Wireless optical coherent communication has a higher detection sensitivity (20–23 dB) compared to direct detection technology and is more suitable for long-distance communication [1]. The wavefront of an optical signal reaching the receiving surface is affected by atmospheric turbulence [2] and produces distortion and disturbance, which in severe cases can interrupt communication [3]. Adaptive optics, a technology that can effectively suppress the wavefront distortion caused by atmospheric turbulence [4], has become a commonly used turbulence suppression method in the field of laser communication today [5–7].

One approach is to use spatial optical mixing as a key technology for coherent detection. This involves mixing light beams through spatial optical devices and directly focusing and coupling the combined light signal to a balanced detector. The corrected signal light and wavefront of the local oscillator light must be kept as closely matched as possible [8]. Another method is to use a fiber-optic optical hybrid, which requires the optical signal to be coupled into the hybrid through fiber optics and mixed with local oscillator light. After mixing, it is connected to a balanced detector through fiber optics, and the wavefront of the signal light needs to be corrected to improve and stabilize the coupling efficiency [9, 10]. Whether a spatial or fiber-optic optical hybrid is used, if the wavefront of the signal light is directly sensed and corrected, appropriate splitting processing of the received signal is required for wavefront detection and information transmission [11]. However, the majority of research on applying adaptive optics to laser communication currently focuses on optimizing beam characteristics [12], expanding channel capacity [5] through multiplexing [13], and optimizing wavefront correction algorithms. Most of these simulations and experiments are conducted in simulated indoor turbulence conditions [11]. Compared to the miniaturized, low-cost laser communication wavefront correction technology used in actual near-ground turbulent environments, there are relatively few experimental reports and technical details available. Laser communication typically uses the near-infrared atmospheric window band with a wavelength of 1550 nm. Silicon-based near-infrared wavefront sensors require near-infrared light signals to be converted into visible light signals and imaged [14]. Compared with the visible light band, higher power is required to obtain complete wavefront information, which inevitably diverts some power to reduce the actual coupling transmission efficiency. At the same time, the detection accuracy of near-infrared wavefront sensors is lower than that of visible-light bands. Taking the Shack Hartmann wavefront sensor Haso4 FIRST (operating wavelength range: 400–1100 nm) and Haso4 NIR (operating wavelength range: 1500–1600 nm) as examples, their wavefront measurement accuracy in absolute mode (rms) is λ/100 and λ/35, respectively [15]. Because of their high cost, practical application solutions for near-infrared wavefront sensors based on indium gallium arsenide (InGaAs) substrates are not feasible.

In the field of astronomical observation, the adaptive optics uses Rayleigh or sodium beacons to image atmospheric sodium layer atoms generated by stimulated D2 line resonance scattering from a controllable sky for wavefront sensing and correction; it enables clear observations of celestial bodies and approaching diffraction limits [16]. Wireless optical coherent communication systems often use beacon lights for beam alignment, tracking, and capturing, thereby establishing communication links [17]. Beacon light can usually be coaxially emitted with a signal light using a beacon light band, similar to the communication window band. In this method, wavefront correction of the communication band can be achieved refer to the previous study [18]. Combined with previous theoretical analyses regarding the propagation characteristics of lasers with different wavelengths under atmospheric turbulence condition [19], this study conduct the test adopting a self-developed wireless optical coherent communication system to perform beacon wavefront correction for real-time video signal transmission. The objective is to explore the performance enhancement capabilities of wavefront correction in wireless optical communication systems. The designed system aims to improve correction accuracy, minimize signal optical power loss, and significantly reduce the system hardware costs.

