Atmospheric Turbulence Research Articles

Propagation characteristics of partially coherent twisted off-axis double-vortex beams in atmospheric turbulence

We propose a partially coherent twisted off-axis double vortex (PCTODV) beam and investigate its propagation characteristics in atmospheric turbulence. By employing the extended Huygens–Fresnel principle and the Wigner distribution function, we derive the corresponding analytical expressions and perform numerical simulations to validate our findings. The findings reveal that PCTODV beams possess a wider array of tunable parameters than single vortex beams with central phase singularities, which is beneficial for atmospheric turbulence propagation. The twist factor size notably affects the beam evolution rate in turbulence, with an optimized twist factor enhancing resistance to turbulence. Moreover, factors such as increased wavelength, larger initial beam waist, greater inner turbulence scale, higher refractive index structure constant, and reduced M2 factor contribute to improved transmission stability. These insights advance the understanding of vortex beam propagation in turbulent atmospheric optical communication systems.

Performance investigation of an OAM-SK optical communication system based on a PCNN-LDPC under atmospheric turbulence

This paper proposes a probabilistic convolutional neural network-low density parity check (PCNN-LDPC) demodulation scheme for orbital angular momentum shift keying free-space optical (OAM-SK-FSO) communication systems, with a focus on its bit error rate (BER) performance. Initially, the original information sequences were encoded by a low-density parity check (LDPC) and transformed into superposition state Laguerre Gaussian (LG) beams using a 16-Ary mapping scheme. The transmission of LG beams through atmospheric turbulence was then simulated using the power spectral inversion method, and the dataset was constructed and trained using a convolutional neural network (CNN). During demodulation, the CNN adaptive demodulator was integrated with the LDPC decoding algorithm. Classification probabilities from the CNN adaptive demodulator were used in the LDPC decoding process to enhance the channel estimation credibility. The computational results demonstrate that the BER of the PCNN-LDPC significantly outperforms both the CNN adaptive demodulator and CNN-LDPC demodulation strategy. Additionally, the performances of three LDPC decoding algorithms—min-sum (MS), normalized min-sum (NMS), and offset min-sum (OMS)—are compared, revealing that the probabilistic convolutional neural network-normalized min-sum (PCNN-NMS) achieves the best BER performance, highest convergence efficiency, and greatest decoding stability. These findings provide theoretical references and technical support for studying the BER performance of OAM-SK-FSO communication systems.

Periods of constant wind speed: how long do they last in the turbulent atmospheric boundary layer?

Abstract. We perform a statistical analysis of the occurrence of periods of constant wind speed in atmospheric turbulence. We hypothesize that such periods of constant wind speed are related to characteristic wind field structures that, when interacting with a wind turbine, may induce particular dynamical responses. Therefore, this study focuses on characterizing the constant wind speed periods in terms of their lengths and probability of occurrence. Atmospheric offshore wind data are analyzed. Our findings reveal that long constant wind speed periods are an intrinsic feature of the marine atmospheric boundary layer (ABL). We confirm that the probability distribution of such periods of constant wind speeds follows a Pareto-like distribution, admitting power law behavior for periods exceeding the large-eddy-turnover time. The power law characteristics depend on the local conditions and the precise definition of wind speed thresholds. A comparison to wind time series generated with standard synthetic wind models and to time series from ideal stationary turbulence suggests that these structures are not characteristics of small-scale turbulence but seem to be consequences of larger-scale structures of the atmospheric boundary layer and thus are multi-scale. Given the results, we show that the continuous-time random walk (CTRW) model, as a non-standard wind model, can be adapted to generate time series of the wind speed whose statistics match the statistics of observed periods of constant wind speed.

Predicting atmospheric turbulence for secure quantum communications in free space

Predicting atmospheric turbulence for secure quantum communications in free space

Enhancing Free Space Optical System Performance through Fog and Atmospheric Turbulence using Power Optimization

Free Space Optical (FSO) communication is gaining traction as a pivotal technology for next-generation communication systems, offering extremely high data rates, unlicensed bandwidth, and rapid transmission capabilities. However, its performance is significantly hindered by atmospheric factors such as turbulence and fog. This paper presents a comprehensive model for FSO communication designed to optimize performance under various atmospheric conditions. We assess channel capacity across a spectrum of weak to strong atmospheric turbulence using a Gamma-Gamma channel distribution. To mitigate channel losses, our system employs Wavelength Division Multiplexing (WDM) and multi-beam Multiple Input Multiple Output (MIMO) technologies. Results indicate that the integration of diversity techniques and WDM substantially enhances system performance in adverse weather conditions. Furthermore, power optimization is achieved through the implementation of optical amplifiers and feedback mechanisms from the receiver to the transmitter to adjust the transmitter power in accordance with received Bit Error Rate (BER). The proposed power-optimized WDM MIMO system demonstrates a remarkable BER of 1.48884e-15, while extending the transmission link distance to 2500 meters with a Q factor of 21.5 even under strong atmospheric turbulence conditions.

