## 1 Introduction
The MC method is mainly concentrated on the fields of wireless optical communication, underwater target detection and remote sensing, of which, research into light transmission in optical communication is the earliest, dating back to the 1960s [20]. In recent years, [PERSON] proposed a more general random channel model for turbid seawater, and based on the model, the path loss and impulse response of the channel were evaluated [21]. In 2017, [PERSON] quantified the received power loss and channel dispersion for different water types, transmission distances, divergence angles and receiving angles based on different scattering phase function models, and affirmed the accuracy and stability of the SS phase function [22]. In 2020, [PERSON] illustrated and improved the convergence of the MC integration model by introducing different sampling methods. The MC integration model based on partial importance sampling has higher computational efficiency in high-order scattering scenarios [23]. However, the research into underwater target detection based on the MC method started relatively late. On the basis of [PERSON]'s research [24], in 2005, the first systematic research into underwater target detection was carried out using standard MC; three different MC programs were proposed that keep track of the status of polarization after every scattering event were described. Based on the research of polarization, a backscattered light coherence investigation was added, an electric field MC (EMC) approach for directly simulating coherent backscattering (CBS) of coherent or partially coherent polarized light was proposed by [PERSON] [25]. To further improve the EMC model, a transmission matrix-based electric field MC (TEMC) method was introduced to study the propagation characteristics of Bessel beams with different orbital angular momentum (OAM) in turbid media in which beam transmission patterns, intensity attenuation, and the degree of polarization (DOP) through turbid media of varying thickness were analyzed [26].Based on a semi-analytic MC technique, in 2019, [PERSON] built an MC model to simulate Lidar signals based on the simultaneous inherent in situ optical properties of seawater. The Lidar measurements and the MC simulation can provide both the Lidar signals and the retrieved Lidar attenuation coefficient \(\alpha\). In 2020, [PERSON] proposed an Oceanic Lidar Emulator (OLE), which is an improved semi-analytic MC-based Lidar simulator with the capability of dealing with the physics of light propagating through a wind-driven rough air-sea interface and into the ocean, being scattered by subsurface phytoplankton and reflected from the sea bottom, and returning to the Lidar receiver. As an important part of underwater detection, the reflection characteristic of the target is a very key factor affecting the quality of detection and imaging. To describe the underwater imaging process more accurately, with the basic principle of MC simulation, it is an effective method to organically combine BRDF based on the microsurface principle. Some scholars have carried out related research work; in 2006, [PERSON] designed the random process between photons and crop canopy, using field measured BRDF data to validate MC model. The results showed that the simulated BRDF with MC model was in good accordance with the field data [27]. In 2015, [PERSON] proposed a wetland aquatic vegetation canopy BRDF-MC model, which involved determining track photon value, and performing an aquatic vegetation total weight calculating process corresponding to track the photon value. The method enabled the realization of the cap layer structure parameter-obtaining process and the BRDF-MC model-establishing process in a precise manner [28]. Recently, model-optimization algorithms based on the two theories have been successively proposed and applied in the fields of radiation uncertainty classification [29] and 3D canopy modeling [30].