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Abstract
The performance of the underwater optical communication (UWOC) systems was primarily limited by the low optical transmission efficiency due to the beam divergence and water interference. It has been proved in our previous works that holographic beam shaping can effectively increase the optical transmission efficiency and therefore the communication distances and speed. The conventional hologram optimisation method treated each pixel as an independent variable, leading to a large search space and a slow process. In this work, we proposed to use a small set of parameters to describe the beam shaping holograms that were able to limit the beam divergence and compensate for the wavefront distortion. This significantly reduced the number of variables to be optimised and enabled the optimisation to be more efficient and effective. In a proof-of-concept experiment based on the off-the-shelf components, the proposed method was able to generate the optimal hologram within 20 iterations while achieving a tenfold increase in the optical transmission efficiency for a 30 m link at 100 Mbps.
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1. Introduction
Underwater wireless communication plays a pivotal role in the ocean exploration [1,2]. Existing underwater wireless communication systems are mainly based on acoustic [3], radio-frequency [4] and optical [5] technologies. Acoustic communication [6,7] is the mainstream option due to its long transmission distance (>1 km) and relatively good tolerance to the turbulence. However, its data rate is limited to ∼kbps [8]. This has become the main obstacle for many modern sensing and imaging technology to be deployed in the underwater environment [9]. In contrast, the radio-frequency (RF) communication can achieve much higher data rates [10]. Due to the high propagation loss, however, RF technology can only support underwater wireless communication within a few meters [11]. Underwater wireless optical communication (UWOC) has become an active area of research lately due to its potential to achieve high data rates at moderate distances [12,13]. In addition, the latency of the underwater optical links is also extremely low since the signal travels at light speed [14].
A typical UWOC link consists of an optical transmitter, a transmission channel, and an optical receiver [15]. At the transmitter side, the central wavelength of the light source usually lies between 400 nm to 550 nm [16,17], which corresponds to the low attenuation window of the ocean water [18]. This helps to maximise the transmission efficiency of the optical power in the water. Both laser diodes (LDs) [16,19,20] and light-emitting diodes (LEDs) [17,21,22] can be used as light sources for UWOC. While the LDs normally enjoy higher modulation bandwidth [23,24], the output power of LEDs can be much higher. The pulsed lasers [25] can deliver extremely high peak intensity that is useful for long-distance underwater communication links. On the other hand, the emergence of the micro-LED technology could potentially increase the modulation bandwidth of LEDs [26]. At the receiver side, the photodetectors need to be very sensitive given the low level of the received optical power [27]. However, the background noise can become an issue for the most sensitive photodetectors. The photodetectors used in the previous UWOC demonstrations include PIN photodiodes [28,19], avalanche photodiodes (APDs) [29], single-photon avalanche diodes (SPADs) [27] and photomultipliers (PMTs) [30,31]. The coding scheme is a critical part of any communication system with high level of loss and noise. Majority of the UWOC demonstrations used on-off keying (OOK) due to its simplicity [32,33]. It has demonstrated that orthogonal frequency-division multiplexing (OFDM) scheme was able to increase the spectrum utilization to achieve significantly higher data rate [34,35]. Multiple inputs and multiple outputs (MIMO) scheme was also very effective in further improving the overall performance of the UWOC systems [36]. Equalizer was proposed to alleviate nonlinear impairments and inter-symbol interference for the performance enhancement in UWOC systems [37]. Adaptive optical system was experimentally demonstrated to increase the optical dynamic range for highly sensitive UWOC links [38]. Adaptive optics for UWOC can even carry OAM modes through oceanic turbulence by using a phase retrieval algorithm or neural network [39,40].
