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Numerical Fourier simulations of tip-tilt LGS indetermination for the EAGLE instrument of the European ELT

In this paper we focus on wide Field of View (FoV) Adaptive Optics (AO) correction for the EAGLE instrument for the European Extremely Large Telescope (E-ELT). The main goal is to increase the Ensquared Energy (EE) so as to reach decent spectroscopic SNRs as well as achieving a good spatial resolution. This typically means that more than 40% of the PSF flux has to be gathered into a 75x75 mas2 box. Moreover, for such an application, the correction does not have to be uniform over the whole 5 arcmin FoV but just has to be optimised in a few directions, i.e. the scientific targets. In that frame we study the performance of Multi-Object AO (MOAO) systems, where we focus on the influence of the Guide Star constellations and the consequences of using Laser Guide Stars (LGS) for wavefront sensing. Unfortunately, for such sources, low-order modes such as tip/tilt modes cannot be measured. We have therefore developed a new method allowing us to partially simulate such effects in analytical AO simulation codes, which is highly detailed in this paper. Thanks to this method, we have been able to derive preliminary results in terms of system design as well as sky coverage.