pigmented colorants: dependence on media and time - Cornell ...

describes the scattering and absorption of light at each scattering event (account-
ing for the size, shape and density of every particle, as well as the and relative
indices of refraction). The Mie scattering functions are very numerically expen-
sive to compute. Therefore, efficient approximations have been presented from
the optical literature for sparse or dense particle densities (called hazy and murky,
respectively) [NMN87]:
PhazyMie(cos α)=1+9
PmurkyMie(cos α)=1+50
8
1 + cos α
2
1 + cos α
2
32
98
(4.5)
where α is the angle between the incident and outgoing directions. Another
popular approximation to the Mie functions in the Henyey-Greenstein phase func-
tion [Bli82]:
PhenyeyGreenstein(cos α, g) =
1 − g 2
(1 + g 2 − 2g cos α) 3/2
(4.6)
The function takes an asymmetry parameter g (the mean cosine of the phase
function), which varies from strong retro-reflection (g 0). Isotropic scattering is achieved when g =0.
Kozakov presented a successful method of calculating the characteristics of
paint based on Monte Carlo methods [Koz04]. In the work, a statistical model
of a paint coating was developed involving interaction between photons, particles,
and the binding medium, as well as the photon path length between collisions.
The model accounts for a single pigment and medium (titanium white in alkyd
enamel) and actual paint reflectance data was measured and utilized in the work.