## 2 Materials and Methods
### Monte Carlo Simulation  
The Monte Carlo technique is a widely used approach toward sampling probability density functions for simulating a wide range of problems. The first use of the method for photon transport in biological materials was [PERSON] and [PERSON] in 1983, which considered isotropic scattering [46]. [PERSON] et. al. introduced anisotropic scattering into the Monte Carlo simulation of biological tissues, implementing a simulation that propagated photons using cylindrical coordinates, which introduced the Hop/Drop/Spin nomenclature for organizing the program [47]. [PERSON] et al. reformulated the program using photon propagation based on Cartesian coordinates, which made the program much simpler to convey in written form [48]. [PERSON] and [PERSON] adapted and augmented the work of [PERSON] andPrahl to write the Monte Carlo Multi-Layered (MCML) program that considers tissues with many planar layers with different optical properties [8]. Monte Carlo technique simulates the behavior of the elementary parts of a physical system. In regards to light propagation through a medium, this technique uses quantum nature of light and simulates the propagation of photon flux [49]. In general, there are two Monte Carlo techniques: corpuscular and wave [50]. Both methods have their advantages and disadvantages. The \"Wave Monte Carlo\" treats the propagation of radiation as a wave propagation. It describes the propagation of a wave through a set of screens that contains scattering particles. The resultant wave becomes stochastic due to the interference between the unscattered and scattered waves. As a result, we get the complex amplitude of the random field. An ensemble of the obtained fields for the statistically independent sets of screens is the calculated intensity distribution. This technique is particularly applied for the mono-direction radiation. In contrast, the \"Corpuscular Monte Carlo\" treats the propagation of radiation as a corpuscula (photon) flux. This technique performs the statistical calculation of the ensemble of photons--the average number of photons depending on the coordinate equals to the intensity distribution. \"Corpuscular Monte Carlo\" is applied for both the weakly and strongly scattering media. Another feature of this method is that it is not supposed to model the fixed position of the scatterers. It instead models the events of the photon-particle interaction with the desired probability density. From this point of view, the Brownian movement of scatterers is considered in the simulation by default. Choosing each method is a matter of opinion, since both show similar results [50]. We have chosen the \"Corpuscular Monte Carlo\" technique for our simulation. First, we simulated the initial uniform intensity distribution of a laser beam with diameter equal to 4 mm and wavelength equal to 0.65 \(\upmu\)m. The random number generator was used to calculate the initial position of each of the \(2.5\times 10^{11}\) photons within the beam aperture. Afterward, we calculated the trajectory of propagation of each photon through the 5-mm layer of scattering medium consisted of a monodisperse spheres of 1-\(\upmu\)m diameter and refractive index of 1.582 (refractive index of the medium was 1.33). The influence of relative refractive index is rather complicated [51]. For small particles, the influence on the forward-scattering signals is mainly due to the part of the internal reflection if the relative refractive index deviates from 1. However, when the relative refractive index is close to 1, the effects on the forward-scattered light from both the surface reflection and internal reflection are great. For large particles, the contributions of the surface reflection and the internal reflection to the forward-scattered light are much weaker than the diffraction when the relative refractive index deviates from 1. When the relative refractive index is very close to 1, the effects on the forward-scattered light from the internal reflection are great.