Application of Nonuniform FFT to Spherical Near-Field Antenna Measurements

This article investigates on the use of nonuniform fast Fourier transform (NUFFT) to solve spherical near-field transformation problems. Traditional postprocessing algorithms make use of conventional FFT for the transformation of measured grids with uniform sampling. More recently, the processing of irregular sampling grids has been introduced by means of matrix-based algorithms. The benefits of both type of algorithms are combined in this article with the implementation of the spherical wave expansion (SWE) summation and its adjoint with NUFFT. This allows the processing of fields with the efficiency of the FFT approaches and the versatility of the matrix operators. To this end, the NUFFT will be introduced and it will be shown how it can be implemented to accelerate the multidimensional summations required in the SWE calculations. Numerical investigations will be introduced to demonstrate the computational gains achieved with negligible approximation errors. Finally, the NUFFT will be tested on three different spherical near-field postprocessing problems: far-field transformation of near fields measured with spiral scanning, phaseless measurements on spherical surfaces with different sampling grids, and antenna diagnostics.