We investigate the correlation function of the intensity of a light beam with a very broad initial profile (in the plane wave limit) as it propagates through a turbulent atmosphere. We explicitly compute, to leading order, the irreducible part of the correlation function for various propagation distances and separations between observation points. The result for large separations exhibits universal power-law behavior, decaying in a power-law fashion for all propagation lengths. For small separations, the correction is independent of the distance between the points. For small distances (weak scintillation regime) it is small and grows according to a power law with increasing z; for large distances (strong scintillation regime) it is small and decreases according to a power law with increasing z; however, in the intermediate regime of moderate scintillations it becomes of order unity, and our expression for the first correction becomes inapplicable.