Patent ID: 7045169

Claim:
A method of providing at least one optical property of a coating system having a coating adjacent a base sheet comprising: a) providing a radiative transfer equation that relates a number of physical characteristics of the coating system selected from the group consisting of coating thickness, coating pore size distribution, coating pigment particle size, a coating pigment particle size distribution, a coating roughness, scattering coefficient, absorption coefficient, anisotropy factor, and optical properties of a base sheet to one or more optical properties for a coating system selected from the group consisting of gloss, brightness, and opacity, wherein providing the radiative transfer equation comprises application of diffusion approximation to transport of light, said diffusion approximation defining average radiance U(r,t) as follows: D∇ 2 U ( r,t )−μ a U ( r,t )−∂ U ( r,t )/∂ t=S ( r,t ), wherein isotropic source density is denoted by S(r,t), r and t are the variables of position and time, and D is the diffusion coefficient which is defined in units of length as D=1/3[μ a +μ s (1−g)] in terms of the absorption and scattering coefficients μ a and μ s , respectively, and g is the anisotropy factor; b) solving the equation by inputting a number of the physical characteristics of the coating system to obtain at least one optical property output of the coating system; and c) formulating a pigment coating including the obtained at least one optical property output.