Scintillations due to multiscale phase screens

The statistics of multiscale phase screens encompasses three fluctuation regimes: an inertial power-law regime, a short-scale (quadratic) dissipative regime, and a long-scale energy-input regime. We introduce a simple, analytically tractable, and numerically convenient model for such a screen and employ this model to analyze, compute, and classify the range profile of the scintillation index associated with a plane wave modulated by the screen. The screen classification is based on the ratios of the short scale and the long scale to the inertial scale, which is an inverse measure of the magnitude of the random phase fluctuations injected by a purely inertial screen. A screen is designated weak or strong, according to whether both ratios are less than or greater than 1, and moderate in the intermediate case (one ratio greater than 1 and one ratio less than 1). The scintillation profile increases quadrati- cally with the range in the perturbation region near the screen and approaches a constant saturation level far from the screen. Weak screens produce monotonically increasing profiles, which saturate at less than 1. Moderate and strong screens produce profiles that saturate practically at 1. However, moderate screens produce profiles with a weak maximum because of the interplay between the inertial and the energy-input mechanisms. Moreover, the magnitude of this maximum can vary only in a narrow range whose bounds are determined by the inertial power-law exponent. Strong screens produce profiles with a pronounced maximum because of the interplay between the dissipative and the inertial mechanisms. The magnitude of this maximum scales with the logarithm of the screen strength (or the wave number) and therefore is unbounded in that sense.