Spherical Near-Field Scanning With Higher-Order Probes

A general method for higher-order probe correction in spherical scanning is obtained from a renormalized least-squares approach. The renormalization causes the normal matrix of the least-squares problem to closely resemble the identity matrix when most of the energy of the probe pattern resides in the first-order modes. The normal equation can be solved either with a linear iterative solver (leading to an iterative scheme), or with a Neumann series (leading to a direct scheme). The computation scheme can handle non-symmetric probes, requires only the output of two independent ports of a dual-polarized probe, and works for both phi and theta scans. The probe can be characterized either by a complex dipole model or by a standard spherical-wave representation. The theory is validated with experimental data.