In dual-wavelength free-space optical communication systems, the wavefront distortion differences caused by the wavelength difference of the signal and beacon lights cannot be completely corrected. In this study, according to the method of geometric optics, the relationship between the wavefront phases of the signal and beacon lights is analyzed by establishing a mathematical model of the cross-correlation ratio of the arrival-angle fluctuation and phase relationship of different Gaussian-beam wavelengths under weak turbulence near the surface. The numerical results show that after Gaussian beams of different wavelengths propagate through the same atmospheric channel, the cross-correlation number of the arrival-angle fluctuation decreases with an increase in the wavelength difference, waist radius, and turbulence intensity, and increases with an increase in propagation distance. The beam-wavefront phase difference increases with an increasing wavelength difference. Finally, a wavefront distortion correction experiment of a dual-wavelength adaptive optical system verified the correctness of the wavefront phase-difference relationship between the signal light and beacon light established in this study.

In this study, we have investigated the propagation characteristics of single-mode Laguerre–Gaussian (LG) beams under field atmospheric turbulence conditions. We constructed a 1200 meter experimental platform for representing vortex beams in the field. Accordingly, we analyzed the spot changes in an LG beam after transmitted through atmospheric turbulence. Based on the principle of Fresnel diffraction and the random phase screen method, we studied the evolution and spiral spectrum distribution of low-order LG beams transmitted by atmospheric turbulence by numerical simulation. Moreover, we carried out an experimental study regarding the LG beam propagation characteristics mainly based on field experiments. The experimental results indicate that after near-surface turbulent propagation, the LG beam gradually spreads, degree of phase singularity drift becomes larger, and spot size of the Gaussian beam grows faster than that of the LG beam with greater propagation distances. Finally, we concluded that LG beams are not significantly affected by turbulence. It also lays a foundation for the experimental study of vortex beam detection and wavefront correction at the receiving end in multiplexing communication.

Atmospheric turbulence causes signal beam wavefront distortion at the receiving end of a coherent detection system, which decreases the system mixing efficiency. Based on the coherent detection theory, this study establishes a mathematical model of wavefront distortion with mixing efficiency and mixing gain. It also analyzes the improvement limits of wavefront correction on mixing efficiency and mixing gain under different atmospheric turbulence intensities and experimentally measures them. Simulation results show that the mixing efficiency can be improved to 51%, 55%, and 60% after correcting for tilt, defocus, and astigmatism terms, respectively, when turbulence intensity D/r₀ is 2. The mixing gain with homodyne detection is 3 dB higher than heterodyne detection. Meanwhile, the wavefront correction orders required for optimal mixing efficiency are higher than the heterodyne correction order. In the experiment, Haso4 NIR + DM 40 was used, and the turbulence intensity D/r₀ was 2. After the closed-loop control algorithm corrects the tilt, defocus, and astigmatism terms, the indoor experimental results showed that the mixing efficiency is improved to 36%, 47%, and 62%, respectively. The outdoor experimental results showed that the mixing efficiency improved to 36%, 51%, and 68%, respectively.

This paper introduces a single LED and four photodetectors (PDs) as a visible light system structure and collects the received signal strength values and corresponding physical coordinates at the PD receiving end, establishing a comprehensive dataset. The K-means clustering algorithm is employed to separate the room into center and boundary areas through the fingerprint database. The bald eagle search (BES) algorithm is employed to optimize the initial parameters, specifically the weights and thresholds, in the extreme learning machine (ELM) neural network, and the BES–ELM indoor positioning model is established by region to improve positioning accuracy. Due to the impact exerted by the ambient environment, there are fluctuations in the positioning accuracy of the center and edge regions, and the positioning of the edge region needs to be further improved. To address this, it is proposed to use the enhanced weighted K-nearest neighbor (EWKNN) algorithm based on the BES–ELM neural network to correct the prediction points with higher-than-average positioning errors, achieving precise edge positioning. The simulation demonstrates that within an indoor space measuring 5 m × 5 m × 3 m, the algorithm achieves an average positioning error of 2.93 cm, and the positioning accuracy is improved by 86.07% relative to conventional BP neural networks.

A mathematical model considering the effects of amplitude and phase random fluctuations on the signal-to-noise ratio (SNR) of heterodyne detection was established, and the effects of irradiance and phase fluctuations on the performance of heterodyne detection were investigated. The results show that the inner scale of turbulence significantly affects the SNR. The first 20 Zernike modes have a greater effect on the SNR of the heterodyne detection system. The SNR is affected more significantly by phase fluctuations than by irradiance fluctuations. The SNR decreases by four orders of magnitude because of amplitude and phase fluctuations.

In space optical communication, owing to the influence of atmospheric turbulence, optical beams lose focus and become phase-distorted, which reduces the communication quality. Considering the polarization dependence of liquid crystal spatial light modulators and the dispersion effect of liquid crystal materials, the energy utilization rate of liquid crystal adaptive optics systems is low. In this study, a dual liquid crystal spatial light modulator adaptive optics system based on the GS algorithm is used to correct the wavefront distortion of a signal beam under different atmospheric turbulence intensities, and the Strehl ratio (SR) is used as the evaluation index. The simulation results show that the SR of the corrected system can be increased from 0.23, 0.41, and 0.72 to 0.77, 0.89, and 0.95, respectively. The corrected beam spot was more concentrated and the light intensity at the center of the beam spot was stronger. The experimental results show that, after the distortion wavefront is corrected by the dual liquid crystal spatial light modulator, the average gray value of the 10 × 10 pixels in the center of the spot increases from 159.3, 113.1, and 58.4 to 253.4, 247.7, and 198.3, respectively.