Fourth-order moment of the light field in atmosphere for moderate and strong turbulence

TL;DR

This paper derives an explicit expression for the fourth-order moment of the light field in atmospheric turbulence, accounting for both moderate and strong turbulence regimes, and explores its implications for intensity fluctuations and scintillation.

Contribution

It provides a novel explicit formula for the fourth moment of light fields in turbulence, including effects of partial saturation and finite detector aperture.

Findings

Expression agrees with previous results in fully saturated regime

Captures effects of partial saturation on photon correlations

Analyzes transmittance fluctuations considering detector aperture

Abstract

Collisionless Boltzmann equation is used to describe the intensity correlations in partially saturated and fully saturated regimes in terms of photon distribution function in the phase space. Explicit expression for fourth moment of the light fields is obtained for the case of moderate and strong turbulence. Such expression consists of two terms accounting for two regions in the phase space that independently contribute to the correlation function. It is shown that present solution agrees with previous results for fully saturated regime. Additionally it embodies the effect of partially saturated radiation where the correlations of photon trajectories are important and the magnitude of the scintillation index is well above the unity. Fourth moment is used to study the fluctuations of transmittance which consider the effect of finite detector aperture.