An Efficient Calculation of the Far Field Radiated by Non-Uniformly Sampled Planar Fields Complying Nyquist Theorem

An efficient and accurate method to calculate the far field radiated by non-uniformly sampled planar apertures using the non-uniform fast Fourier transform (NUFFT) is shown. The sampled fields in the planar aperture have to comply the Nyquist theorem. The method takes into account the amplitude of the unit cell radiation pattern, which allows to compute more accurately the copolar and crosspolar components of the far field. Due to the generality of the NUFFT, it also allows to overcome some limitations of the FFT when computing the radiated fields of reflectarrays with periodicity larger than half a wavelength. Because the NUFFT is precision-dependent, a discussion of how its accuracy can affect the computed radiated fields is carried out. Numerical examples are provided to show the accuracy and performance of the NUFFT with regard to the FFT and direct evaluation of the fields. Finally, a study of computing times comparing the FFT, NUFFT and direct evaluation is presented.