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

Abstract

The time evolution of experimental intensity¯uctuation distributions of a laser beam propagating through atmospheric turbulence is discussed. Experimental data, collected under conditions ranging from low to strong scintillation, are compared with four theoretical probability-density functions by means of fractional moments.

Ratio of Two Independent Lindley Random Variables

“…More recently, the properties of non-integer moments have found application in the study of random resistor networks, chaos, and diffusion-limited aggregation (see Weiss et al ( 39 ), and references therein). Also, one is referred to Consortini and Rigal [ 8 ] and Innocenti and Consortini [ 14 ] for the usefulness of fractional moments in atmospheric laser scintillation. Using the software Maple, and Eq.…”

“…The integrals , and are called (complete) gamma and incomplete gamma functions respectively, whereas the integral is called the complementary incomplete gamma function. For negative values, gamma function can be defined as , where is an integer, (see, for example, Abramowitz and Stegun [ 1 ], and Gradshteyn and Ryzhik [ 14 ], among others). The function defined by is known as beta function (or Euler’s function of the first kind).…”

Experimental Technique Using an Interference Pattern for Measuring Directional Fluctuations of a Laser Beam Created by a Strong Thermal Turbulence

“…Many experimental investigations [29][30][31][32] have been carried out in order to enable a best understanding of the laser beam behaviour when it propagates through a heated turbulent medium. In this paper, we have focused our interest on the study of directional fluctuations of a thin laser beam.…”