The Global-Multi Conjugated Adaptive Optics (GMCAO) approach offers an alternative way to correct an adequate scientific Field of View (FoV) using only natural guide stars (NGSs) to extremely large ground-based telescopes. Thus, even in the absence of laser guide stars, a GMCAO-equipped ELT-like telescope can achieve optimal performance in terms of Strehl Ratio (SR), retrieving impressive results in studying star-poor fields, as in the cases of the deep field observations. The benefits and usability of GMCAO have been demonstrated by studying 6000 mock high redshift galaxies in the Chandra Deep Field South region. However, a systematic study simulating observations in several portions of the sky is mandatory to have a robust statistic of the GMCAO performance. Technical, tomographic and astrophysical parameters, discussed here, are given as inputs to GIUSTO, an IDL-based code that estimates the SR over the considered field, and the results are analyzed with statistical considerations. The best performance is obtained using stars that are relatively close to the Scientific FoV; therefore, the SR correlates with the mean off-axis position of NGSs, as expected, while their magnitude plays a secondary role. This study concludes that the SRs correlate linearly with the galactic latitude, as also expected. Because of the lack of natural guide stars needed for low-order aberration sensing, the GMCAO confirms as a promising technique to observe regions that can not be studied without the use of laser beacons. It represents a robust alternative way or a risk mitigation strategy for laser approaches on the ELTs.
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