Atmospheric turbulence induced phase distortions: the principal component analysis and optimized correction strategy

In this paper, we propose a method to correct phase aberrations caused by atmospheric turbulence based on principal component analysis (PCA). The results show that the method based on principal components (PCs) can effectively correct atmospheric turbulence induced phase distortions, whether the Kolmogorov spectrum is satisfied or not. The PCs showed higher sensitivity on key terms than Zernike polynomials (ZPs). PCs achieved percentage decrease in residual error exceeding 67% from 3^rd to 4^th term, and about 53% from 7^th to 8^th term. Meanwhile, the percentage decrease in error decreases slowly and evenly between different terms of ZPs less than 26%. Especially in the strong turbulence environment, PCs can use fewer terms to achieve higher correction accuracy. In addition, the minimum number of terms of PCs and ZPs required to satisfy different imaging criteria are also fitted, which provides data references for the rapid deployment of the model in different turbulent environments. This work provides wat we believe to be new ideas and strategies for image-based wavefront sensor-less adaptive optics to tackle the inherent trade-off between accuracy and computational efficiency, and further lays the foundation for faster and more accurate intelligent correction.