You have no idea what a Laser guide star looks like? Have a look at an image taken with a CCD camera at the 1.2m telescope on Calar Alto. The launching telescope of the Laser beam is about 270m apart! The sodium layer in the atmosphere that is excited by the Laser beam is located at an altitude from about 80 km to 100 km. Therefore the "expected" spot is not a spot but a line (cigar)!