Turbulence Compensation Research Articles

Turbulence Compensation based on pix2pixGAN for the Free Space Optical Communication of Orbital Angular Momentum Multiplexing

Turbulence Compensation based on pix2pixGAN for the Free Space Optical Communication of Orbital Angular Momentum Multiplexing

Turbulence compensation with pix-to-pix generative adversarial networks in vector vortex beams

Orbital angular momentum (OAM) has significantly propelled free space optical communication (FSOC) towards achieving ultra-large transmission capacities, but mode-crosstalk in atmospheric turbulence limits its application. Here, we propose a proof-of-concept turbulence compensation approach utilizing pix-to-pix generative adversarial networks (pix2pixGAN) that does not rely on the wavefront sensor. The model captures the complex relationships between distorted optical fields and phase screens through extensive training, after which the phase screen is directly recovered from the well-trained model by identifying the corresponding distorted image to compensate for distortions. Using this model, the Strehl ratio improvement is measured at 35.7%, 8.9%, and 1.7% under three distinct turbulence conditions, respectively. Furthermore, the recognition of vector vortex beams (VVBs) integrating with the pix2pixGAN significantly improves average mode accuracy from 2% to over 99%. Additionally, the exploration of VVB-based communication further elucidates pix2pixGAN's role in enhancing communication quality. These findings suggest a potential advancement in developing a novel neural network-based strategy to compensate for transmission distortions under intense turbulence.

Self-adaptive integrated photonic receiver for turbulence compensation in free space optical links

In Free Space Optical (FSO) communication systems, atmospheric turbulence distorts the propagating beams, causing a random fading in the received power. This perturbation can be compensated using a multi-aperture receiver that samples the distorted wavefront on different points and adds the various signals coherently. In this work, we report on an adaptive optical receiver that compensates in real time for scintillation in FSO links. The optical front-end of the receiver is entirely integrated in a silicon photonic chip hosting a 2D Optical Antenna Array and a self-adaptive analog Programmable Optical Processor made of a mesh of tunable Mach–Zehnder interferometers. The photonic chip acts as an adaptive interface to couple turbulent FSO beams to single-mode guided optics, enabling energy and cost-effective operation, scalability to systems with a larger number of apertures, modulation-format and data-protocol transparency, and pluggability with commercial fiber optics transceivers. Experimental results demonstrate the effectiveness of the proposed receiver with optical signals at a data rate of 10 Gbit/s transmitted in indoor FSO links where different turbulent conditions, even stronger than those expected in outdoor links of hundreds of meters, are reproduced.

Turbulence causes kinematic and behavioural adjustments in a flapping flier.

Turbulence is a widespread phenomenon in the natural world, but its influence on flapping fliers remains little studied. We assessed how freestream turbulence affected the kinematics, flight effort and track properties of homing pigeons (Columba livia), using the fine-scale variations in flight height as a proxy for turbulence levels. Birds showed a small increase in their wingbeat amplitude with increasing turbulence (similar to laboratory studies), but this was accompanied by a reduction in mean wingbeat frequency, such that their flapping wing speed remained the same. Mean kinematic responses to turbulence may therefore enable birds to increase their stability without a reduction in propulsive efficiency. Nonetheless, the most marked response to turbulence was an increase in the variability of wingbeat frequency and amplitude. These stroke-to-stroke changes in kinematics provide instantaneous compensation for turbulence. They will also increase flight costs. Yet pigeons only made small adjustments to their flight altitude, likely resulting in little change in exposure to strong convective turbulence. Responses to turbulence were therefore distinct from responses to wind, with the costs of high turbulence being levied through an increase in the variability of their kinematics and airspeed. This highlights the value of investigating the variability in flight parameters in free-living animals.

Direct prediction and compensation of atmospheric turbulence for free-space integer and fractional order OAM multiplexed transmission links.