2.1. System Composition

An adaptive optical system for free-space coherent optical communication is shown in Fig. 1. The source sequence encoded by the video encoder was modulated by a lithium niobate phase modulator using a 1550 nm wavelength carrier for signal phase modulation. The phase-modulated optical signal was amplified by an erbium-doped fiber amplifier (EDFA) and combined with a beacon light of 980 nm-wavelength through a wavelength-division multiplexer (WDM). After the combination, the two coaxial beams were emitted through an optical antenna using off-axis transmission. Owing to atmospheric channel attenuation and turbulence at the receiving end, the two coaxial optical signals received by the optical antenna acted directly on a deformable mirror for reflection. After dichroic mirror divides the two parallel beams of the signal light and beacon light, the beacon light passes through a 4f system, where wavefront information is collected by a wavefront sensor and fed back to a computer. The distorted wavefront was corrected by controlling the deformable mirror, after which the signal light was coupled into the single-mode fiber of the hybrid through a focusing lens. The four optical signal outputs obtained by mixing were applied pairwise to two identical dual-balanced detectors, with one signal used for frequency control and polarization control and the other channel used for demodulation processing to complete the transmission of video information. The transmission distance of the free-space link was 1.3 km from South Second Ring Road in Xi’an City to the sixth floor of Xi’an University of Technology. The measurement was conducted on April 16, 2021, under sunny conditions with a southwest wind at level 2. The signal optical power output by the transmitting end was approximately 50 mW. In contrast, the beacon’s optical power was approximately 30 mW. The signal laser and local oscillator laser were both Koheras Basik E15 (NHT Photonics, Birkerød, Denmark) narrow-linewidth fiber lasers with a hybrid model (COH-24; XSoptix, CT, USA), a balance detector model of BPD-002 (Luna Innovations, VA, USA), a wavefront sensor model of the Shack-Hartmann wavefront sensor Haso4 FIRST (Imagine Optics, Orsay, France), and a deformable mirror model of Alpao DM69 (Alpao, Montbonnot, France). Figure 2 shows the experimental link, a physical image of the wireless optical coherent communication, and a diagram of the receiving optical path. In Fig. 2(b), The output parallel light received by the receiving antenna has a spot diameter of 8 mm. After being reflected by flat mirror 1, deformable mirror and flat mirror 2 respectively, it reaches the 4f system, which is composed of two plano convex lenses, of which the input beam lens is 175 mm, the focal length of the output lens is 75 mm, and the 8 mm spot is compressed to 3.4 mm. The effective area size of the wavefront sensor is 3.6 × 4.6 mm, the resolution is 32 × 40, and the focal length of the coupling lens is 125 mm.

Figure 1. Block diagram of wireless optical coherent communication system with adaptive optics. PRBS, pseudo-random binary sequesnces; WDM, wavelength division multiplexing; EDFA, erbium-doped fiber amplifier.

Figure 2. Diagrams of (a) wireless optical coherent communication experimental and physical link, and (b) receiving optical path.

The signal transmitted through atmospheric channels is affected by atmospheric turbulence. When only the influence of wavefront distortion on the optical field is considered, the signal light field at the receiving end can be represented as

In Eq. (1), A_s(x, y, t) represents the distribution of the signal light field, and φ(x, y, t) represents the wavefront distortion caused by atmospheric turbulence. Compared with spatial hybrids, fiber-optic hybrids have a more streamlined structure and higher integration. Therefore, this system uses fiber-optic hybrids, which require the coupling of optical signals to single-mode fibers. According to the principle of mode-field matching, the coupling efficiency of the signal optocoupler into single-mode optical fibers can be expressed as [20]:

In Eq. (2), E_f (x, y, t) is the optical field distribution of E_s(x, y, t) located at the fiber end face after being focused by a lens, and E₀(x, y, t) is the Gaussian distribution of single-mode fiber beam transmission [21],

In Eqs. (3) and (4), f is the focal length of the focusing lens, λ is the wavelength, k = 2π/λ is the wavenumber, and ω₀ is the mode field radius of the single-mode fiber. Wavefront distortion introduced by atmospheric turbulence reduces the coupling efficiency and stability of optical fibers [20]. For practical coherent detection systems, while maintaining a certain value of local oscillator power without considering the influence of the polarization state, the intermediate frequency signal output can be expressed as follows [22]:

In Eq. (5), A_s, A_L represents the amplitudes of the signal light and the local oscillator light, respectively, ω_S, and ω_L represent the frequencies of the signal light and the local oscillator light, k_p represents the modulation depth, m(t) is the normalized modulation signal, φ is the actual phase, e is the amount of elemental charge, η_n is the quantization efficiency, h is the Planck constant, v is the electromagnetic wave radiation frequency, and f is the carrier frequency of the intermediate frequency signal.

Based on the error rate of binary phase shift keying systems [22],

In Eq. (6), the signal-to-noise ratio (SNR) can be calculated from the intermediate frequency signal in Eq. (5).

2.2. Data Measurement and Experimental Results

Figure 3 shows the wavefront reconstruction process using a Shark-Hartmann wavefront sensor based on the Zernike mode method. Because the wavefront can be represented by a set of orthogonal Zernike coefficients, it can be seen in Fig. 3(a) that the tilted components of the wavefront (tilt at 0° and tilt at 90°) have more significant fluctuations than other high-order components, and the proportion of wavefront distortion tilted components is independent of the turbulence intensity, accounting for approximately 80%. Therefore, the distortion and fluctuation of the tilted components were the main reasons for the overall wavefront distortion and fluctuation. Figures 3(b) and 3(c) show the wavefronts reconstructed at different times. Because the receiving antenna has a Cassegrain-like structure with an obstruction ratio, a hollow structure exists for the reconstructed wavefront. The presence of atmospheric turbulence and attenuation makes it difficult for the wavefront sensor to reach the minimum detection threshold for signals received by the molecular aperture within an equal interval of sampling time, resulting in the failure of reconstruction in some areas of the wavefront and an incomplete display of the wavefront as a whole.

