A Propagating Plane-Wave-Based Near-Field Transmission Equation for Antenna Gain Determination from Irregular Measurement Samples

In order to accurately determine the far-field gain of an antenna under test from near-field measurements, a general transmission equation between the ports of a transmitting and a receiving antenna is derived. The formulation is based on a propagating plane-wave expansion of the electric field and allows one to use a derivation based on far-field concepts separately for all entries of the plane-wave spectrum. It is shown that the equation is a generalization of the Friis transmission equation to the near-field case and the equation is compared with spherical multipole-based transmission equations for single and multiple antenna systems. The new transmission equation is integrated into the Fast Irregular Antenna Field Transformation Algorithm, which now allows one to determine the antenna gain pattern not only from canonical measurement surfaces as planes and spheres but also from highly irregular sample distributions. Examples using near-field data from both simulations and measurements are given to prove the validity of the formulation and to illustrate the capabilities of the implementation. In particular, it is also shown that accurate gain determination is possible from incomplete near-field measurements and that appropriate probe correction is important.