LDPC-coded OAM shift-keying FSO communication system with dual-pattern CNN demodulator

An LDPC-coded orbital angular momentum shift-keying (OAM-SK) free space optical (FSO) communication system with a dual-pattern convolutional neural network (CNN) demodulator is put forward to resist the adverse effect of atmospheric turbulence (AT). Diverging from the standard single-pattern CNN demodulator, the proposed method inputs a dual OAM light pattern into the demodulator. The first pattern stems from the Laguerre-Gaussian OAM-SK light focused by a convex lens, while the second is acquired post-cylindrical lens modulation. The dual-pattern CNN demodulator can extract richer features from the incoming light, enhancing the recognition accuracy for OAM-SK modes. This advancement notably enables the recognition of OAM-SK modes with opposite orbital quantum numbers, a challenging task for standard single-pattern CNN demodulators. We have refined communication reliability by integrating LDPC coding with OAM-SK, and LDPC decoding has also been explicitly designed for OAM-SK channels. Simulations validate our proposed method, achieving a recognition accuracy 0.869 under strong AT (Cn2=5×10−14m−2/3). We use the image transmission as a benchmark; the dual-pattern CNN demodulator enhances the LDPC-coded OAM-SK FSO link, achieving a 30 dB boost in the image’s PSNR compared to the traditional CNN demodulation. The bit error rate (BER) drops to 3.8e−5, achieving significant advancement in comparison to the single-pattern CNN demodulators.

Analysis and performance improvement of 60 GHz mm-wave based hybrid RoF and RoFSO system under atmospheric turbulence using FFE + DFE electronic equalizer

Analysis and performance improvement of 60 GHz mm-wave based hybrid RoF and RoFSO system under atmospheric turbulence using FFE + DFE electronic equalizer

Analysis of beam wandering and influence of partial coherence on fourth-order moment of the light field in turbulent atmosphere

Analysis of beam wandering and influence of partial coherence on fourth-order moment of the light field in turbulent atmosphere

Sculpting isolated optical vortex knots on demand

The rapid development of optical technologies, including optical trapping, enhanced imaging, and microscopy, necessitates fundamentally new approaches to higher-dimensional optical beam shaping. We introduce a rigorous theoretical approach for sculpting three-dimensional, topological particle-like objects, such as optical knots or links, including precise control of their individual parts. Universally applicable to knots created using braided zero lines, our method is validated through theoretical analysis and experimental measurements. The proposed approach enables new degrees of freedom in multi-dimensional singularities shaping, including rotations, shifts, and rescaling of their parts for enhanced stability in complex media. These results may find applications in the fields of three-dimensional optical trapping, manipulation, and subwavelength microscopy, as well as probing and imaging through atmospheric or underwater turbulence.

Experimental Study on Phase Scintillation of Optical Transmission in Atmospheric Turbulence

The propagation of a beam in atmospheric turbulence causes phase fluctuations due to random variations in the atmospheric refractive index, leading to wavefront distortions. This paper analyzes the mechanisms of wavefront phase changes caused by atmospheric turbulence under different weather conditions and transmission distances. Local wavefront distortions are analyzed using Gaussian curvature, and wavefront distortions are assessed using peak-to-valley values, root mean square values, and the mean square error of the wavefront distortions. Additionally, the effects of different wavelengths and temperatures on wavefront distortions are studied. The experimental results show that the positive and negative Gaussian curvature peak values decrease in the order of snowy day (0.530, −0.850) μm−1, heavy rain (0.345, −0.447) μm−1, dust storm (0.412, −0.057) μm−1, light rain (0.297, −2.75 × 10−3) μm−1, sunny (0.154, −0.3 × 10−3) μm−1, and cloudy (0.107, −0.1 × 10−3) μm−1, with local distortions also decreasing in this order. The peak-to-valley values, root mean square values, and mean square error of the wavefront distortions decrease in the order of heavy rain (129.41 μm, 31.82 μm, 55.18 μm2), dust storm (74.1 μm, 18.84 μm, 51.40 μm2), snowy day (72.09 μm, 17.50 μm, 49.49 μm2), light rain (70.03 μm, 17.11 μm, 37.69 μm2), sunny (57.23 μm, 16.50 μm, 21.84 μm2), and cloudy (52.8 μm, 16.12 μm, 14.40 μm2). Shorter wavelengths exhibit greater phase fluctuations than longer wavelengths, and the degree of distortion increases with temperature. This study lays a theoretical foundation and provides experimental evidence for optical transmission in atmospheric turbulence.