Figure 3. Wavefront information collected using Shark-Hartmann wavefront sensor: (a) Beacon optical Zernike coefficient variation curve, (b) reconstructed complete wavefront, and (c) reconstructed incomplete wavefront.

The collected wavefront data were analyzed according to Eqs. (1)–(7), using following parameters: Wavelength λ = 1550 nm, coupling lens focal length f = 12.5 mm, single mode fiber radius ω₀ = 4.5 μm, the photoelectric conversion coefficient η = 0.9, and A_L = 1,000 × A_s. Semi-experimental simulations and direct measurements were performed independently. Figure 4 shows the variation curve of the intermediate frequency signal and bit error rate over time caused by wavefront distortion. The random wavefront distortion caused by atmospheric turbulence reduces the energy concentration of the spot at the focal plane fiber end face, and the fluctuation in coupling efficiency leads to random fluctuations in the envelope of the intermediate frequency signal. The quality of the intermediate frequency signal determines the modulation effect, and the larger the peak value of the intermediate frequency signal, the higher the signal-to-noise ratio, and the lower the corresponding bit error rate. When the minimum amplitude of the intermediate frequency signal cannot satisfy the minimum demodulation level requirement, corresponding errors are generated, leading to unstable communication links and terminals. Therefore, it is necessary to perform real-time wavefront correction to improve communication system performance and establish link stability.

Figure 4. Impact of wavefront distortion caused by atmospheric turbulence on system performance. (a) Intermediate frequency signal, (b) error rate.

Considering the actual cost of the project (The high cost of InGaAs substrates presents a significant barrier to the adopting it in this project) and the accuracy of wavefront sensing detection (the accuracy of Haso4 FIRST is superior to that of Haso4 NIR), the wavefront of the signal light was corrected by wavefront sensing using a beacon light. Because of the different light source characteristics and wavelengths of the signal and beacon lights, the wavefront information that reaches the deformable mirror at the same time is also different when transmitted through random atmospheric media. If only the closed-loop operation of adaptive optics is implemented for the beacon light wavefront, it is not possible to correct the signal light wavefront accurately due to various errors between the communication branch and the wavefront sensing branch. Although the wavelengths of the two beams of light have a certain relationship, correction cannot be directly based on the proportional coefficient relationship between the two wavelengths owing to other factors, such as color and optical path differences [23]. When only closed-loop correction is applied to the beacon light, the coupled optical power output of the signal light is low, indicating that the wavefront distortion of the signal light cannot be adequately repaired. Therefore, it is necessary to integrate the optical power of the signal light and wavefront data of the beacon light to achieve a closed-loop adaptive optical system and improve the overall communication performance.

Figure 5 shows a wavefront-free sensing correction system using signal optical power as a feedback evaluation indicator. It consists of a deformable mirror, fiber coupling, optical power meter, and computer as a loop. The power meter was the RY-3200B (Chips Gate, Guangdong, China). The hill climbing algorithm, simulated annealing algorithm, and stochastic parallel gradient descent algorithm were used for the initialization iteration process [24]. Using the stochastic parallel gradient descent algorithm, the calculated voltage has a higher precision bit compared with other algorithms, and the calculated voltage is only an integer multiple of the gain. Thus, this algorithm yields higher accuracy in fitting the wavefront phase. When the coupling power of the signal light reached its maximum, the wavefront of the signal light was effectively corrected, and the reference wavefront corresponding to the beacon light at the current time was recorded.

Figure 5. Wavefront correction without wavefront sensing using (a) system blind optimization schematic diagram, (b) blind optimization iteration curve with hill climbing algorithm, (c) simulated annealing algorithm, and (d) stochastic parallel gradient descent algorithm.

If the instructions on the deformable mirror are maintained, the coupling efficiency will be significantly improved, but the wavefront disturbance caused by atmospheric turbulence will also cause fluctuations in coupling efficiency. Therefore, to improve coupling efficiency, further closed-loop operations are required to suppress the amplitude fluctuations of the intermediate frequency signal caused by the fluctuation of the coupling optical power as much as possible. Using the wavefront information collected by the wavefront sensor when the coupled optical power reached its maximum value as the reference wavefront, a proportional integral differential control algorithm was used to perform closed-loop control of the adaptive optical system [25]. Figure 6 shows the uncorrected (i.e., the instruction on the deformable mirror is 0) and closed-loop-corrected wavefront peak valley and root-mean-square values. The reconstructed wavefront was the actual collected wavefront minus the previously recorded reference wavefront [23].

