge, general properties of the electromagnetic field are exploited to estimate the field, namely, the minimum complexity of the field, and the continuity of the first derivatives. These properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results, respectively. The proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas. The quality of the interpolation and its robustness to noise are investigated. Despite its simplicity, the interpolation method is able to properly estimate the near field from a random coarse sampling of 2λ. The quality of the near-field interpolation is also confirmed by deriving the far-field. These promising results pave the way for the development of fast antenna measurement procedures.