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Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings

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Abstract

Attempts were made to evaluate mathematically and empirically the accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings in the color using industries. To this end, an innovative inversed mathematical evaluation procedure was concocted which comprised of plotting the absorption and scattering constants of the Kubelka–Munk model or any of its various modified form or replacements theories against the intrinsic optical coefficients of the respective exact radiation transfer theories, namely Chandrasekhar for opaque and van de Hulst for translucent media. The results prove mathematically that the Kubelka–Munk model for opaque media is a sound theory and its various suggested modifications or replacements do not improve the color match prediction of opaque surface coating media. This mathematical conclusion was further confirmed by color match prediction of actual opaque paint samples. On the other hand, the mathematical prediction for translucent media illustrated a completely different picture, depicting nonlinearity between the optical constants and the respective concentrations of colorants. This implies that much further work has to be carried out to derive invertible new equations to enforce linearity to such situations or make use of alternative artificial intelligent procedures which are designed especially for nonlinearity.

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Acknowledgment

The authors wish to express their appreciation for the support of the center of excellence for color science and technology.

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Authors and Affiliations

  1. Department of Color Physics, Institute for Color Science and Technology, P.O. Box 16765-654, Tehran, Iran

    M. Gorji Bandpay, F. Ameri & K. Ansari

  2. Center of Excellence for Color Science and Technology, Institute for Color Science and Technology, P.O. Box 16765-654, Tehran, Iran

    S. Moradian

  3. Department of Polymer Engineering and Color Technology, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran

    S. Moradian

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  1. M. Gorji Bandpay
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Correspondence to F. Ameri.

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Bandpay, M.G., Ameri, F., Ansari, K. et al. Mathematical and empirical evaluation of accuracy of the Kubelka–Munk model for color match prediction of opaque and translucent surface coatings. J Coat Technol Res 15, 1117–1131 (2018). https://doi.org/10.1007/s11998-018-0056-5

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