Minimum diameter of a laser projector for some perspective-based laser guide-star tilt retrieval schemes

Because of the finite speed of light, a laser guide Star that is seen from the side is not exactly a straight line. When such a laser guide star is used to sense tip-tilt with some of the perspective-based techniques that are used to retrieve an absolute tip-tilt laser, such nonstraightness introduces an error. We estimate this effect for various diameters of a laser projector, assuming a Kolmogorov turbulence spectrum and figuring the maximum achievable Strehl ratio. We found that under poor seeing conditions the effect is not negligible and that laser projectors larger than those currently used are required.