We assume, in the following, that the technique described by TF90 is fully implemented. Of the various conditions to be met in order to have the applicability to their technique we briefly discuss the one strictly related to the problem under investigation in this paper. We refer to the assumption that the position of the various LGSs on the Sodium layer is known. Obviously the exact knowledge of the LGSs positions solve the absolute tilt determination problem. However it is to be pointed out that the position of the LGSs required in the TF90 paper is characterized by an uncertainty such that a ray from the laser beacon at an height of km to a given point on the telescope aperture can be located on each disturbing layer with an uncertainty much smaller than r0.
Assuming the maximum height of substantially disturbing layer of the order of km it is easy to see that this will translates into an angular displacement of the LGS beacon as seen from the ground of the order of:
This angular displacement is to be compared with the rms fluctuation upward tilt angle of the LGS beacon given by the usual relationship (Acton 1995; Brandt et al. 1987; O'Byrne et al. 1995; Sarazin & Roddier 1990):
This calculation shows that, while ground to layer perturbation is usually high enough to destroy any useful tilt information on the LGS, it is not so large to rule out one of the basic assumption made by TF90 in order to make the conical anisoplanatism correction a feasible technique.