Atmospheric optical turbulence arises due to random fluctuations in the refractive index of air, which distort wavefronts of propagating optical beams, leading to phenomena such as intensity scintillation, beam wander, and general wavefront distortions [1]. Traditional methods for turbulence measurement include single-point techniques, such as temperature pulsation methods and optical scintillation-based measurements, which rely on tracking variations in intensity or phase along a single path [2]; recent studies have even explored various aspects of atmospheric turbulence measured with deep learning tools [3], [4], [5], [6]. Zhang et al. [7] investigated the second-order statistics of partially coherent electromagnetic rotating elliptical Gaussian vortex beams through non-Kolmogorov turbulence, providing insights into beam coherence and polarization effects. Similarly, Lv et al. [8] analyzed the statistical properties of controllable partially coherent radially and azimuthally polarized beams in anisotropic ocean turbulence, demonstrating how optical coherence lattices can be tailored to mitigate turbulence-induced distortions. Furthermore, Ye et al. [9] studied the propagation properties of rotating elliptical Gaussian optical coherence lattices in oceanic turbulence, showing their ability to resist turbulence effects through controlled beam rotation. These works highlight the importance of optical beam shaping and coherence management in overcoming atmospheric turbulence, complementing the approach proposed in this manuscript, which leverages optical vortex density as a turbulence metric. Unlike these studies, our work directly correlates turbulence intensity with vortex density, providing a quantitative method that is applicable in controlled laboratory conditions and potentially scalable to real-world scenarios.

The temporal analysis of a signal provides detailed information about the microscopic movements associated with the phenomenon that generates it, such as dynamic data from atmospheric turbulence scenarios. There are multiple descriptors that facilitate the study of image sequences. For example, by processing the temporal signal corresponding to each pixel individually, without considering neighboring pixels, this technique provides a unique descriptor for each pixel. The spatial variations in these descriptors enable the identification of different activities within the same speckle pattern, allowing spatial discrimination within the analyzed sample. Among the commonly used descriptors are the laser speckle contrast [10], spatio-temporal correlation [11], autocorrelation [12], the moment of inertia of the co-occurrence matrix [13], and the Fujii averaged differences descriptor [14], [15], [16], or the generalized differences descriptor [17], among others.

In a previous work, a new descriptor was proposed to study changes in speckle patterns during a dynamic process, based on the density of optical vortices in images corresponding to time history speckle pattern (often referred to by the acronym THSP) [18]. The temporal history of speckle diagrams is constructed from a temporal sequence of speckle images. This method produces a visual representation where the horizontal dimension of the THSP image represents time, and the vertical dimension represents space. Phase singularities, or vortices, are associated with points on the wavefront where the intensity of the light field is zero and the phase is undefined. To locate these points, it is necessary to know the phase of the optical field, which is not available in intensity images such as THSP. However, phase singularities can also be identified in complex-valued fields synthesized from intensity distributions. By applying a two-dimensional Laguerre-Gauss transform algorithm, a complex pattern, referred to as a “pseudo field”, is obtained to differentiate it from the original field that produced the intensity pattern [18], [19], [20].

The use of Laguerre-Gauss (LG) modes in optical vortex characterization has been extensively studied in various contexts. Deng and Guo [21] explored the dynamics of collinear LG beams in nonlocal nonlinear media, revealing novel soliton structures that could be leveraged in turbulence studies. Furthermore, Deng et al. [22] introduced the concept of elegant Hermite–Laguerre–Gaussian beams, providing a unified framework for describing complex beam profiles. The propagation and transformation of LG beams in strongly nonlocal nonlinear media have also been extensively investigated [23], demonstrating their robustness under different environmental conditions. Additionally, the behavior of radially polarized elegant light beams was studied by Deng et al. [24], offering insights into their propagation characteristics. Moreover, Deng and Guo [25] analyzed the propagation of LG beams in nonlocal nonlinear media, highlighting the influence of beam parameters on their stability and evolution. These studies establish a solid foundation for the application of LG modes in optical vortex analysis. In this work, we leverage LG-based vortex detection techniques to extract phase singularities and quantify turbulence effects, providing a novel application of these well-established theoretical models.

An approach to characterize phase singularities is that proposed by Wang et al. [19], where the gradient of the pseudo field at the vortex is analyzed, drawing an analogy with the polarization vector of a wave. Anisotropic ellipses associated with the pseudo-phase are defined, enabling the location of an optical vortex on the Poincaré sphere. In optical vortex metrology, phase singularities located at the poles of the Poincaré sphere are of great interest due to their stability. Conversely, singularities located at the equator, where the real and imaginary planes intersect along a straight line, are challenging to locate and are thus known as unstable singularities. In low-activity images, the presence of unstable vortices arising from electronic noise, rather than sample activity, is particularly noticeable. To remove these vortices, a filter based on the Poincaré sphere was designed [18].

The previously mentioned descriptor is suitable to evaluate a sequence of images associated to the propagation through controlled atmospheric turbulence. The density of phase singularities in the propagation of images through atmospheric turbulence is studied under controlled laboratory conditions. We analyze the temporal evolution of each image column, revealing that the density of vortices in these sections correlates with the intensity of turbulence, enabling its quantification by this method.