  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.

Instrumentation and Methods for Astrophysics;Atmospheric and Oceanic Physics