Using an incoherent target return to adaptively focus through atmospheric turbulence

A laser beam propagating to a remote target through atmospheric turbulence acquires intensity fluctuations. If the target is cooperative and provides a coherent return beam, the phase measured near the beam transmitter and adaptive optics, in principle, can correct these fluctuations. Generally, however, the target is uncooperative. In this case, we show that an incoherent return from the target can be used instead. Using the principle of reciprocity, we derive a novel relation between the field at the target and the returned field at a detector. We simulate an adaptive optics system that utilizes this relation to focus a beam through atmospheric turbulence onto a rough surface.