Estimation and correction of optical aberrations induced by atmospheric turbulence through adaptive optics systems for telescopes using shack–hartmann wavefront sensors

Abstract

Atmospheric turbulence introduces random fluctuations in the refractive index of the air, which distort optical wavefronts and degrade the image quality of astronomical observations. Adaptive optics (AO) systems are designed to estimate and correct these aberrations close to real time, allowing telescopes to operate close to their theoretical diffraction limit. In this work, the estimation and correction of optical aberrations induced by atmospheric turbulence are studied through computational simulations of an AO system based on a Shack–Hartmann wavefront sensor. The physical and statistical description of atmospheric turbulence is modeled using Kolmogorov theory with Von Kármán generalization, and its effect on wavefront propagation is analyzed through the Fried parameter r0. Simulations are performed using the Object Oriented Python Adaptive Optics (OOPAO) tool, with system parameters inspired by the PAPYRUS optical bench at the Observatoire de Haute-Provence, France. Wavefront reconstruction is carried out using a modal representation based on Zernike polynomials, and correction is applied through a deformable mirror operating in both open-loop and closed-loop configurations. The performance of the AO system is evaluated for different turbulence strengths using the root-mean-square wavefront error, the Strehl ratio, and the resulting point spread function (PSF). The results show that closing the control loop significantly reduces the wavefront error and improves image quality under moderate and weak turbulence conditions. However, under very strong turbulence, the correction becomes limited, indicating the limits of the chosen system configuration. This study highlights the capabilities and limitations of Shack–Hartmann wavefront sensor-based AO systems under controlled and idealized conditions. This work provides a basis for improving future adaptive optics simulations aimed at enhancing astronomical image quality, while leaving open the possibility of extending the analysis to more advanced wavefront sensors in order to achieve more robust and realistic system performance.