Aperture averaging of optical scintillations in the turbulent atmosphere

We have developed approximate expressions for the aperture-averaging factor of optical scintillation in the turbulent atmosphere. For large apertures and weak path-integrated turbulence with a small inner scale, the variance of signal fluctuations is proportional to the -7/3 power of the ratio of the aperture diameter to the Fresnel zone size. If the inner scale is large, the variance is proportional to the -7/3 power of the ratio of the aperture diameter to the inner scale. In strong path-integrated turbulence, two scales develop. That portion of the variance associated with the smaller scale is proportional to the -2 power of the ratio of the aperture diameter to the phase coherence length. That portion of the variance associated with the larger scale is proportional to the -7/3 power of the ratio of the aperture diameter to the scattering disk. These simple approximations are within a factor of 2 of the measurements.