Scintillation averaging and fade statistics

This work develops expressions for the variance and power spectral density (PSD) of atmospherically induced amplitude fluctuations of a propagating beam of light, also known as scintillation. This extends a recently published analytic approach for atmospheric propagation studies, previously applied to the phase properties of a propagating beam. In addition to laying out the general principles for manipulating log-amplitude expressions, this work develops novel expressions for scintillation under aperture, path, wavelength, and temporal averaging, first separately and then as a unified expression. The PSD expression is then used to find several statistics of fades of given depth and duration, including fade probability, rate, and average duration. Results are shown throughout to agree with existing literature and wave-optics simulations.