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.