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As the Extremely Large Telescope (ELT) nears operational status, the focus is made on maximizing its capabilities to produce the best possible images. Among other influential factors, the differential pistons – caused by the joint presence of spiders breaking the spatial continuity of the wavefront and low-order aberrations from various origins – significantly impact the overall image quality and must therefore be addressed. Our study is centered on utilizing Neural Networks (NN) to accurately estimate the ELT’s six differential pistons in the presence of turbulence residuals using a 2x2 Shack-Hartmann wavefront sensor (SHWFS). The results of this work could be applied to instruments like HARMONI or MORFEO, which will be equipped with 2x2 SHWFS for their natural guide star wavefront sensing. In our earlier work, the use of ResNet networks fed with data covering all pupil/SHWFS rotation angles demonstrated success in piston estimation. In that study, a simplified atmospheric turbulence model was employed, consisting solely of turbulence residuals, implying perfect correction for frequencies below the deformable mirror’s cutoff frequency. In this paper, we propose to evaluate the network’s performance under more realistic atmospheric turbulence conditions relevant to the ELT. We show that the network can still extract differential piston information from single-frame images, while exhibiting increased uncertainty in its estimation. However, using 10-frame averaged images leads to a significant improvement in root mean square error (RMSE) performance. We conclude this work by addressing remaining open questions and outlining potential future research directions. These findings contribute to refining the NN models usage for cophasing applications, addressing alignment challenges, and enhancing ELT instrumentation performance.
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