Short-term average optical-beam spread in a turbulent medium

On the basis of the extended Huygens–Fresnel principle, a general expression is derived for the short-term average optical-beam spread, as measured with respect to the instantaneous center of energy of the beam, of an initially coherent optical-beam wave propagating in a weakly inhomogeneous medium. The present analysis applies to the near field of the effective coherent transmitting aperture, where the beam wanders (dances) as a whole and does not break up into multiple patches or blobs. Central to the analysis is the short-term average mutual coherence function (MCF) of a spherical wave. This quantity is obtained from the corresponding long-term MCF by removing the random tilt of the wave front. Analytic expressions for the short-term beam spread are presented for the case of a Kolmogorov spectrum and the short-term average MCF derived by Fried. As expected, the short-term, turbulence-induced beam spread is always less than the corresponding long-term beam spread. Analytic and numerical results are given for the short-term average irradiance at focal range f, which is always greater than the corresponding long-term average irradiance.