Residual tip-tilt motion of LGS in monostatic scheme

There is analyzed the possibility the general tilt correction of the wave front on base of the laser guide star (LGS) signal. The calculation of the image motion of the spherical wave (that position the source of radiation also fluctuated) with random center is conducted. The exact formula for random vector defining the position of the image of the spherical wave in focal plane of the telescope is offered. The variance of residual fluctuations has been calculated. The variance behavior of this residual motion from optical experiment parameters are analyses. The similar problem under solution of the some practical tasks, including the possibility of the wave front "global" tilt correction with using single LGS, can be appeared.