Sample size influence on optical scintillation analysis 1: Analytical treatment of the higher-order irradiance moments

Abstract

The statistical distribution of the experimentally obtained higher-order moments of optical scintillation probability density is studied. It is shown that this distribution is strongly dependent on the size of the data sample. At reasonable sample sizes the correct estimation of the theoretical value is improbable. At practically available sample sizes the region of the most probable values of the estimated higher-order moment is almost independent of the scintillation probability density function (PDF). The distinction between the candidate PDFs is almost impossible at reasonable sample sizes.

The Use of Weather Forecasts to Characterise Near-Surface Optical Turbulence

“…The DGA data are integrated over 1 min, a standard value for large aperture scintillometers (e.g. Hill and Ochs 1978;Ben-Yosef and Goldner 1988). Contrary to the above-discussed path averaging, this time averaging has no counterpart in many optical systems using instantaneous propagation conditions.…”

<title>Characterization of laboratory-generated turbulence by optical phase measurements</title>

“…As can be seen in these plots, the generated turbulence exhibits the properties of locally isotropic turbulence at all locations within the aperture; thus, the generated voltage is 50 volts; there is one screen in the chamber; the average temperature is 42. C. [4][5][6][7][8][9] turbulence appears to be isotropic. Note also on these plots that the magnitude oftb.…”

Statistical Properties of Estimates of the Moments of Laser Scintillation

“…A theoretical evaluation of Fr, (q) was presented by Ben-Yosef and Goldner [23] as an approximation for Fq (q) . The PDF for qk is the derivative of F9k (q) with respect to q .…”

“…Since the measured moments must be normalized by the estimated mean irradiance, an exact theory for the distribution of these sample moments is very difficult . Recently, a theory has been developed [23] for the distribution of the higher moments of laser scintillation when the mean irradiance is known . Some results of this theory indicate that the higher moments are very difficult to estimate with the typical sample sizes currently available .…”

“…The simulation of realizations of estimates of the PDF is computationally more efficient and permits evaluation of the cumulative distribution function of estimates of higher moments . Two sets of simulations are presented in this paper : one set evaluates the work of reference [23], and the other set evaluates a model PDF for typical strong-scattering scintillation data [15] .…”