Accelerated near-field algorithm of sparse apertures by non-uniform fast Fourier transform

We present an accelerated algorithm for calculating the near-field of non-uniform sparse apertures with non-uniform fast Fourier transform (NUFFT). The distances of the adjacent units in non-uniform sparse apertures are unequal and larger than half a wavelength. The near-field of apertures can be calculated by the angular spectrum method and the convolution methods, and according to the different convolution kernels, the convolution methods can be divided as the Fresnel kernel convolution and the Rayleigh-Sommerfeld kernel convolution. The Fresnel kernel is the approximation of the Rayleigh-Sommerfeld kernel in the far regions of the near-field zone. In uniform apertures, the three methods can be accelerated by fast Fourier transform (FFT). However, FFT should be replaced by NUFFT for non-uniform sparse apertures. The simulation results reveal that the Rayleigh-Sommerfeld convolution with NUFFT (RS-NUFFT) can be applied to all aperture sizes, distributions and near-field distances. After investigating the error sources in RS-NUFFT, the techniques (padding zeros for apertures, increasing sampling rate for the convolution kernel) are developed for increasing the calculation accuracy of RS-NUFFT.