Influencing factor analysis of the Principal Component Analysis for the characterization and restoration of phase aberrations resulting from atmospheric turbulence

Restoration of phase aberrations is crucial for addressing atmospheric turbulence in light propagation. Traditional restoration algorithms based on Zernike polynomials (ZPs) often encounter challenges related to high computational complexity and insufficient capture of high-frequency phase aberration components, so we proposed a Principal-Component-Analysis-based method for representing phase aberrations. This paper discusses factors influencing the accuracy of restoration using Principal Components (PCs), mainly sample space size and the sampling interval of D/r₀, which is used to characterize the strength, with r₀ being the atmospheric coherence length and D being the pupil diameter, on the basis of characterizing phase aberrations by PCs. The experimental results show that a larger D/r₀ sampling interval can ensure the generalization ability and robustness of the principal components in the case of a limited amount of original data, which can help to achieve high-precision deployment of the model in practical applications quickly. In the environment with relatively strong turbulence in the test set of D/r₀ = 24, the use of 34 terms of PCs can improve the corrected Strehl ratio (SR) from 0.007 to 0.1585, while the Strehl ratio of the light spot after restoration using 34 terms of ZPs is only 0.0215, demonstrating almost no correction effect. The results indicate that PCs can serve as a better alternative in representing and restoring the characteristics of atmospheric turbulence induced phase aberrations. These findings pave the way to use PCs of phase aberrations with fewer terms than traditional ZPs to achieve data dimensionality reduction, and offer a reference to accelerate and stabilize the model and deep learning based adaptive optics correction.