We use physical optics to simulate LGS propagation and imaging in a Shack-Hartmann wavefront sensor (WFS). We model different launch telescope (LT) sizes and realistic LT aberrations, the turbulent atmosphere, a sodium layer of finite thickness, the downlink propagation of the return light, an 8m-telescope, and finally the planned Very Large Telescope (VLT) Adaptive Optics Facility 40×40 GRAAL WFS. We study both long-exposure and instantaneous images on the WFS and compute spot size statistics. The results agree with observations obtained in the VLT telescope guider camera and enable us to optimize the LT diameter and devise design rules.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.