An Efficient Two-Stage Method for Correcting 3-D Positioning Errors of the Measuring Probe in a Non-Redundant Spherical Scan

A robust procedure for compensating for inaccuracies caused by 3-D positioning errors in the measurement of the near-field (NF) data required by the non-redundant (NR) spherical near-to-far-field (NtFF) transformations for long antennas is presented in this article. These errors may arise from hardware defects and positioners’ controlling inaccuracies, which may cause the probe to deviate from the intended spherical scan surface and prevent it from reaching the NR sampling points required by either of the two NR representations for long antennas. To account for these errors, the method proceeds through two steps. The first step, called spherical wave correction, compensates for the phase shifts due to radial displacements from the intended scanning sphere. As a result of this correction, the NF samples belong to the intended scanning sphere, but at points different from those required by the adopted NR representation, thus impairing the subsequent NF reconstruction via the optimal sampling interpolation (OSI) algorithm. Such an algorithm enables one to efficiently build the iterative scheme used in the second step, which makes it possible to effectively retrieve the NF samples at the prescribed NR positions. Test results are shown to numerically validate the capability of the developed two-step compensation technique to correct even significant and pessimistic 3-D positioning errors affecting the collection of the NF data.