The high propagation loss of the optical beams in the water is still the main obstacle for the distance of UWOC links to be increased beyond 150 m even under the most pristine water conditions [41]. In the presence of the turbulence and water pollution, the distance and speed of the UWOC links will be reduced significantly [42]. The propagation loss is primarily caused by the water absorption and divergence of the optical beam. While the attenuation coefficient of the water channel cannot be improved in practice, it has been demonstrated in the previous works that the holographic beam shaping technique can be used to limit the divergence of the optical beam and allow a significantly higher portion of the optical energy to be captured by the photodetector [43]. For the speckle problem caused by holographic modulation, a speckle reduction solution [44] has also been proposed to enhance the modulation performance. As a result, both the transmission distance and data rates can be improved. In addition, the holographic technique can also compensate for the optical aberrations to further improve the quality of the communication links. The optimisation of the beam shaping holograms plays a key role in maximising the transmission distance and data rates. However, each hologram consists of tens of thousands of pixels. The conventional hologram optimisation process treats each pixel as an independent variable [45–47]. This results in an extremely large search space for the optimal hologram and makes the optimisation process slow and ineffective.
In this work, we proposed a novel method to describe the beam shaping holograms by a small set of parameters. The parameterised holograms were able to limit the beam divergence and the wavefront distortion caused by the water channel. This significantly reduced the number of variables to be optimised, leading to a faster and more effective optimisation process. In a proof-of-concept experiment, we demonstrated that the proposed method was able to significantly enhance the communication quality over a 30 m underwater optical link at a data rate of 100 Mbps. We expect that both the link distance and data rate can be further improved with purpose-built components.
2. System design
Figure 1 shows the experimental setup of our UWOC testbed. At the transmitter end, a pseudo-random binary sequence (PRBS) was utilised as a standard test signal of communication performance. It was processed offline for PAM4 mapping and carrier frequency modulation. An arbitrary waveform generator (AWG, PicoScope 5242D) was used to convert the processed signal to the laser, via the bias-T. A 450nm pigtailed single-mode laser diode (Thorlabs LP450-SF15) was selected as the light source. As mentioned in the above, this corresponded to the low attenuation window of the water channel. The laser driver provided a constant DC current of 45 mA to the laser diode to produce an output power of ∼8 mW. A fibre-coupled collimator (Thorlabs F671FC-405) was used to slow the divergence of the launched laser beam. The wavefront of the collimated beam was spatially modulated by a phase-only liquid crystal on a silicon (LCOS) device (CamOptics SP55). The LCOS device has a resolution of 1920*1080 with pixel pitch of 6.4 um. Subsequently, the laser beam passed through a Fourier lens (L1) to generate the desired beam shape. A beam expansion system (L2: f=100mm, L3: f=500mm) was used to further enlarge the shaped beam before it was launched into the underwater channel. Our previous work has shown this beam expansion system was able to effectively enhance the optimal transmission distance without increasing the spatial frequency of the holograms displayed on the LCOS device. A 5-meter water tank was used as the underwater optical channel. Mirrors were placed at both ends of the water tank to achieve longer distances transmission tests. The attenuation coefficient of the water channel in this work was measured to be 0.22.
At the receiver end, the received light was split into two paths by a beam splitter (BS). Part of the light was fed into an avalanche photodiode (APD, Thorlabs APD430A2/M) with a responsivity of 32 A/W at 450 nm when operating with a M factor of 100. The output of APD was acquired by an oscilloscope (Keysight DSOX4054A) for offline signal processes. The rest of the light at the receiver end illuminated a camera for the inspection of the beam quality. It should be noted that the use of the BS and camera in this setup was purely for the monitoring purpose in this study. The information captured by the camera was not used in our optimisation process. In the practical applications, both the BS and the camera can be removed.
During the real-time optimisation process, the received optical power by the APD was used as the merit function. Based on this feedback, the beam shaping holograms displayed on the LCOS device will be automatically updated following the optimisation algorithm. Detailed information about the parameterisation of the beam shaping holograms and the optimisation algorithm will be given in the next section.
