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Context. The science case studies and the optimized designing of the future adaptive optics-fed extremely large telescope instruments require the precise simulation of their adaptive optics system, potentially over their whole field of view, whatever the adaptive optics flavor the instruments will be equipped with. Aims. We simulate the anisoplanatism e ect on the extremely large telescope single conjugate adaptive optics point spread function. Our interest in this expected degradation of the correction performance with respect to the o -axis distance is in terms of the point spread function Strehl ratio and profile. Methods. Adaptive optics simulations at the scale of extremely large telescopes are challenging given the large parameter space to explore for the adaptive optics dimensioning and the large number of degrees of freedom at play for a given set of simulation parameters. To address this problem, we have used three di erent simulation tools with increasing degree of fidelity compared to a real adaptive optics system. The first is based on analytical formulae and allowed us to derive the Strehl ratio degradation with the o -axis distance. The second is a Fourier-based code and provided us with both the Strehl ratio and the point spread function profile in the field. The last is an end-to-end code based on the graphical processing unit technology and also provided us with the Strehl ratio and the point spread function profile in the field. Results. The three tools we used demonstrated a fast execution time even at the extremely large telescope scale. Cross-checks between the di erent codes were performed and demonstrated the coherency of the results. In addition to the expected degradation of the adaptive optics performance with the field angle, we demonstrated that in the simulation conditions applicable to the E-ELT, the single conjugate adaptive optics point spread function remains topped with a coherent core even at o -axis distances as large as 60 arcsec and consequently very low Strehl ratios. We also studied the impact of the outer scale on the point spread function profile, demonstrating that the aforementioned Airy-like pattern is observable even when the outer scale is larger than the telescope diameter. Conclusions. These results could push for the preservation over a large field of the optical quality of any common path optics between the telescope and the instruments in single conjugate adaptive optics mode. This could o er some astrometric capabilities to these instruments operating in this adaptive optics mode.

Anisoplanatism effect on the E-ELT SCAO point spread function. A preserved coherent core across the field