**3. Methods**

There are two main approaches for calculation of scattering in paint layer. The first is the continuous medium approach. Roughly speaking, this means that a ray never hits the same flake even when it is reflected exactly backwards. In other words, scattering of two adjacent rays is statistically independent: when a ray hits a flake, the ray shifted by just a bit may miss it. The most famous method of practical calculations in this situation is the light transport equation (LTE). It can be solved via MCRT in the continuous medium when successive scattering or absorption events are independent. Such behavior takes place in the case of infinitesimal flakes (gas mode) or to be precise, in case when the vertical separation of flakes is much greater than their diameter.

When the flakes are large or are packed densely with large concentration, this assumption is violated and calculations deviate from the real flake ensemble properties. Thus, we need the second approach to calculate light interaction here. Nonetheless, MCRT still can be used but now the ray goes in an empty space populated with some individual flakes that do not overlap. If these flakes are large enough then a ray might hit the same flake several times. Since this is the same flake, the corresponding scattering events are correlated.

Below we shall compare the LTE and the accurate approaches.