Atmospheric turbulence has an adverse impact on orbital angular momentum (OAM) beam transmission, resulting in power fluctuations and mode crosstalk. These challenges are particularly pronounced in OAM multiplexing links. In this paper, we propose and demonstrate a novel network architecture that integrates convolutional layers and residual structures to address the issue of turbulence phase compensation. By harnessing the local feature learning capability of convolutional layers and the information-preserving function of residual structures, we aim to mitigate the adverse effects of network depth on information loss. By employing the proposed network, we compensate the turbulence phase directly using the received intensity distributions for free space multiplexed integer and fractional order OAM links, respectively. The obtained results show that the received optical power can be improved for more than 10 dB for integer order OAM multiplexed FSO links under weak to strong turbulence conditions, while 9 dB for fractional-order OAM multiplexed FSO links. Moreover, mode crosstalk can be reduced for about 10 dB under 4 OAM modes multiplexed links under turbulence strength D/r0=5. The proposed deep learning based atmospheric turbulence compensation method can predict phase screens rapidly and accurately, thus enhancing the dependability of future OAM multiplexing technology.

Learning to Navigate in Turbulent Flows With Aerial Robot Swarms: A Cooperative Deep Reinforcement Learning Approach

Aerial operation in turbulent environments is a challenging problem due to the chaotic behavior of the flow. This problem is made even more complex when a team of aerial robots is trying to achieve coordinated motion in turbulent wind conditions. In this paper, we present a novel multi-robot controller to navigate in turbulent flows, decoupling the trajectory-tracking control from the turbulence compensation via a nested control architecture. Unlike previous works, our method does not learn to compensate for the air-flow at a specific time and space. Instead, our method learns to compensate for the flow based on its effect on the team. This is made possible via a deep reinforcement learning approach, implemented via a Graph Convolutional Neural Network (GCNN)-based architecture, which enables robots to achieve better wind compensation by processing the spatial-temporal correlation of wind flows across the team. Our approach scales well to large robot teams -- as each robot only uses information from its nearest neighbors -- , and generalizes well to robot teams larger than seen in training. Simulated experiments demonstrate how information sharing improves turbulence compensation in a team of aerial robots and demonstrate the flexibility of our method over different team configurations.

Turbulence Compensation for Receiving and Coherent Combining via Phased Fiber Laser Array

We first demonstrate atmospheric turbulence compensation and optical coherent combining using a phased fiber laser array with the largest channels of sub-apertures. With multi-dimensional control of piston and tip/tilt phases on each sub-aperture, the co-phasing and adaptive fiber coupling of receiving beamlets have been achieved in all-fiber structure, and the mean received power increased by about 12 times and the scintillation index caused by turbulence decreased from 0.275 to 0.041 compared with open loop. This experiment shows the practicability and adaptive optics ability of the phased fiber laser array and suggests the great potential of its applications in urban free-space optical communications.

Turbulence compensation for radar imaging carrying orbital angular momentum based on convolutional neural network

The spiral phase front (SPF) and orbital angular momentum (OAM) of vortex electromagnetic waves (VEMW) have attracted extensive attention in radar imaging. However, VEMW is extremely sensitive to atmospheric turbulence (AT), which will lead to distortion of the SPF and diffusion of the OAM modes. Furthermore, refractive-index fluctuations will cause absorption and fluctuations in the speed of VEMW. Specifically, SPF distortion leads to phase errors, which is demonstrated as defocus of the scatterer in the image. Atmospheric absorption and fluctuations in VEMW speed suffer amplitude error and phase error, which are manifested as amplitude variation with range and positioning errors, respectively. Generally, refractive-index fluctuations feature significant spatial and temporal variability, making it difficult for conventional algorithms to obtain accurate compensation. In this paper, a data-driven-based convolutional neural network (CNN) approach is proposed to improve imaging performance. The CNN is taken to learn the mapping function of images with atmospheric errors to label images without turbulence effects, and then the trained CNN model is integrated into imaging system to improve the imaging quality. The numerical simulation verifies that the method can effectively compensate for turbulence effects and obtain high-resolution images.

