Generalized approach to compensate for low- and high-frequency errors in fast Fourier transform-based phase screen simulations

Abstract

Fast Fourier transform-based phase screen simulations give accurate results only when the screen size (G) is much larger than the outer scale parameter (L₀). Otherwise, they fall short in correctly predicting both the low and high frequency behaviors of turbulence-induced phase distortions. Subharmonic compensation is a commonly used technique that aids in low-frequency correction but does not solve the problem for all values of screen size to outer scale parameter ratios (G/L₀). A subharmonics-based approach will lead to unequal sampling or weights calculation for subharmonics addition at the low-frequency range and patch normalization factor. We have modified the subharmonics-based approach by introducing a Gaussian phase autocorrelation matrix that compensates for these shortfalls. We show that the maximum relative error in structure function with respect to theoretical value is as small as 0.5% to 3% for (G/L₀) ratio of 1/1000 even for screen sizes up to 100 m diameter.

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