Special functions for beam drift in atmospheric turbulence

In order to improve the sighting accuracy of a tracking and sighting system, the application of special functions in laser beam drift occurred in atmospheric turbulence was studied. Based on special functions and modified Von Karman spectrum, some expressions are derived for the variance of the beam drift in the slant path. Numerical simulation shows that neglecting the higher-order terms of the special function will not significantly reduce the laser beam pointing accuracy for a long-distance transmission. When the outer scale of turbulence L0 is rather small, the outer scale of the turbulence has great effect on beam wander. When L0 increases, the variance of the beam wander will increase slowly and approach saturation. In the same outer scale of turbulence, the increase in transmitting aperture （original beam width）and transmitting zenith angle will prevents beam from drifting. Especially, the variance of the beam drift decreases rapidly when zenith angle is close to π/2. Numerical simulation shows the above results are useful for improving the accuracy of the tracking and sighting system.