Matching target color in polyolefins by estimating pigment concentrations using a four-flux model

In applications of computer color formulation where color stimuli are optically thick (e.g., textiles, coatings, etc.), a simple single-constant or two-constant theory (e.g., Kubelka-Munk model) would suffice. To accurately predict reflectance and transmittance of materials with optical thickness ranging from optically thin to optically thick (e.g., plastics), mathematically complex radiative transfer theories (e.g., many-flux models) have been recommended. A many-flux model can even predict color formulation involving special-effect pigments (e.g., metallic, pearlescent, etc.), but implementation of such models is manyfold complicated. In the current study, applicability of a relatively simple Maheu-Letoulouzan-Gouesbet (MLG) four-flux radiative transfer model to optically varying pigmented polyolefins is thoroughly investigated. First, the MLG model was implemented to determine absorption and scattering coefficients of over 120 pigments where a new mean relative absolute spectral error (MRASE) between measured and calculated spectral reflectance and transmittance of the calibration samples was minimized as an objective function. Second, currently determined absorption and scattering coefficients were further validated by color recipe prediction of 350 historical product colors. Measured and predicted reflectance curves were compared in units of MRASE, CIEDE2000 color difference, metamerism index, root mean square error, and goodness-of-fit coefficient. Moreover, transmission matching was evaluated in units of percent difference between the required and predicted average transmittance. Results showed that with the current implementation of the MLG four-flux model, color recipes of at least 95% of the target colors can be predicted within the acceptability thresholds in units of different error metrics used in the study.