# Study of Sea Fog Environment Polarization Transmission Characteristics
## 2 The Physical Attributes of a Complicated Environment such as Marine Fog
### Fundamental Method for Polarization Transmission in Marine Environments  
In a sea fog environment, polarized light collides with particles of sea fog during transmission, resulting in refraction, absorption, and scattering, which significantly reduces the polarization intensity of polarized light. If the diffuse reflection induced by multiple scattering is disregarded, the intensity change law of light radiation can be written directly as [13]:  
\[\frac{dI_{\lambda}}{k_{\lambda}\rho d_{s}}=-1 \tag{6}\]  
According to Equation (6), the incident wavelength is \(\lambda\). The intensity of the radiation (\(I_{\lambda}\)), the coefficient of extinction cross-section (\(k_{\lambda}\)), the thickness of the medium during transmission (s), and the density between particles (\(\rho\)) are required. When \(s=0\), \(I_{\lambda}(0)\) represents the initial light wave radiation intensity of incoming light. When \(s_{1}\
eq 0\), it shows the intensity of light wave radiation after transmission through a medium of thickness \(s_{1}\).  
\[I_{\lambda}(s_{1})=I_{\lambda}(0)exp(-\int_{0}^{s_{1}}k_{\lambda}\rho d_{s}) \tag{7}\]  
If the transmission medium is spread evenly, the extinction section coefficient \(k_{\lambda}\) is independent of distance \(s_{l}\), and the transmission route length can be calculated as follows:  
\[\mu=\int_{0}^{s_{1}}\rho d_{s} \tag{8}\]  
Introducing Formula (8) into Formula (7), the relationship between incoming radiation intensity and emitted radiation intensity is as follows:  
\[I_{\lambda}(s_{1})=I_{\lambda}(0)exp(-k_{\lambda}\mu) \tag{9}\]  
In a homogeneous medium environment, the intensity attenuation of the radiation transmission of light waves follows an exponential distribution, and the exponential independent variable is the product of the extinction coefficient and the path, as determined by the preceding Formula (9). This is [PERSON]'s law.  
Currently, most radiative transfer models in the United States and overseas alter their parameters in the vertical direction, and there is no examination of horizontal atmospheric parameters. According to their physical definitions, the horizontal optical characteristics and radiation intensity of the atmosphere are the same in all models. If \(Z\) is used to denote the longitudinal space distance, the atmospheric radiative transfer equation can be expressed more generally as follows:  
\[\cos(\theta)\frac{dI(z;\theta,\varphi)}{k\rho dz}=-I(z;\theta,\varphi)+J(z; \theta,\varphi) \tag{10}\]where \(\theta\) represents the zenith angle, \(\varphi\) represents the azimuth, and \(J\) represents the source function. Similarly, if we want to address the multiple scattering of light in an environment of sea fog, we must incorporate the atmospheric optical thickness of light transmission in the vertical direction:  
\[\tau=\int_{z}^{\infty}k\rho dz \tag{11}\]  
The fundamental equation of radiation transmission based on the multiple scattering issue under the premise that the earth's atmospheric plane is parallel is derived by the calculation:  
\[\mu\frac{dI(z;\theta,\varphi)}{d\tau}=-I(z;\theta,\varphi)+J(z;\theta,\varphi) \tag{12}\]  
In Equation (12), \(\mu\) represents the cosine of zenith angle \(\theta\).