3. Optimisation principle
A desired beam shape would be able to have a minimum divergence over the transmission distance and resistant to the wavefront distortion caused by the transmission medium. Two types of parameters were used to parameterise the beam shaping holograms in this work. The first type was based on the biconic Fresnel lens. The phase function of the Fresnel biconic lens can be described by the following equation
Fig. 2. Beam shaping hologram based on the (a) biconic Fresnel lens modulation, (b) Zernike polynomial modulation and (c) with additional Zernike modulation.
The second type of parameters used to describe the beam shaping holograms were based on the Zernike polynomials. They can be represented by Eq. (2)
where ai (i=1∼15) were the coefficients of the Zernike function (Zi). These Zernike coefficients were expected to compensate for the low-order aberrations in weakly scattering media [48]. Figure 2(b) showed a phase hologram randomly generated using the Zernike polynomials. Figure 2(c) showed an updated hologram when the Zernike polynomial Fig. 2(b) was added to Fig. 2(a).The biconic Fresnel lens parameters were expected to limit the beam divergence over long-distance while the Zernike parameters were expected to compensate for the wavefront distortion and scattering caused by the water channel. The rotation of the biconic Fresnel lens and Zernike components also compensated for the asymmetry of the transmission channel.
After the parameterisation of the beam shaping holograms, the number of variables to be optimised was reduced from above hundreds to 18 when both biconic Fresnel lens modulation and Zernike modulation were applied. When only the biconic Fresnel lens modulation was used, the number of parameters was reduced to as low as 3. This significantly reduces the search space and the complexity required for the optimisation algorithm.
In this work, the simulated annealing (SA) algorithm was used for the rapid generation of the beam shaping holograms. Figure 3 shows the general flow chart of the SA algorithm. The X represents a specific set of parameters $X = ({{a_1},{a_2}, \ldots {a_N}} )$, corresponding to a specific hologram. The value of the subscript N depends on the control parameters of the hologram, in our work N=3 for conic Fresnel and N=15 for Zernike polynomial. The F represents the optimization function value, that is, the measured power value of the beam at the receiving end after the beam is modulated by the corresponding hologram.
The initial parameter set, Xold, was randomly generated. The corresponding merit function, Fold, was based on the optical power received by the APD detector. The perturbation ΔX is randomly generated. During each iteration, a perturbation ΔX will be added to the existing parameter set Xold. The performance of the new set of parameters, Xnew, will be evaluated. If the performance was improved, Xnew would be accepted as the existing parameter set for the next iteration. Otherwise, the acceptance depends on the Metropolis criterium [49], i.e. the Boltzmann probability function
It should be noted that other advanced optimisation algorithms can be used, which may lead to a more efficient optimisation process with even better performance. However, this work focused on the parameterisation of the holograms, which was compatible with any optimisation algorithms.
4. Experimental results
In this work, the holographic beam shaping was carried out for UWOC links at 5 m, 10 m, 15 m, 20 m, 25 m, and 30 m respectively. At each link distance, we captured the beam profiles at three different configurations. The first configuration without the phase modulation was used as the benchmark for the comparison. In the second configuration, only the biconic Fresnel modulation was applied on the launched optical beam. In this case, only the beam divergence was limited. In the third configuration, both the biconic Fresnel modulation and the Zernike modulation were applied. During the optimisation process, the algorithm required no knowledge of the link distance. Figure 4 shows the optimised beam holograms and the corresponding beam profiles at the receiver end for each configuration at each link distance. For a fair and clear comparison, the camera settings, i.e. the exposure time and gain, were kept the same between different measurements. It can be seen that the beam intensity at the centre was elevated effectively after the application of our beam shaping method. The additional Zernike modulation was able to further concentrate the energy at the receiver end.
