# Extending UWOC System Applications through Photon Transmission Dynamics Study in Harbor Waters
## 2 Materials and Methods
### Selection of Appropriate Scattering Phase Function  
The transmission dynamics of photons in underwater channels are illustrated in Figures 1-3. \(\varphi_{0}\) and \(\psi_{0}\) represent the initial elevation angle and azimuth angle in Figures 1 and 2, respectively. It is important to note that the fixed z-axis is always perpendicular to the Reception Plane. Photons emitted from the light source undergo multiple scatterings by particles within the water, following various trajectories. Some of these photons, termed 'On-target photons', reach the photosensitive surface of the receiver and are absorbed, as shown by the blue line. Others, known as 'Off-target photons', deviate from the receiver's aperture and FOV after multiple scatterings shown by the green line, as depicted in Figure 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Harbor** & & & & \\
**Water Types** & _a (m\({}^{-1}\))_ & _b (m\({}^{-1}\))_ & _c (m\({}^{-1}\))_ & _\(\omega_{0}\)_ \\ \hline Harbor-I & 0.187 & 0.913 & 1.10 & 0.83 \\ Harbor-II & 0.374 & 1.826 & 2.20 & 0.83 \\ Harbor-III & 0.561 & 2.739 & 3.30 & 0.83 \\ Harbor-IV & 0.748 & 3.652 & 4.40 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The optical parameters of four types of Harbor water [44]. Figure 1: Schematic diagram of On-target photon and Off-target photon in underwater channel. Figure 2 illustrates the multiple scattering events that a photon emitted from the light source undergoes before reaching the Reception Plane. The initial elevation angle and azimuth angle, denoted as \(\varphi_{0}\) and \(\psi_{0}\), respectively, correspond to those presented in Figure 1. The angle \(\varphi_{1}\), \(\varphi_{2}\), \(\ldots\varphi_{n}\) represent the scattering angles of the photon at each event, while \(\psi_{1}\),\(\psi_{2}\), \(\ldots\psi_{n}\) denote the azimuth angles associated with these events, with \(n\) indicating the \(n\)-th photon scattering occurrence. A notable feature in this figure is the gray dotted lines, which depict the photon's motion coordinate system. This system undergoes continuous transformations with each scattering event, reflecting the dynamic nature of the photon's path. The specifics of how this coordinate system is determined by the Equation (14). Additionally, it is important to highlight that the x, y, and z axes shown in Figure 2 are part of a fixed coordinate system. This system is established by the positioning of the transmitter and receiver, providing a stable reference frame for understanding the photon's motion and scattering behavior. Additionally, the interaction between seawater particles and photons results in two distinct types of light: Forward-scattering light and Backscattering light [21; 36], as shown in Figure 3. In the simulation process, the receiver is positioned on the z-axis. The distance between the Transmission Plane and the Reception Plane is governed by a variable known as the attenuation length. The Transmission Plane lies within the x-y plane and is parallel to the Reception Plane, maintaining no angle of declination. This configuration ensures that both the Transmission Plane and Reception Plane are perpendicular to the z-axis, as depicted in Figure 3. This perpendicular arrangement is crucial for accurately simulating the propagation of light or signals in the system and analyzing their interactions with various environmental factors. Figure 3: Forward-scattering light and Backscattering light in underwater channel. Figure 2: Photon motion coordinate systems in underwater channel. In underwater environments, the scattering direction of a photon post-collision with seawater particles is generally random. To evaluate the distribution of light energy following such scatterings, the volume scattering phase function is employed [44; 45].