Reciprocity of the Turbulent Atmosphere*

The reciprocity theorem of Helmholtz is extended to the clear turbulent atmosphere. Two impulse responses (Green’s functions) are defined to characterize optical propagation in opposite directions between two parallel planar apertures separated by the turbulent atmosphere. It is shown that these impulse responses satisfy the same reciprocity condition as the free-space impulse responses do. This result underlies recent studies of adaptive communication systems for the turbulent channel.