## 4 Monte Carlo Simulation
### MC Techniques for Photon Propagation in Turbid Medium  
The MCS and Photon-Tracing Algorithm (PTA), which rely on randomised trials and geometric optics, respectively, are combined to create the Monte Carlo Ray-Tracing (MCRT) method [134]. In this section, MCS methods for the movement of photons in a seawater medium will be discussed. Four MC approaches are discussed in this section. These approaches use the same statistical criteria to calculate the photon travel path following a scattering event. Generally, as explained in the MCS Framework subsection, the underlying formulations of MCSs are based on well-defined PDFs and the associated CDF for the framework elements [73]. These methods are for photon migration in turbid media, which are the albedo weight-based (AW) method, the albedo-rejection (AR) method, the absorption-scattering path  
Figure 12: Typical optical receiver layout [50]. length rejection (ASPR) method, and the microscopic Beer-Lambert's Law (mBLL) method; Figure 13 displays them. The AW approach examines a system generating numerous photon groups, and then a proportion of these photons are lost by absorption after each collision. The photon group starts to release an original weight equal to one. After every collision, the present weight will be multiplied via the albedo to consider the lack of absorbed photons, and the group keeps travelling in the dispersed direction with a lower weight. This approach has the advantage of not wasting calculations since all photon packets finally reach the detector. Many research publications [135; 136] supported this method. The ASPR takes two random integers evenly distributed in \((0,1)\). Furthermore, as with the AW method, the paths preferred via recorded photons in the ASPR and AR techniques rely on the distribution of the medium's scattering and absorption coefficients [137; 15; 138]. We may examine the problem of photon transmission using the mBLL by considering the non-absorbing media and then using the weight factor [138; 15]. This indicates that recorded photons will select the same paths independently of the distribution of the medium's absorption coefficient, and the weight factor given to all those paths varies according to the equation provided in [15]. Also, it contains all the mathematical formulas for determining path lengths and assigning weight factors for the previous MC approaches. The authors also offered theoretical justifications and numerical evidence demonstrating the statistical equivalence of the four techniques. In [66], the authors provided a simulation based on the AR approach. The primary benefit of this technology would be that it simulates what naturally occurs by following every single photon produced via a system. As expected, the absorbed photons' computing time will be lost throughout this scenario. According to [PERSON] et al. 's research [15], the overall probability of receiving a photon is comparable across all MC approaches. Moreover, these approaches are statistically equivalent, having slight changes related to the convergence time. Comparing the AW method to the AR method reveals that the AR method will require more released photons for convergence in most cases. The photon in the AR method is detected or lost in the same way that photons are observed in a time-resolved study utilising the time-dependent individual photon count method. At the same time, the noise on the simulated response replicates the Poisson statistics, which generally describes noise through experimental tests. Therefore, the AR approach physically simulates transmission better than the AW approach, in which the simulated photons are energetic groups of photons instead of real photons. Light transmission is a collection of simulated photons using the MC method. Every photon's position, weight, and direction are used to distinguish it. When the photon is released, it travels regularly until it is absorbed or hits the receiver. That procedure continues until the receiver records an appropriate number of photons.