Theory of refractive scattering in scintillation phenomena

Abstract For a plane wave incident upon a thin plane one-dimensional phase-changing screen that has an outer scale Lo, an inner scale Li and an intervening inverse power-law spectrum (spectral index p), calculations are made of the spatial power spectrum of intensity fluctuations in a reception plane parallel to the screen. The outer scale is taken to be large compared with the Fresnel scale F, and results are obtained for a range of values of the spectral index and of the mean square fluctuation of phase (ΔΦ) 2 . For large values of (ΔΦ) 2 , lens action occurs in the screen, producing focal action in the reception plane. A lens scale F [2 (ΔΦ) 2 ] 1 4 is defined, as well as a focal scale l that varies from L o [(ΔΦ) 2 ] −1 2 at p = 5 to L o [2 (ΔΦ) 2 ] −1 at p = 2. When refractive scattering dominates, l−1 is the upper roll-off angular spatial frequency for intensity fluctuations in the reception plane whether this is the focal plane or not. The lower roll-off angular spatial frequency occurs at a scale such that its geometric mean with the focal scale is equal to the Fresnel scale. Refractive scattering dominates even for weak scattering if p ~ 5 or p > 5. For lower values of p, diffractive scattering dominates unless the lens scale exceeds the focal scale. Refractive scattering dominates when the focal scale is small compared with the lens scale. Saturation of the intensity spectrum occurs when the focal scale is small compared with the Fresnel scale. The scintillation index tends to unity as (ΔΦ) 2 → ∞ for all p. The turbulence parameter approximation is satisfactory for a range of spectral indices near 2, but not for p ~ 3 and p > 3.

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