A generalized approach to compensate for low and high frequency errors in FFT 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 ($L_0$). Otherwise, they fall short in correctly predicting both the low and high frequency behaviours of turbulence induced phase distortions. Sub-harmonic 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 $(G/L_0$). 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 0.5-3% for $(G/L_0$) ratio of 1/1000 even for screen sizes up to 100 m diameter.