Pointing Error Statistics in Optical Beam Tracking

In tracking optical beams from a source, a pointing error signal is derived from photodetecting the field in the receiver focal plane. This error signal is then used in some manner to control a gimballed system that continually points the receiver optics toward the source. When the source field undergoes turbulent transmission, the optical beam is attenuated and scattered, and the field is randomly defocused at the receiver. In this case the pointing error of the tracking system will evolve as a random vector process in time, statistically related to the random scattering, the photodetection process, and the dynamics of the gimballing system. Such vector processes have probability densities that satisfy well-known differential equations. These equations are derived in terms of accepted scattering models and tracking systems, assuming quadranttype error detectors are used in the focal plane. Approximate solutions are obtained and analyzed for typical operating conditions, and the manner in which the degree of scattering degrades the entire pointing operation is shown.