We present a new method for the generation of atmospheric turbulence phase screens based on the frequency shift property of the Fourier transform. This method produces low spatial frequency distortions without additional computation time penalties associated with methods using subharmonic subgrids. It is demonstrated that for simulations of atmospheric turbulence with finite outer scales, the performance of our method with respect to the statistical phase structure function of the screen meets or exceeds other methods with respect to agreement with theory. We outline small-scale accuracy issues associated with modelling non-Kolmogorov spectral power laws using existing techniques, and propose a solution. For simulations of long-range propagation through atmospheric optical turbulence, our method provides various advantages over standard methods.
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