Modeling the PDF for the irradiance of an uplink beam in the presence of beam wander

Recent studies of ground-to-space beam propagation have revealed significant departures from Rytov theory when the beam diameter w0 is on the order of the atmospheric coherence width r0. It has been shown that such departures from Rytov theory are primarily a consequence of beam wander and other low-order aberrations. In this paper we discuss modeling of the probability density function (PDF) for uplink beams. In particular, we show how the PDF transitions from lognormal statistics when w0/r0 << 1 to the negative exponential distribution when w0/r0 >> 1. The most interesting regime is the transition region near w0/r0 = 1, where the statistical behavior of tracked and untracked beams differs significantly.

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