Method to estimate wavefront error in a ground-LEO optical uplink beam

Laser links offer secure communication channels at speeds unreachable with conventional RF technology. Optical links between satellites are in use now in commercial and defense programs, yet at some point, the satellites must communicate with the ground. To overcome the potential bottleneck there, laser links to an optical ground station (OGS) must also be implemented, which requires the signal beams to traverse the atmosphere. Turbulence distorts the beam; achieving the potential bandwidths theoretically allowed by coherent communication protocols requires that the distortion be corrected. The problem may be mitigated by adaptive optics (AO) incorporated into the OGS. Correcting the downlink beam is relatively straightforward, since wavefront measurements may be made by reference to light from the satellite, which may indeed be the signal laser beam itself. Uplink compensation is challenging, however, because the beam from the OGS must be directed ahead of the satellite’s apparent position to account for the finite speed of light. In general, there is no source at the required position for wavefront sensing. In this paper I describe a method to estimate the wavefront aberration in the uplink direction using measurements only from the wavefront sensor (WFS) in the downlink AO system. The two-part method first exploits the non-zero angular acceleration of the satellite from the perspective of the OGS to estimate a layered atmospheric C_n² profile. Then, using a Taylor-flow model of the turbulence, a tomographic solution to the WFS measurements is projected onto the profile, from which aberration along lines of sight well outside the isoplanatic angle may be recovered. I illustrate the method with results from numerical simulations which demonstrate useful correction at point-ahead angles up to 10 arcsec.