# Crossing statistics of laser light scattered through a nanofluid

## TL;DR

This study analyzes the crossing statistics of speckle patterns in laser scattering through nanofluids, extending zero-crossing analysis to non-Gaussian regimes to better understand particle dynamics.

## Contribution

It introduces a generalized crossing statistics framework that accounts for non-Gaussian fluctuations and noise, improving the accuracy of particle speed estimation in nanofluids.

## Key findings

- Increasing temperature enhances Gaussian and non-Gaussian prediction agreement.
- Maximum crossings often occur away from the mean level, requiring multi-threshold analysis.
- The generalized total crossing effectively quantifies deviations from Gaussianity.

## Abstract

In this paper, we investigate the crossing statistics of speckle patterns formed in Fresnel diffraction region by a laser beam scattering through a nanofluid. We extend $zero-crossing$ statistics to assess dynamical properties of nanofluid. According to joint probability density function of laser beam fluctuation and its time derivative, theoretical framework for Gaussian and non-Gaussian regimes are revisited. We count number of crossings not only at {\it zero} level but also for all available thresholds to determine the average speed of moving particles. Using probabilistic framework in determining crossing statistics, {\it a priori} Gaussianity is not essentially considered, therefore even in presence of deviation from Gaussian fluctuation, this modified approach is capable to compute relevant quantities such as mean value of speed more precisely. Generalized total crossing which represents the weighted summation of crossings for all thresholds to quantify small deviation from Gaussian statistics is introduced. This criterion can also manipulate the contribution of noises and trends to infer reliable physical quantities. The characteristic time scale for having successive crossings at a given threshold is defined. In our experimental setup, we find that increasing sample temperature leads to more consistency between Gaussian and perturbative non-Gaussian predictions. The maximum number of crossing does not necessarily occur at mean level indicating that we should take into account other levels in addition to {\it zero} level to achieve more accurate assessments.