Techniques for arbitrary sampling in two-dimensional Fourier transforms

In this paper, we discuss two effective methods for computing optical propagations using two-dimensional (2D) discrete Fourier transforms: the matrix triple product (MTP) and the chirp z-transform (CZT) and analyze their performance both in theory and via benchmarks compared to the performance of a traditional padded fast Fourier transform (FFT). We show that, in many regimes of interest for phase-retrieval algorithms, the MTP or CZT is comparable to or better than the FFT in terms of run time while offering more flexible control over the sampling. We propose that for many applications, the CZT makes a robust general purpose alternative to the padded 2D FFT.