By adding a random phase to the initial field of a beacon,an atmospheric transmission numerical simulation model of 2D extended beacon model is presented,and its feasibility is verified.For extended beacons with different sizes,the images of extended beacons in focal plane Shack-Hartmann sensor are obtained,and the required number of minimum random realizations is analyzed under vacuum and atmosphere turbulence transmission.This lays a foundation for further studying the influence of extended beacons on adaptive optics system correction.