Probability density cloud as a geometrical tool to describe statistics of scattered light

TL;DR

This paper introduces a geometric approach using probability density clouds to analyze the first-order statistics of scattered light, linking geometric parameters to phase statistics and deriving a closed-form moment-generating function for intensity.

Contribution

It presents a novel geometrical framework for describing scattered light statistics and connects cloud parameters to phase properties, with a practical example included.

Findings

Closed-form moment-generating function for intensity derived

Geometric parameters linked to phase statistical properties

Illustrative example with exponentially modified normal distribution

Abstract

First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.