Fade statistics of a ground-to-satellite optical link in the presence of lead-ahead and aperture mismatch

In a recent publication [J. Opt. Soc. Am. A25, 1594-1608 (2008).JOAOD60740-323210.1364/JOSAA.25.001594] we developed expressions for the tilt errors that arise from the effects of lead-ahead and aperture mismatch when transmitting a laser beam from the ground to a satellite. We extend these results to examine the fade statistics of the irradiance at the satellite due to these tilt errors and turbulence induced scintillation. The system concept is that the light from a beacon on the satellite is received by the ground station and a derived signal is used to drive a tracking/pointing system for the uplink beam. However, the beam must be pointed ahead along the satellite track to intercept the satellite (lead-ahead), and physical constraints may require that the beam transmit aperture is different in size or location than the aperture receiving the beacon signal (aperture mismatch). These two issues cause the light entering the receiving aperture (tracker) and the beam exiting the transmit aperture (pointer) to traverse somewhat different turbulence volumes, which limits the ability of the tracking/pointing system to place the maximum flux on the satellite.