Figure 5 showed the progression of the optimisation algorithm for the 20 m UWOC link when both the biconic Fresnel lens modulation and Zernike modulation were applied. As mentioned in the above, the unit of the merit function values corresponded to one quantised output level of the photodetector used in this work. It can be seen that the algorithm successfully converged to an optimal setting after about 15 cooling iterations. During this typical optimisation process, the algorithm tested 25 sets of parameters in each cooling iteration. Each test took ∼150 ms, which was primarily limited by the response time of the LCOS device used in this work. Therefore, the 15 cooling iterations shown in Fig. 5 tested 375 holograms and took less than 1 minutes. This is significantly faster than the previous works [42–45], which required to tested thousands of holograms. The improvement of the optimisation speed is mainly due to parameterisation of the holograms, which reduced the number of optimisation variables from >100 to fewer than 20. Again, more advanced optimisation algorithms can be used to further speed up the process.
Figure 6 showed the beam energy at different distance without the modulation, with the biconic Fresnel lens and both biconic Fresnel lens and Zernike parameters respectively. The beam energy is measured by a power meter (S120VC, Thorlabs) with an active area of 9.7mm *9.7mm. It can be seen that the holographic beam shaping can significantly increase the energy of the beam. After the beam shaping, the received energy is increased by tenfold. Particularly, the gain is up to 15x at 10 meters. The coupling efficiency of the power meter is higher than that of the APD due to the larger active area, so Fig. 6 shows a significantly higher power enhancement than Fig. 5.
Subsequently, the laser diode was modulated with the PAM4 format at 100Mbps. Figure 7 showed the eye diagrams captured at 20 m. Without the beam shaping Fig. 7(a), the eye diagram can be barely distinguished. After the beam shaping was applied Fig. 7(b-c), the amplitude of the received signal was increased significantly. This was consistent with the camera inspection shown in Fig. 4. These results further confirmed that our methods were able to reduce loss in the transmission process and increase the power of the receiver.
Fig. 7. Eye diagrams at 20 meters, (a) without modulation, (b) with biconic Fresnel lens modulation and (c) with both biconic Fresnel lens and additional Zernike modulation.
The bit error rates (BER) were measured at different transmission distances and system configurations. The results were shown in Fig. 8. It can be seen that the beam shaping was able to effectively improve the link quality in all the transmission distances. The Zernike modulation was able to bring additional performance enhancement, particularly at short range. It can be interpreted that the beam divergence was the predominant factor for the performance of long-distance UWOC links. At longer distances, the improvement in beam shaping was less effective. This is primarily due to the spatial resolution of the LCOS device. However, it is possible to increase the transmission distance of the same beam shaping holograms by optimising the optical setup shown in Fig. 1, e.g. increasing the launched beam sizes to the LCOS device or the magnification ratio of the relay systems.
5. Conclusion
In this work, we proposed a novel method to describe the complex beam shaping holograms for the UWOC applications by a small set of parameters based on the biconic Fresnel lens and Zernike coefficients. This significantly reduced the optimisation dimensions for the beam shaping holograms from hundreds of thousands to no more than 18. This enabled a rapid and effective generation of the beam shaping holograms for different link distances. The generated holograms were able to limit the beam divergence and compensate for the wavefront distortion by the water channel. This led to an increase in the transmission efficiency of the optical energy. As a result, the performance of the UWOC links was significantly enhanced.
In a proof-of-concept experiment, we demonstrated a 30m/100Mbps PAM4 underwater optical link in the Jerlov II water condition. Our optimisation process based on the parameterised beam shaping holograms was able to reach the optimal hologram within fewer than 15 iterations. The optical power received by the APD detector was increased by 10x while the BER was reduced by about half after optimisation. In the current experimental environment, the biconic Fresnel modulation was significantly more effective than the Zernike modulations. Therefore, the beam divergence was the predominant factor for the system performance. However, it is also possible that the optical distortion caused by the water was too random to handle. Further works in different water conditions are required to reach a definitive answer.
It is worth noting that this work was carried out with off-the-shelf components. Particularly, the output power of the LD was only ∼8 mW. However, the proposed method was compatible with any types of light sources, photodetectors and data coding schemes. With purpose-built components, the link distance and data rates of our demonstration can be significantly improved in the future.
Funding
Natural Science Foundation of Jiangsu Province (BK20200351); National Natural Science Foundation of China (62105059).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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