ELTs Adaptive Optics for Multi-Objects 3D Spectroscopy : Key Parameters and Design Rules

In the last few years, new Adaptive Optics [AO] techniques have emerged to answer new astronomical challenges: Ground-Layer AO [GLAO] and Multi-Conjugate AO [MCAO] to access a wider Field of View [FoV], Multi-Object AO [MOAO] for the simultaneous observation of several faint galaxies, eXtreme AO [XAO] for the detection of faint companions. In this paper, we focus our study to one of these applications : high red-shift galaxy observations using MOAO techniques in the framework of Extremely Large Telescopes [ELTs]. We present the high-level specifications of a dedicated instrument. We choose to describe the scientific requirements with the following criteria : 40% of Ensquared Energy [EE] in H band (1.65um) and in an aperture size from 25 to 150 mas. Considering these specifications we investigate different AO solutions thanks to Fourier based simulations. Sky Coverage [SC] is computed for Natural and Laser Guide Stars [NGS, LGS] systems. We show that specifications are met for NGS-based systems at the cost of an extremely low SC. For the LGS approach, the option of low order correction with a faint NGS is discussed. We demonstrate that, this last solution allows the scientific requirements to be met together with a quasi full SC.