Turbulence Impacted Beam Statistics and Image Topology with Lorentz Dipole Oscillation
Shouvik Sadhukhan, C. S. Narayanamurthy
TL;DR
The paper addresses turbulence robustness in free-space optical beams by modeling beam intensities as Gaussian Mixture Models embedded in the Symmetric Positive Definite (SPD) manifold $SPD_n(\mathbb{R})$ under an affine-invariant Riemannian framework. It combines Lorentz dipole oscillator dynamics with dipole-dipole coupling and gradient forces to explain turbulence compensation, using geodesic distances on $SPD_n(\mathbb{R})$, Gram–Charlier expansions, and KDE to quantify topology and density differences across turbulence conditions. Experimental validation with PMMA slabs demonstrates that dipole synchronization substantially suppresses scintillation, reduces higher-order distortions, and aligns turbulence-affected statistics with the turbulence-free baseline, as reflected by decreasing affine-invariant distances and increasingly positive Pearson correlations. The framework enables precise similarity/dissimilarity assessments and suggests practical benefits for secure free-space optical communication, turbulence-resilient imaging, and compression of turbulence-impaired data, with future work on refined GMM distances and integration with data-driven turbulence control tools.
Abstract
This work presents a rigorous statistical and geometric framework for analyzing turbulence-impacted beam propagation and image topology with results obtained using a PMMA slab. The approach models beam intensity distributions as n-dimensional data set represented through Gaussian Mixture Models (GMMs), embedding them into the manifold of Symmetric Positive Definite (SPD) matrices. By employing information geometric tools, geodesic distances, and affine-invariant Riemannian metrics, we establish a principled methodology for quantifying similarity and dissimilarity among beam images. Experimental results demonstrate topological distance trends, distance statistics, and correlation measures for different turbulence scenarios, including polarized and unpolarized cases. Histograms of distance statistics reveal stable statistical features, with correlation coefficients highlighting the turbulence-induced variability in PMMA-based beam propagation. The framework not only provides a systematic foundation for analyzing optical beam statistics under turbulence but also opens avenues for advanced applications such as deep learning-based feature reduction, image compression, and secure free-space optical (FSO) communication. Future directions include refining the GMM-EM based distance measures, comparative scatter analysis, and developing robust statistical tools for turbulence imaging. Overall, this study bridges theoretical modeling, experimental validation, and potential technological applications in adaptive and applied optics.