Complex-point dipole formulation of probe-corrected spherical near-field scanning of electromagnetic fields using symmetric higher-order probes

A computationally efficient probe-corrected electromagnetic theory is presented for computing the field of an arbitrary source of finite extent (test antenna) from measurements with a known symmetric probe on a surrounding spherical surface. The new theory, which can deal with higher-order probes, has exactly the same computational complexity as the standard theory, which can deal only with first-order probes. By representing the probe with complex-point dipoles, the new theory avoids the use of translation and rotation theorems as well as differential operators. The disadvantage of the new theory is that it requires the use of nonlinear optimization to determine the probe model. Numerical validation is achieved through an example involving a complicated source measured with a square waveguide probe.