Fractional moments and their usefulness in atmospheric laser scintillation

Abstract

Use of moments of non-integer order (called fractional moments) in statistical optics is proposed for discriminating between candidates for probability density functions (PDFs) of the scintillation intensity to overcome the experimental problems encountered by using integer moments. Low-order (< 2) fractional moments allow comparison of experimental data with theoretical PDFs of the intensity in different scintillation regimes. A comparison procedure, based on two low-order measured fractional moments, is described and tested by utilizing Monte Carlo samples from three distributions commonly used in atmospheric propagation (Ln, LnME and K). The bin width required to discriminate between different distributions and the effect of noise are investigated. Examples of application to experimental data are presented.