Gaussian phase autocorrelation as an accurate compensator for FFT-based atmospheric phase screen simulations

TL;DR

This paper introduces a Gaussian phase autocorrelation matrix to improve FFT-based atmospheric turbulence simulations, significantly reducing phase structure-function errors across various screen size to outer scale ratios.

Contribution

The novel Gaussian phase autocorrelation method enhances FFT-based simulations by compensating residual errors, improving accuracy for all G/L0 ratios.

Findings

Reduces maximum phase structure-function error to within 1.8%

Effective across all G/L0 ratios, including small values

Addresses high-frequency undersampling and subharmonic weighting issues

Abstract

Accurately simulating the atmospheric turbulence behaviour is always challenging. The well-known FFT based method falls short in correctly predicting both the low and high frequency behaviours. Sub-harmonic compensation aids in low-frequency correction but does not solve the problem for all screen size to outer scale parameter ratios (G/$L_0$). FFT-based simulation gives accurate result only for relatively large screen size to outer scale parameter ratio (G/$L_0$). In this work, we have introduced a Gaussian phase autocorrelation matrix to compensate for any sort of residual errors after applying for a modified subharmonics compensation. With this, we have solved problems such as under sampling at the high-frequency range, unequal sampling/weights for subharmonics addition at low-frequency range and the patch normalization factor. Our approach reduces the maximum error in phase structure-function in the simulation with respect to theoretical prediction to within 1.8\%, G/$L_0$ = 1/1000.