Effective Rayleigh range of partially coherent beams propagating through the turbulent atmosphere

The concept of the Rayleigh range of partially coherent beams is extended from free space to the turbulent atmosphere. The general analytical expression for the effective Rayleigh range of partially coherent beams propagating through the turbulent atmosphere is derived. It is shown that the longer the free-space Rayleigh range is, the more the effective Rayleigh range is affected by turbulence, which is illustrated by numerical calculation examples.