## 1 Introduction  
Nowadays, underwater activities are becoming more and more important. These underwater activities include sea exploration, underwater surveillance, monitoring, rescue, etc. Communication in underwater environments is crucial. One communication approach is to use electrical or optical cables; however, their transmission distance and flexibility are limited. Another approach is to use wireless communication via radio-frequency (RF) transmission [1]; however, radio waves have high attenuation during transmission through water. Acoustic waves can also be used in underwater communication, and they have a much lower absorption than RF transmission in water [2]. However, acoustic communication has limited transmission bandwidth and high latency [3]. In order to provide communication between autonomous underwater vehicles (AUVs), divers or sensor nodes, visible light communication (VLC) [4; 5; 6; 7; 8; 9; 10] can be used to provide underwater wireless optical communication (UWOC). VLC is one implementation of optical wireless communication (OWC) [11; 12] using the visible optical spectrum to carry data, and it is also considered as a potential candidate for future 6G networks [13; 14]. UWOC can provide high-bandwidth and high-flexibility underwater communication [15; 16; 17; 18; 19]. Apart from communication under water, direct communication between the water-air interface is also highly desirable [20; 21; 22; 23]. Air-to-water wireless transmission is crucial for sending control information or instructions from unmanned aerial vehicles (UAVs) or ground stations above the sea surface to AUVs. On the other hand, water-to-air wireless transmission is also required to transmit real-time information from AUVs or sensor nodes to UAVs above the water surface. This scenario is illustrated in Figure 1, in which communications between UAVs and AUVs across the water-air interface is implemented by VLC. As VLC also supports wide fields-of-view (FOV), several AUVs can receive signals from a single UAV. The system also supports network scalability. The data received by a UAV can be repeated and retransmitted to neighbor UAVs, which in turn retransmit to ground stations via VLC, infrared (IR) or RF links. Although water-air communication offers many advantages, water-air VLC transmission presents many challenges, such as water absorption and turbulence. Previously, we successfully demonstrated a water-to-air optical camera-based OWC system [23], which is also known as optical camera communication (OCC) [24; 25]; however, the reverse transmission (i.e., air-to-water) using OCC has not been analyzed. It is worth noting that for the prior water-to-air OCC system, since the camera is located in the air, the image of the light source would be magnified due to diffraction. Hence, the pixel-per-symbol (PPS) decoding in the OCC pattern would be easier. In the proposed air-to-water OCC system reported here, since the camera is located in the water, the image of the light source in the air will be  
Figure 1: Scenario of communications between UAVs and AUVs across the water–air interface implemented by VLC. The data received by the UAV can be repeated and retransmitted to neighbor UAVs, which in turn retransmit to ground stations via VLC, infrared (IR) or RF links. AUV: autonomous underwater vehicle; UAV: unmanned aerial vehicle. diminished due to diffraction. Hence, the PPS decoding in the OCC pattern will be more difficult. According to our analysis, when viewing a light source in water from air (i.e., the prior water-to-air OCC system), assuming the distance between the light source and the water-air interface is \(h\), the light source image appears shallower by \(\sim\)0.75\(h\) and magnified. However, when viewing the light source in air from water (i.e., the present air-to-water OCC system), also assuming the distance between the light source and the water-air interface is \(h\), the light source image appears further away by \(\sim\)1.33\(h\) and diminished. For the OCC system, the distance would affect PPS decoding.