A simplified mode diversity coherent receiver based on non-mode-selective photonic lantern and Kramers-Kronig detection

This paper proposes a mode-diversity space optical communication receiver for long-range space optical communication, which can compensate for the effect of atmospheric turbulence and be applied between 2 km and 16 km space optical communication with a low-cost, low-power and low-complexity feature. The receiver uses a non-mode selective photonic lantern as a mode demultiplexer, merging using an equal gain combining (EGC) algorithm and a Kramers-Kronig (KK) detection technique to accomplish the optical detection of high-dimensional modulated format signals. The performance of the receiver under different turbulent conditions is experimentally investigated, showing significant compensation for atmospheric turbulence. The experimental results show that the proposed scheme achieves a gain of 4–5 dB at BER = 3 × 10−3 compared to a single-mode fiber (SMF) receiver under moderately strong turbulent conditions.

Atmospheric Turbulence Compensation Based on Deep Learning to Correct Distorted Composite Bessel-Gaussian Beam

Atmospheric Turbulence Compensation Based on Deep Learning to Correct Distorted Composite Bessel-Gaussian Beam

Predictive correction method based on deep learning for a phase compensation system with frozen flow turbulence.

We propose a deep learning method that includes convolution neural network (CNN) and convolutional long short-term memory (ConvLSTM) models to realize atmospheric turbulence compensation and correction of distorted beams. The trained CNN model can automatically obtain the equivalent turbulent compensation phase screen based on the Gaussian beams affected by turbulence and without turbulence. To solve the time delay problem, we use the ConvLSTM model to predict the atmospheric turbulence evolution and acquire a more accurate compensation phase under the Taylor frozen hypothesis. The experimental results show that the distorted Gaussian and vortex beams are effectively and accurately compensated.

Wavefront distortion correction of superposed optical vortices based on deep multi-branch compensation network

Optical vortices with orbital angular momentum play a crucial role in many fields such as target detection, quantum entanglement, and space optical communication. However, the wavefront distortion of optical vortices caused by atmospheric turbulence during free-space transmission is a major obstacle to practical applications. In this work, a deep-learning-based method is proposed for wavefront correction of distorted superposed optical vortices under various turbulence intensities. First, the Zernike polynomial expansion method is used to numerically simulate the atmospheric turbulence phase screen conforming to the Kolmogorov statistical law which assumes that turbulence is locally uniform and isotropic, in which the first 10 Zernike polynomials are adopted. Then, according to the distinct wavefront distortion features of different polynomials, a deep multi-branch compensation network (DMCN) is designed to adaptively and more accurately learn the mapping relationship between the intensity distribution profile of distorted optical vortices and the corresponding turbulent phase screen. The distorted superposed optical vortices dataset for network training is obtained by experimental measurement. Finally, the turbulence compensation screen predicted by the trained DMCN is verified experimentally and the results show that our wavefront distortion correction method based on DMCN can accurately predict the turbulent compensation screen and improve the mode purity of superposed optical vortices to more than 80% within 40 ms when using a workstation computer under various turbulence intensities, which has apparent advantages compared with traditional algorithms.

An Atmospheric Turbulence Compensation Algorithm Based on FSM-DM Cascaded AO Architecture for FSO Communications

Free-space optics (FSO) communication enjoys desirable modulation rates at unexploited frequency bands, however, its application is hindered by atmospheric turbulence which causes phase shifting in laser links. Although a single deformable mirror (DM) adaptive optics (AO) system is a good solution, its performance remains unsatisfactory as the proportion of tilts aberrations becomes relatively high. This condition happens when the incident angle of the laser beam for the optical receiver dynamically shifts. To tackle this problem, we introduce a fast steering mirror (FSM), DM cascaded AO architecture, based upon which we also propose an atmospheric turbulence compensation algorithm. In this paper, we compare the compensation ability of FSM and DM towards tilts aberrations. Furthermore, we gain model matrices for FSM and DM from testbed and simulatively verify the effectiveness of our work. For a Kolmogorov theory-based atmospheric turbulence disturbed incident laser beam where the tilt components take up 80% of the total proportion of wavefront aberrations, our proposed architecture compensates the input wavefront to a residual wavefront root mean square (RMS) of 116 wavelength, compared to 16 wavelength for single DM architecture. The study intends to overcome atmospheric turbulence and has the potential to guide the development of future FSO communications.

