The aperture-averaging factor associated with optical scintilations of unbounded plane and spherical waves is calculated for the weak fluctuation regime using a modified spectrum of refractive-index fluctuations that features a high wave number bump. Previous analyses were based on more conventional spectral models and the results were limited to asymptotic regimes depending on the ratio of the first Fresnel zone size (L/k)$+$HLF$/ to inner scale l$-0$/. Simple interpolation formulas are developed here for all such ratios, and comparisons of results with numerical integration values and experimental data show excellent agreement.
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