Figure 6. The variation curves of the beacon light wavefront before and after correction: (a) The peak-to-valley (PV) values of the wavefront. (b) The root mean square (RMS) value of the wavefront.

For the corrected case, the mean wavefront peak-to-valley (PV) value is 7.76 μm, with a variance of 1.64 μm; The mean wavefront PV value is 1.64 μm, with a variance of 0.059 μm. For the corrected case, the mean wavefront PV value is 1.68 μm, and the variance is 8.3 × 10⁻² μm; The mean wavefront PV value is 0.31 μm, with a variance of 4.6 × 10⁻³ μm; Which indicates that the wavefront is effectively corrected while also effectively suppressing its volatility.

Figure 7 is the coupling power change curve with increasing iteration times. In Fig. 7, the stochastic parallel gradient descent algorithm can increase the coupling power from −30 dBm to about −17 dBm. When the deformable mirror maintains the surface shape that reaches the maximum power, although it can still maintain a high coupling optical power, compared with the adaptive optics closed-loop state, the fluctuation of the coupling efficiency due to the wavefront time change caused by atmospheric turbulence is greater than the adaptive optics closed-loop state. The purpose of adaptive optics wavefront correction for wireless optical coherent communication system is to improve the coupling efficiency while maintaining a more stable coupling power output.

Figure 7. Coupling power change curve with increasing iteration times.

Figure 8 shows the variation curve of the coupled optical power with respect to the number of iterations. In Fig. 8, it can be observed that the coupled optical power increased through correction from −44.49 dBm to −27.76 dBm. The coupling power was effectively corrected for both overall improvement and fluctuation characteristics. Consequently, the system’s isolation measures approximately 45 dB without correction, and 30 dB with correction.

Figure 8. Coupled optical power variation curve: (a) Adaptive optics uncorrected, (b) adaptive optics corrected.

Figure 9 shows the power spectral densities of the uncorrected (without frequency stabilization) and corrected intermediate frequency signals (with frequency stabilization). In Fig. 9, it can be seen that the spectral peak of the corrected intermediate frequency signal is sharper with a frequency of 120 MHz, and the power spectral density in the closed-loop situation has a gain of approximately 20 dB compared with the uncorrected carrier. The signal-to-noise ratio of the intermediate frequency signal was significantly improved, which is equivalent to improving the mixing efficiency of the backend coherent detection system. Meanwhile, the corrected intermediate frequency signal introduces excess harmonic components owing to the device characteristics of the balanced detector with high mixing efficiency.

Figure 9. Power spectral density of intermediate frequency signal: (a) Uncorrected by adaptive optics, (b) corrected by adaptive optics.

Based on frequency control, the intermediate frequency signal received by the coherent optical communication was demodulated according to the principle shown in Fig. 1. The analog-to-digital conversion module uses ADS5463EVM (Texas Instruments, TX, USA), the clock module uses TSW4806EVM (Texas Instruments), and the signal processing board uses TSW1400EVM (Texas Instruments) [26]. Figure 10 shows a schematic diagram of the decoding of the coherent detection baseband signals without and after correction. The results showed that the baseband signal had more burrs in the uncorrected case, whereas the baseband signal was more regular in the corrected case. Data acquisition, intermediate frequency carrier recovery, clock recovery, decoding, and network card reception were performed on either the I- or Q-channel of the intermediate frequency current to complete real-time online signal processing, recover the baseband signal, and achieve uninterrupted and smooth video playback under adaptive optics real-time correction.

Figure 10. Real-time transmission of baseband signal and video in the coherent detection system: (a) Uncorrected adaptive optics, (b) after adaptive optics correction.

By applying adaptive optics technology to wireless optical coherent communication systems, the correction process integrates the coupled optical power of the signal light and the wavefront data of the beacon light. The wavefront of the signal light was corrected using real-time correction of the wavefront of the beacon light. While improving and stabilizing the coupling power, smooth and uninterrupted video transmission of the entire optical communication system can be maintained. The implementation of the scheme effectively corrects the wavefront of the unmeasured signal light, improves the overall communication performance, and reduces the application cost of adaptive optics in wireless optical coherent communication systems.

The authors would like to thank Jiali Wu for suggestions with writing process. We would also like to express our sincere gratitude to the anonymous reviewers for their valuable feedback.

The National Natural Science Foundation of China (Grant No. 61377080); Henan University of Technology Doctoral Initiation Fund (Grant No. 31401616); The Innovative Funds Plan of Henan University of Technology (Grant No. 2022ZKCJ13).

The authors declare no conflicts of interest.

The data that support the findings of this study are available from the corresponding author upon reasonable request.