Aperture averaging of optical scintillations based on a spectrum with high wave number bump

Analytic expressions are obtained for the aperture-averaging factor associated with optical scintillations of unbounded plane waves and spherical waves in the weak fluctuation regime. This analysis is based on a modified spectrum of refractive-index fluctuations that features inner scale and a high wave number bump. Asymptotic results for both small- and large-aperture receivers compared with the first Fresnel radius (L/k)1/2 are used to construct simple interpolation formulas, which are generally within 5% of exact numerical-integration values in the case of a plane wave and within 12% of exact values for a spherical wave. On comparison with published experimental data on spherical waves, we found similar agreement, with maximum error 8%.