Image jitter of a laser guide star in a monostatic formation scheme

The image jitter of a spherical wave with a random center is calculated. A rigorous formula is proposed for a random vector that determines the image position of the spherical wave at the focus of the telescope under the condition that the source position also fluctuates. The variance of these fluctuations is calculated. The dependence of the variance on parameters describing the optical experiment is analyzed. The analysis of this problem is of interest for solving of a number of practical tasks including the analysis of the possibility of solution of the tilt problem upon using a laser guide star.