An Efficient Method to Compensate for Known 3-D Probe Position Errors in a NF-FF Transformation with Spherical Scanning using a Minimum Number of Measurements

In this work, an efficient two-step algorithm to compensate for 3-D probe positioning errors, which occur in a near-field-far-field transformation (NF-FFT) using a minimum number of spherical NF measurements, is developed and numerically assessed. Firstly, a so called spherical wave correction is exploited to correct the phase shifts caused by the deviations from the nominal spherical surface. Then, an iterative technique is employed to recover the NF samples at the exact sampling points from those, altered by 2-D mispositioning errors, attained at the previous step. Once the correctly positioned samples have been retrieved in such a way, an optimal sampling interpolation formula is used to accurately determine the massive input NF data for the classical spherical NF-FFT. Numerical tests will be shown to prove the capacity of the devised method to correct even severe 3-D positioning errors.