Sinc method for generating and extending phase screens of atmospheric turbulence.

We present a method, based on sinc series approximation, for generating and extending phase screens of atmospheric turbulence in real time to arbitrary lengths. Unlike phase screen representations based on the Fourier series, the sinc approximation is naturally suited to problems on infinite domains and thus avoids the problem of artificial periodicity inherent in the Fourier series. In particular, phase screens generated using the sinc method have accurate non-periodic statistics throughout the computational domain. They can also be extended using a conditional probability distribution without having to deal with artifacts of periodicity. This is a crucial feature for long time-dependent simulations of dynamic turbulence that require very long phase screen realizations. Both the generation and extension methods take advantage of special structures inherent in the sinc approximation, leading to light memory footprints and fast computations based on the FFT. Numerical results demonstrate the accuracy of the sinc method, reproducing the correct ensemble averaged statistics as well as the sample statistics of single realizations. In other words, the sinc method preserves ergodicity when this is a feature of the turbulence model. We also verify the computational efficiency of the proposed methods.

Numerical simulation of optical propagation using sinc approximation.

This paper further develops a recently proposed method for computing the diffraction integrals of optics based on sinc series approximation by presenting a numerical implementation, parameter selection criteria based on rigorous error analysis, and example optical propagation simulations demonstrating those criteria. Unlike fast Fourier transform (FFT)-based methods that are based on Fourier series, such as the well-known angular spectrum method (ASM), the sinc method uses a basis that is naturally suited to problems on an infinite domain. As such, it has been shown that the sinc method avoids the problems of artificial periodicity inherent in the ASM. After a brief review of the method, the detailed error analysis we provide confirms its super-algebraic convergence and verifies the claim that the accuracy of the method is independent of wavelength, propagation distance, and observation plane discretization; it depends only on the accuracy of the source field approximation. Based on this analysis, we derive parameter selection criteria for achieving a prescribed error tolerance, which will be valuable to potential users. Numerical simulations of Gaussian beam and optical phased array propagation verify the high-order accuracy and computational efficiency of the proposed algorithms. To facilitate the reproduction of numerical results, we provide a Matlab code that implements our numerical approach for the Fresnel diffraction integral. For comparison, we also present numerical results obtained with the ASM as well as the band-limited angular spectrum method.