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.

中文翻译：

---

非均匀 FFT 在球形近场天线测量中的应用

本文研究了使用非均匀快速傅立叶变换 (NUFFT) 来解决球面近场变换问题。传统的后处理算法利用传统的 FFT 对具有均匀采样的测量网格进行变换。最近，通过基于矩阵的算法引入了对不规则采样网格的处理。本文将这两种算法的优点与球面波展开 (SWE) 求和的实现及其与 NUFFT 的结合相结合。这允许以 FFT 方法的效率和矩阵运算符的多功能性来处理字段。为此，将介绍 NUFFT，并将展示如何实施它来加速 SWE 计算所需的多维求和。将引入数值研究来证明在近似误差可忽略不计的情况下实现的计算增益。最后，NUFFT 将在三个不同的球面近场后处理问题上进行测试：使用螺旋扫描测量的近场远场变换、具有不同采样网格的球面无相测量以及天线诊断。