Fractional moments and their usefulness in atmospheric laser scintillation

Correlations of Deflection Angles of a Laser Beam in a Hot Turbulent Jet of Air: Theoretical Determination and Experimental Measurement of the Structure Coefficient of Refractive Index Fluctuations

“…This causes random deflections of the laser beam, generates random phase modulations in the laser beam wave front, and then creates random fluctuations of the light wave amplitude by the diffraction process. Many papers have been devoted to the study of phase and intensity fluctuations of the laser beam in random media [12] and other studies have been carried out the possibility of using the fractional moments [13], or the methods for solving the parabolic equation of moments [14]. It is well known that the directional fluctuations of the laser beam are more suitable for studying turbulence because they are very sensitive to turbulence inhomogeneities.…”

Monitoring evolution of laser atmospheric scintillation statistics by use of fractional moments

“…The quantity chosen for comparison is called`®tting error' and is given by [3] Since M1 is equal to 1 by de®nition, FE is zero for fˆ1, while, for a generic value of f the smaller FE, the better the agreement between theoretical and experimental moments of order f .…”

“…It has been proposed and successfully used to study the onset of strong scintillation by numerical simulations [14]. In this paper, while referring to the previous paper [3] for the one-parameter distributions, some theoretical features of the BM PDF are shown, which are useful for applying the fractional moment method.…”

“…For this comparison, a method based on the use of low-order fractional moments is applied [3,4]. This method, summarized in Section 3, can be applied to any scintillation regime from a very low to a very strong one, because low-order moments can be accurately estimated from experimental data.…”

“…On the other hand, fractional moments of order less than two can be correctly estimated. This has been shown both by sampling sets of a typical number of data from known PDFs using a Monte Carlo method [3] and by computing the normalized cumulative functions directly from experimental data [7].…”