## 2 Materials and Methods
### Monte Carlo Simulation
The absorption coefficient for such conditions (i.e., for the selected wavelength and refractive index) will be negligible according to [52]. Thus, no absorption will appear, and we do not have to track whether a particular photon should be excluded from the simulation. The concentration value, or a number of spheres per cubic millimeter, of the scattering suspension was varied approximately from \(10^{5}\) to \(10^{6}\) mm\({}^{-3}\). In order to define the trajectory of the photon, three key parameters have to be calculated. First, free path length \(l\)--the distance between two scattering events or between two sequential interactions between the photon and a particle (Equation (2)). Second, scattering angle \(\theta\)--the angle between the current and the new direction of photon's propagation (Equation (3)). Third, azimuthal angle \(\varphi\)--the angle between the projection of the new direction on the plane perpendicular to the initial direction of the photon's propagation (Equation (4)). \[l=-\ln(\xi_{l})/\mu_{s}, \tag{2}\]\[\cos\theta= \begin{cases}\frac{1}{2g}\cdot\left[1+g^{2}-\left(\frac{1-g^{2}}{1-g^{ +}2g\xi_{\theta}}\right)^{2}\right],\text{ if }g>0\\ 2\xi_{\theta}-1,\text{ if }g=0\end{cases} , \tag{3}\]  
\[\varphi=2\pi\xi_{\varphi\sigma}, \tag{4}\]  
where \(\xi_{l},\xi_{\theta},\xi_{\varphi}\)--random numbers uniformly distributed within the interval [0, 1), \(\mu_{s}\)--scattering coefficient, \(g\)--anisotropy factor. The direction of photon after a scattering event is defined by scattering diagram or phase function [53; 54]. The phase function is a function of the probability density of scattering in the direction s' of a photon moving in the direction s, i.e., a function that characterizes the elementary act of scattering. In other words, the phase function describes the angular distribution of the intensity of light scattered by an elementary volume. The shape of the scattering diagram depends on the wavelength of the incident radiation, the size of the scatterer, and the relative refractive index [55]. The phase function is also characterized by the mean cosine of the scattering angle g, or the so-called anisotropy factor [56]. Anisotropy factor g shows the degree of isotropy of scattering process. If particle scatters light equally in all directions, then \(g=0\); if a particle scatters more energy in the forward direction, then \(g>0\); if a particle scatters more energy in the backward direction, then \(g<0\). Comprehensive study on the dependance of anisotropy factor on the radiation wavelength and scattering particle diameter can be found in [57; 58; 59; 60]. Scattering coefficient \(\mu_{s}\) is one of the key parameters of a scattering medium. It is measured in inverse millimeters and characterizes the scattering strength per unit length. The scattering coefficient is calculated using Mie theory [8]. After calculation of free-path length, scattering and azimuthal angles of the new position of the photon is defined. If this position was inside the scattering medium, the calculation of the next set of \(l\), \(\theta\), \(\varphi\) is repeated. Once the photon reached the border of the medium, its parameters (e.g., total travelled optical path length, last coordinates, last direction of propagation, total number of encountered scattering events, etc.) were saved, and the photon was traced to the measurements plane (emulation of camera sensor). The procedure is repeated for each photon. When trajectories of all photons were calculated, we obtained the intensity distribution at the measurements' plane. Figure 1 shows the results of the simulation of laser beam propagation through the scattering medium with three different scatterers' concentration values--from \(1.5\times 10^{5}\) mm\({}^{-3}\) to \(7.5\times 10^{5}\) mm\({}^{-3}\). Figure 1: Results obtained from a numerical simulation. Intensity distributions and cross-sections of laser beam propagated through the scattering medium with particular concentration values.