Security enhancement for adaptive optics aided longitudinal orbital angular momentum multiplexed underwater wireless communications.

The frozen-wave-based longitudinal orbital angular momentum multiplexing (LOAMM) system developed in [IEEE Photonics J.10, 7900416 (2018)10.1109/JPHOT.2017.2778238] has the potential to overcome the crosstalk effects induced by turbulence. In this paper, we propose a defocus measurement aided adaptive optics (DMA-AO) technique for turbulence compensation in a LOAMM underwater wireless optical communication (UWOC) system to investigate the enhancement of physical layer security. Relying on a phase retrieval algorithm and probe beam, three amplitude-only measurements obtained from different back focus planes can realize phase reconstruction of distorted OAM beams. Moreover, the so-called mixture generalized gamma-Johnson SB (GJSB) distribution is proposed to characterize the probability density function (PDF) of reference-channel irradiance of OAM. The GJSB allows for obtaining closed-form and analytically tractable expression for the probability of strictly positive secrecy capacity (SPSC) in a single input single output (SISO) system. Furthermore, the average secrecy capacity (ASC) and probability of SPSC for a multiple input multiple output (MIMO) system are investigated. Compared to the traditional OAM multiplexing system based on Laguerre-Gaussian (LG) beams, the LOAMM system with a probe beam assisted DMA-AO technique has potential advantages for improving the security performance in UWOC.

Atmospheric turbulence compensation for OAM-carrying vortex waves based on convolutional neural network

The helical phasefront and orbital angular momentum (OAM) of vortex electromagnetic waves (VEMW) have attracted extensive attention in expanding communication capacity and enhancing radar imaging resolution. However, the VEMW is sensitive to atmospheric turbulence (AT), which will cause helical phasefront distortion and OAM mode diffusion. Hence, a convolutional neural network (CNN) based method for AT compensation is proposed. Specifically, the developed CNN automatically learns the AT characteristic parameters from the distorted VEMW phasefront and reconstructs the equivalent AT phase screen, and then, compensation is achieved by loading the inverse of the predicted phase on the distorted VEMW. The simulations show that the trained CNN has strong generalization capability and can perform high-quality AT prediction for different turbulence strengths and OAM modes, after compensation, the distorted phase is repaired and the mode purity is significantly improved. Moreover, comparing with the conventional AT compensation method, the proposed method shows smaller computational burdens and higher compensation accuracy.

Design and Performance Analysis of NadamSPGD Algorithm for Sensor-Less Adaptive Optics in Coherent FSOC Systems

Sensor-less adaptive optics (SLAO) based on stochastic parallel gradient descent (SPGD) is effective for the compensation of atmospheric turbulence in coherent free-space optical communication (CFSOC) systems. However, SPGD converges slowly and easily falls into local extremes. Therefore, we propose a novel NadamSPGD algorithm for efficient wavefront correction that combines Nesterov-accelerated adaptive moment estimation (Nadam) and SPGD. Specifically, Nesterov’s accelerated gradient momentum (NAG) and adaptive gain coefficients are integrated to conventional SPGD to accelerate its convergence speed and avoid converging to extremum points. Theoretical analysis, numerical simulations and experimental results demonstrate that NadamSPGD can increase the convergence speed by ~50% and significantly improve the robustness of parameters, and thus more efficiently suppress the negative effects of atmospheric turbulence on mixing efficiency (ME) and bit error rate (BER). Our algorithm also presents better dynamic performance under strong turbulence and high Greenwood frequency conditions, and it is more suitable for real-time SLAO systems. This study proves that the NadamSPGD algorithm is suitable for SLAO in the CFSOC system and is a viable substitute for SPGD to improve the quality of optical communications.

