The problem of measuring the global tilt from laser guide star

The random inhomogeneities of the refractive index due to turbulent motion in the atmosphere cause a significant decrease in the theoretical resolution of an optical telescope, cause such well-known effects as scintillation, jitter, and degradation of the optical images. Adaptive optics (AO) systems with a laser guide star (LGS) are designed to eliminate the negative effects. The main limitation of LGS is the problem of measuring the global tilt. We offer the approach to using the LGS signal. The approach, where initially the LGS is considered as a point source of spherical wave with a random center is considered. The results of analytical and numerical calculations are reported. The estimation of sodium column density and height peak of sodium mesospheric layer above large Russian Observatories are presented also.