## 3 Analysis of the Scattering Phenomenon in Underground Mines and Distribution of Dust Particles
### Atmospheric and Dust Particles Scattering and Absorption Parameters in UM  
The distribution and concentration of dust particles suspended in mining tunnels have a strong impact on the propagation of the optical signal and, consequently, on the performance of the VLC system. In general, dust particles can generate two phenomena: (a) absorption of light when dust particles combine with water vapors and the light beam hits them, (b) scattering of light when dust particles consist only of coal or other organic matter and the light beam hits them. Both events can generate severe attenuation of the optical link. Therefore, the relationship between the intensity of the incident light and the intensity of the transmitted light, which can be considered as the intensity attenuation, can be expressed as follows  
\[I_{R}=I_{T}(\alpha_{T},\beta_{T})\exp\left(-\frac{1.5 CLK_{e}}{d}\right), \tag{3}\]  
where \(C\) is the number of suspended particles in the unit volume, also called dust particle concentration, \(\alpha_{T}\) and \(\beta_{T}\) represent the rotation and tilt angles of the LED respectively, \(L\) is the light path, \(d\) denotes the Euclidean distance between the LED and PD, and \(K_{e}\) is the light attenuation coefficient, which is represented with the expression \(K_{e}=k_{sca}+k_{abs}\), being \(k_{sca}\) the scattering coefficient and \(k_{abs}\) the absorption coefficient. Furthermore, \(C\) is a dynamic parameter that can be modeled as an exponential function in terms of the visibility of the UM environment (\(V\)) under the expression \(C=4050V^{-1.016}\). If we consider the basic theory of light atmospheric transmission, \(k_{sca}\) and \(k_{abs}\) allow us to determine the average distance that a photon travels before being scattered or absorbed, respectively. This consideration can be applied to mining tunnels since dust particles can be assumed as aerosols of various sizes. Under this context, the effect of scattering and absorption produced by the interaction of light with dust particles can be modeled under the paradigms of the Rayleigh and Mie theory, respectively [18; 19]. Therefore, \(k_{sca}\) and \(k_{abs}\) are the sum of molecule and aerosol scattering and absorption coefficients, represented as  
\[k_{sca}=k_{sca}^{Ray}+k_{sca}^{Mie}, \tag{4}\]  
\[k_{abs}=k_{abs}^{Ray}+k_{abs}^{Mie}, \tag{5}\]  
where \(k_{sca}^{Ray}\) and \(k_{sca}^{Mie}\) represent the Rayleigh and Mie scattering coefficients respectively, and \(k_{abs}^{Ray}\) and \(k_{abs}^{Mie}\) are the Rayleigh and Mie absorption coefficients respectively. Since the composition of air molecules and dust particles is relatively constant in low-altitude UM areas, \(k_{sca}^{Ray}\) is given by  
\[k_{sca}^{Ray}=\frac{(m_{s}^{2}-1)^{2}(6+3\delta)24\pi^{3}}{(m_{s}^{2}+2)^{2}( 6-7\delta)\lambda^{4}N_{s}}, \tag{6}\]  
where \(N_{s}\) is the molecular number density for air in UM, \(\lambda\) is the wavelength of the transmitted light beam, \(\delta\) is the depolarization factor, and \(m_{s}\) is the refractive index, which at the level of the mining tunnels is expressed as  
\[(m_{s}^{2}-1)\times 10^{8}=8060.51+\frac{2,\!480,\!990}{132.274-\lambda^{-2}}+ \frac{17,\!455.7}{39.32957-\lambda^{-2}}. \tag{7}\]  
On the other hand, \(k_{abs}^{Ray}\) is a combination of different types of light absorption produced by gases such as O\({}_{2}\), O\({}_{3}\), CO\({}_{2}\), among others, which are typical in UM environments. The absorption of light produced by these gases at different wavelengths can be represented through the Atmospheric Radiation Transport Model (MODTRAN), as shown in [27].