Adaptive turbulence compensation and fast auto-alignment link for free-space optical communications.

Free-space point-to-point optical communication often suffers from atmospheric turbulence and device vibration where the environment is harsh. In this paper, by introducing an adaptive system composed of turbulence compensation and fast auto-alignment installation, we propose and experimentally demonstrate an optical communication system that is effective against turbulence and vibration. Turbulence compensation can increase the coupling efficiency by at least 3dB, while fast auto-alignment can reduce the spatial range of beam vibration caused by device vibration by 72.22%. Since the photodiode detector (PD) is sensitive to optical power, reducing the loss of the link improves the communication quality of the system. Bit-error rate (BER) of 10-Gbaud 16-ary quadrature amplitude modulation (16-QAM) signal transmission in the link is also measured under different transmitted power, having ∼8dB power penalty improvement with the adaptive system. In addition, turbulence compensation for higher-order modes such as optical vortex (OV) beams is also implemented, showing a promising prospect in space-division multiplexing (SDM) applications.

Adaptive-Optics-Enabled Quantum Communication: A Technique for Daytime Space-To-Earth Links

Robust quantum channels between satellites and Earth are essential for the anticipated quantum Internet, but remain challenging in daylight, when background photons vastly outnumber qubit photons. Insufficient understanding of atmospheric propagation and turbulence compensation has led to approaches based on prohibitively narrow spectral filtering and unnecessarily low channel efficiencies. This field experiment uses adaptive optics to maximize efficiency while spatially filtering sky noise at the theoretical limit, enabling quantum communication over the daytime sky hemisphere. Requirements for spectral filtering are relaxed enough to accommodate present-day sources of entangled photons.

Estimating Turbulence Distribution over a Heterogeneous Path Using Time-Lapse Imagery from Dual Cameras

Knowledge of turbulence distribution along an experimental path can help in effective turbulence compensation and mitigation. Although scintillometers are traditionally used to measure the strength of turbulence, they provide a path-integrated measurement and have limited operational ranges. A technique to profile turbulence using time-lapse imagery of a distant target from spatially separated cameras is presented here. The method uses the turbulence induced differential motion between pairs of point features on a target, sensed at a single camera and between cameras to extract turbulence distribution along the path. The method is successfully demonstrated on a 511 m almost horizontal path going over half concrete and half grass. An array of Light-Emitting Diodes (LEDs) of non-uniform separation is imaged by a pair of cameras, and the extracted turbulence profiles are validated against measurements from 3D sonic anemometers placed along the path. A short-range experiment with a heat source to create local turbulence spike gives good results as well. Because the method is phase-based, it does not suffer from saturation issues and can potentially be applied over long ranges. Although in the present work, a cooperative target has been used, the technique can be used with non-cooperative targets. Application of the technique to images collected over slant paths with elevated targets can aid in understanding the altitude dependence of turbulence in the surface layer.

Iterative wavefront reconstruction for strong turbulence using Shack-Hartmann wavefront sensor measurements.

An iterative wavefront reconstruction method using Shack-Hartmann wavefront sensor (SHWFS) measurements is presented in this paper. A new cost function for the wavefront reconstruction problem is derived and the solution is obtained iteratively using the gradient descent method. The proposed method aims to effectively handle the scintillated SHWFS measurements and to provide simpler and accurate ways to achieve branch-point-tolerant wavefront reconstruction suitable for adaptive optics compensation of strong turbulence. Simulated iterative wavefront reconstruction results show the effectiveness of the proposed method. A laboratory optical testbed is also presented to show the experimental implementation of the proposed method.