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Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution

Anew Fourier Series atmospheric phase screen generator is introduced. A Fourier Series (FS) is used to represent the wavefront phase as a two dimensional periodic function. The period of the function is chosen to be much larger than the outer scale of the turbulence and thus the FS accurately represents the power in the low spatial frequencies of the wavefront. The accuracy of the representation of the high spatial frequencies is determined by the number of terms used in the FS expansion. The FS based screen generator is capable of simulating atmospheric-induced wavefront phase distortions arising from temporal and/or anisoplanatic conditions. Both the spatial and temporal correlations between wavefront phases screens separated by time and/or angle are properly modeled. The conventional approach of simulating temporal evolution by making a large phase screen and then shifting is avoided. The phase screen generator is presented in an extremely compact and simple vector notation that lends itself for almost immediate implementation on modern mathematical analysis software packages.