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):
is the laser projector aperture and 
is the laser
beacon wavelength.
The ratio 
gives the goodness
of the assumption made in TF90 regarding the LGS absolute position
knowledge: 
means
that the knowledge of the position on the sodium layer is unaffected by
the ground to layer propagation, while 
means that
the Sodium spot displacement due to upward tilt is great enough to make
the rms shift of the light ray equal to r0 on the higher layer.
It can be turned out that such a quantity is given by:
is
obtained.
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.