A generalized approach to compensate for low and high frequency errors in FFT based phase screen simulations

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.