Powerful mesospheric LGSs could give in the near future a strong impulse to the astronomical imaging at diffraction-limited resolution allowing full-sky coverage. With this goal in mind and taking into account the amount of efforts to erect and operate large telescopes one should point out in detail the fundamental limitation of any absolute tilt recovery technique especially under normal seeing conditions.
The results of our simulation show how in the visible range and for the
D = 8.00 m telescope case, even under
exceptional good seeing, the effects of the finite height of the
mesospheric sodium laser in the multi-colour LGS tilt recovery approach
are not completely negligible.
Under normal seeing conditions the effect is even more severe, being the
Strehl degradation of the order of 
.
The situation changes substantially for the D=3.58 m case where Strehl degradation lower than 0.5 appears to occours rarely.
It should be pointed out that the details of the results depend upon the adopted atmospheric model choosen. An atmospherical situation where the spreading of the heights of the disturbing layers is kept to a minimum is less affected than situations where significant layers are placed at strongly different altitudes. This last statement translates into the fact that, at least using multicolour LGSs as tilt-recovery technique, care is to be given to the minimization of the ground layer seeing and that high altitude observing sites can have better results.
The effects of the variation of the effective layer height on the other proposed techniques for the absolute tilt determination should be carefully investigated, together with other types of fundamental limitations, making a clear distinction between the effects due to technologically-limited conditions (e.g. the number of photons per subaperture impose a fundamental limit due to the photon shot noise, but it is related to the power of the laser used to generate the LGS) and the ones strictly inherent to the concept described by the proposed technique.
Finally it is to be pointed out that one could make some additional measurements on the multicolour LGS in order to solve or to minimize the described effects, for example combining this technique with others.
Acknowledgements
Thanks are due to S. Esposito, of the Arcetri Astrophysical Observatory (Italy), for useful hints on the original manuscript.