Improved equivalent optical turbulence method for anisotropic compressible and atmospheric turbulence under different beam transmission distances

The impact of different turbulence on beams can be seen as optical distortions caused by refractive index fluctuations around vortices in turbulence. Therefore, from the perspective of transmission effects, the transmission outcomes of beam in different turbulences can be mutually equivalent. Since the mechanisms of beam propagation in compressible turbulence are not yet fully understood and the relevant theories are not well-established, a preliminary analysis of beam transmission in compressible turbulence is necessary. This analysis will help understand the medium characteristics of compressible turbulence, particularly its similarities and differences with atmospheric turbulence, before the optical effects of compressible turbulence are fully resolved. This paper establishes a connection between anisotropic atmospheric turbulence and compressible turbulence parameters by utilizing the mature solutions of beam in anisotropic atmospheric turbulence. We then employ the optical parameters of anisotropic atmospheric turbulence to represent those in compressible turbulence, leveraging existing solutions to assess beam transmission in compressible turbulence. Building upon the original equivalent method, we extend the dimension of transmission distance, ensuring that beams equivalence is maintained across different turbulence regimes. The results indicate that the equivalent method can effectively adapt to compressible turbulence. By using the equivalent structure function, it is possible to represent compressible turbulence parameters with the atmospheric refractive index structure constant. This method also works across different transmission distances. The method facilitates finding various solutions for beam in compressible turbulence.

Dynamic simulation imaging for complex atmospheric turbulence scenes based on atmospheric coherence length and associated with phase structure function

Dynamic simulation imaging for complex atmospheric turbulence scenes based on atmospheric coherence length and associated with phase structure function

Deep learning techniques for atmospheric turbulence removal: a review

Atmospheric turbulence significantly complicates the interpretation and analysis of images by distorting them, making it hard to classify and track objects within a scene using traditional methods. This distortion arises from unpredictable, spatially varying disturbances, challenging the effectiveness of standard model-based techniques. These methods often become impractical due to their complexity and high memory demands, further complicating the task of restoring scenes affected by atmospheric turbulence. Deep learning approaches offer faster operation and are capable of implementation on small devices. This paper reviews the characteristics of atmospheric turbulence and its impact on acquired imagery. It compares performances of a range of state-of-the-art deep neural networks, including Transformers, SWIN and MAMBA, when used to mitigate spatio-temporal image distortions. Furthermore, this review presents: a list of available datasets; applicable metrics for evaluation of mitigation methods; an exhaustive list of state-of-the-art and historical mitigation methods. Finally, a critical statistical analysis of a range of example models is included. This review provides a roadmap of how datasets and metrics together with currently used and newly developed deep learning methods could be used to develop the next generation of turbulence mitigation techniques.

Impacts of atmospheric turbulence on optic measurements over heterogeneous flat terrain: insights from large eddy simulations.

Atmospheric refraction imposes a fundamental limitation on the accuracy and precision of geodetic measurements that utilize electromagnetic waves. For terrestrial observations at optical wavelengths recorded over flat terrain, the vertical temperature gradient controls the bending of the rays thus affecting mostly the vertical angle measurement. The rules of thumb for mitigating these effects (variation ranges and short-term fluctuations) are based on intuition and practitioner experience. To address the challenge of understanding the impact of refractive index inhomogeneities on the refraction angle without additional instruments, we introduce large eddy simulations (LES) in geodesy. We use the PALM software to simulate realistic atmospheric conditions and investigate first- and second-order variations of the refraction angle using virtual measurements over a flat terrain with surface heterogeneities. We analyze the optimal measurement times to minimize refraction effects, highlighting the potential of LES to help plan measurement campaigns. Additionally, the correlating influence of atmospheric turbulence on the measurements is quantified. We propose a correction model based on the variance inflation factor as a practical tool for incorporating turbulence into a geodetic uncertainty model.

