Simplified equations to calculate mie‐theory parameters for use in many‐flux calculations for predicting the reflectance of paint films

The reflectances of paint films can be predicted from the scattering and absorption characteristics of their pigments using the Kubelka-Munk (K-M) equations. The K-M theory has several limitations. To overcome these, the number of fluxes inside the paint film has been increased from two to four in various proposed mathematical models. A more recent theoretical advancement in the subject was made by Mudgett and Richards by the introduction of the many-flux theory. This theory eliminates several limitations of the K-M theory. The application of this theory is highly complicated as it requires the use of Mie-theory parameters like the single scattering and absorption coefficients and the phase function. In our previous publications, we have proposed simple equation to simulate the Mie-theory phase function. In this article, we give simplified equations to estimate the scattering and absorption coefficients of colorants. The utility of these simplified equations has been established by computing the reflectances of paint films, using the M-F technique for selected particle sizes up to a range of X = 5 ( = 2 π/λ) and refractive indices m = m – ik, where m varies from 1.10 to 2.00 and k = 0.001 to 0.10. (The imaginary part of the refractive index k should not be confused with the single-scattering absorption coefficient.) The results are compared with those obtained by using rigorous Mie-theory equations. The reflectances predicted by the two sets of equations agree well.