Effect of finite outer scale and inner scale of turbulence on aperture averaging of optical scintillations

Abstract

We study the effects of finite outer scale and inner scale of atmospheric turbulence on aperture averaging of optical scintillations. Analytical developments of the aperture- averaging factor have been limited somewhat because of mathematical complexities associated with the integral G equals $CINTb<SUB>1</SUB>(Dx)K(x)xdx. In part, this is due to the MTF model K(x) that characterizes circular aperture and the power spectrum of refractive index fluctuations. So, we derive a modified spectrum of refractive index fluctuations that features inner scale, outer scale and a high wave number bump. And we approximate the circular aperture with a Gaussian aperture model. The analytic expressions are obtained for the aperture-averaging factor associated with optical scintillations of unbounded plane waves in weak fluctuation regime based on a modified spectrum of refractive-index fluctuations and the Gaussian aperture model. This analysis is inclusion of the finite outer-scale and inner-scale are shown to be necessary for quantitative estimates. Our results obtained for the modified model turbulence spectrum significantly differ from those obtained for a Kolmogorov turbulence spectrum. In addition, interpolation expressions are obtained for the aperture- averaging factor associated with optical scintillations of a spherical wave in weak fluctuation regime.