Establishing and Investigating an Effective Atmosphere‐Ocean Cross‐Medium Propagation Model Based on GSM Beams

AbstractUsing the Gaussian‐Schell model (GSM) beam as the light source, this study creates a blue‐green beam atmosphere‐ocean cross‐medium propagation model (AOCPM) based on the extended Huygens‐Fresnel principle and the linear filtering method. The closed expression of the Cross Spectral Density Function (CSDF) of the GSM beam after propagation through atmospheric turbulence, atmosphere‐ocean interface, and ocean turbulence are derived. And the correctness of the model is verified by simulating the changes in intensity, relative beam width, and speckle normalized intensity autocorrelation function during the propagation of the GSM beam through the atmosphere‐ocean cross‐medium under different parameters. The findings demonstrate that the intensity of the GSM beam after being propagated through the atmosphere‐ocean medium presents a speckle‐like Gaussian distribution, the intensity of the GSM beam gradually attenuates, the relative beam width gradually grows, and the speckle normalized intensity autocorrelation function gradually decreases as the turbulence intensity and propagation distance increase. In addition, the increase in wind speed at rough sea surface mainly leads to the attenuation of intensity. The work of this paper provides a new idea for the study of atmosphere‐ocean cross‐medium propagation of blue‐green beams.

Atmospheric turbulence degradation image restoration based on multi-input multi-output U-Net network

Atmospheric turbulence degradation image restoration based on multi-input multi-output U-Net network

Characterizing propagation and vortex-splitting dynamics of Bessel-Gaussian beams in short-range atmospheric conditions.

This study explores the propagation dynamics of Bessel-Gaussian (BG) beams, focusing on vortex-splitting behavior under short-range atmospheric conditions with varying disturbances. Using the split-step beam propagation method, the research reveals that greater atmospheric turbulence and longer transmission distances enhance both the average vortex splitting distance and its variance while reducing the average topological charge of the received OAM mode. Conversely, laminar conditions promote beam stability. Results highlight the high sensitivity of vortex splitting to beam parameters, with topological charge playing a significant role in phase singularity formation and vortex complexity. Additionally, beam width and shape are critical, as larger widths intensify splitting under atmospheric disturbance. Notably, BG beams exhibit greater stability and less vortex splitting than Laguerre-Gaussian beams, particularly in turbulent environments at short distances. These insights advance the understanding of vortex beam dynamics, with important implications for atmospheric remote sensing applications.

Propagation Properties of Partially Coherent Flat-Topped Beam Rectangular Arrays in Plasma and Atmospheric Turbulence

Propagation properties represent a critical aspect of laser beams utilized in free space optical (FSO) communications. We examined the evolution characteristics of the electric field associated with partially coherent flat-topped beam rectangular arrays propagating bidirectionally through the turbulent atmosphere and plasma links. Utilizing the optical transmission matrix, alongside the second moment theory and Wigner distribution functions, we derived analytical expressions for both the intensity distribution and propagation factors of the partially coherent flat-topped beam rectangular arrays affected by the atmospheric turbulence and plasma disturbances. The numerical results indicate that appropriately selecting parameters such as beam order, transverse spatial coherence width, and beam width can effectively mitigate the adverse effects on propagation properties caused by the turbulent atmosphere and plasma. Our results have significant implications for FSO communications within specific environmental contexts.

Design and testing research of LiDAR for detecting atmospheric turbulence

Design and testing research of LiDAR for detecting atmospheric turbulence

Enhanced Neural Architecture for Real-Time Deep Learning Wavefront Sensing.

To achieve real-time deep learning wavefront sensing (DLWFS) of dynamic random wavefront distortions induced by atmospheric turbulence, this study proposes an enhanced wavefront sensing neural network (WFSNet) based on convolutional neural networks (CNN). We introduce a novel multi-objective neural architecture search (MNAS) method designed to attain Pareto optimality in terms of error and floating-point operations (FLOPs) for the WFSNet. Utilizing EfficientNet-B0 prototypes, we propose a WFSNet with enhanced neural architecture which significantly reduces computational costs by 80% while improving wavefront sensing accuracy by 22%. Indoor experiments substantiate this effectiveness. This study offers a novel approach to real-time DLWFS and proposes a potential solution for high-speed, cost-effective wavefront sensing in the adaptive optical systems of satellite-to-ground laser communication (SGLC) terminals.