next previous
Up: Multiple LGSs to

2. Conditions on the multiple LGSs scheme

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 tex2html_wrap_inline884 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 tex2html_wrap_inline888 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):


where tex2html_wrap_inline890 is the laser projector aperture and tex2html_wrap_inline892 is the laser beacon wavelength. The ratio tex2html_wrap_inline894 gives the goodness of the assumption made in TF90 regarding the LGS absolute position knowledge: tex2html_wrap_inline896 means that the knowledge of the position on the sodium layer is unaffected by the ground to layer propagation, while tex2html_wrap_inline898 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:


With a projector aperture of D=0.5 m and median seeing conditions of the order of r0 =0.15 m a figure of tex2html_wrap_inline906 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.

next previous
Up: Multiple LGSs to

Copyright by the European Southern Observatory (ESO)