Performance analysis of the improved seeing limited mode for the Euro50

This paper presents an analysis of the point-spread functions (PSFs),which may be expected in the so-called improved seeing limited mode forthe Euro50 (Extremely large telescope with a 50 m aperture). This modecomprises adaptive control of the deformable secondary mirror of theaplanatic Gregorian telescope configuration using guide stars in a widefield. I may result in efficient compensation of turbulence-inducedwavefront distortion near the ground layer. The prime goal of theinvestigations has been to evaluate the performance, in particular thefull width at half maximum (FWHM) of the K-band PSFs, as a function ofboth the guide star field size and the outer scale of the atmosphericfluctuations. For this reason we have adopted a very simple guide starconfiguration consisting of a circular ring of homogeneously distributedstars. The PSFs are analyzed in the center of the ring. The atmosphereis implemented as the nine layer extended ORM atmosphere described inthe paper. One result of the investigations is that the FWHM of the PSFsis very sesitive to the size of the outer scale. For a layer-commonouter scale of 20 m, that is slightly less than half of the telescopediameter, the FWHM will stay close to the diffraction limit even for aguide star ring diameter of 10'. This makes the improved seeing limitedmode very well suited for a fiber-fed spectrograph located at the F/5Nasmyth focus of the Euro50