As the basic theory for color mixing in intensely light-scattering materials, the Kubelka— Munk single-constant/two-constant theories have played an important role in color science and technology. However, in practice there are some shortcomings. This paper checked the theories with a series of systematical experiments, data processing and analyzing, and has revealed several disagreements with the experimental evidence in the case of the additivity color-mixing law for turbid materials. Explanations on some of these problems are given, which are different from the conventional views.
Kubelka, P., and Munk, F., Ein Beitrag zur potik der Farbanstriche, Z. Tech. Physik, 12, 593 ( 1931).
2.
Duncan, D.R., The Colour of Pigment Mixtures, in "The Proceedings of the Physical Society", London, 1940 , 380-401.
3.
Saunderson, J.L., Calculation of the Color of Pigmented Plastics , J. Opt. Soc. Am., 32, 727-736 (1942).
4.
Nickols, D.G. , and Orchard, S.E., Precision of Determination of Kubelka and Munk Coefficients from Opaque Colorant Mixtures, J. Opt. Soc. Am., 55(2), 162-164 ( 1965).
5.
Donald, A.P. , Applied Color Theory in a Pigments Laboratory , J. Paint Technol., 45(579), 57-62 (1973).
6.
Billmeyer, F.W.J. , and Abrams, R.L., Predicting Reflectance and Color of Paint Films by Kubelka-Munk Analysis I. Turbid-medium Theory, J. Paint Technol., 45(579), 23-30 ( 1973).
7.
Shah, H.S., and Billmeyer, F.W.J. , Kubelka-Munk Analysis of Absorption in the Present of Scattering, Including Surface Reflection Correction to Transmittance, ColorRes. Appl., 10(1), 26-31 (1985).
8.
Davidson, H.R. , Hemmendinger, H., and Landry, J.L.R. Jr., A System of Instrumental Colour Control for the Textile Industry, J. Soc. Dyers Colourists, 79(10), 577-589 ( 1963).
9.
Davidson, H.R. , and Hemmendinger , H., Color Prediction Using the Two-Constant Turbid-Media Theory, J. Opt. Soc. Am. , 56(8), 1102-1109 (1966 ).
10.
Allen, E., Basic Equations Used in Computer Color Matching, II. Tristimulus Match, Two-constant Theory, J. Opt. Soc. Am., 64(7), 991-993 (1974).
11.
Park, J., "A Practical Introduction to Computer Colour Matching", Clipper Letterpress, 1989.
12.
Volz, H.G., "Industrial Color Testing : Fundamentals and Techniques", Wiley-VCH, New York, 1995.
13.
McDonald, R., "Colour Physics of Industry", 2nd edn, Society of Dyers and Colorists, Bradford , 1997.
14.
Xu, H.S., "New Technology on Computer Color Measurement and Matching", China Textile Press, Beijing, 1999 .
15.
Berns, R.S. , "Billmeyer and Saltzman’s Principles of Color Technology", John Wiley, New York, 2000.
16.
Park, M., "Instrumental Colour Formulation", Society of Dyers and Colourists , Bradford, 1994.
17.
Bhattacharya, S.D., Agarwal, B.J., and Patil, V.B., Kubelka- Munk Analyses for Nylon Fabric Dyed with Acid Dyes, Textile Dyer & Printer, 29(10), 15 (1996).
18.
Walowit, E. , McCarthy, C.J., and Berns, R.S., An Algorithm for the Optimization of Kubelka-Munk Absorption and Scattering coefficients, ColorRes. Appl., 12(6), 340 ( 1987).
19.
Marcus, R.T. , and Welker, J., Pigment Volume Concentration Effects in Color Prediction and Practice, J. Paint Technol. , 50(642), 78-83 (1978).
20.
Burlone, D.A. , Formulation of Blends of Pre-colored Nylon Fiber, ColorRes. Appl., 8(2), 114-120 (1983).
21.
Davidson, H.R. , Prediction of the Color of Dye Mixture on Textiles , J. Opt. Soc. Am., 42(5), 331-332 (1952).
22.
Kubelka, P. , New Contributions to the Optics of Intensely Light-scattering Materials, Part I, J. Opt. Soc. Am., 38, 448- 457 (1948).
23.
Kubelka, P. , New Contributions to the Optics of Intensely Light-scattering Materials, Part II, J. Opt. Soc. Am., 44, 330- 335 (1954).
24.
Judd, D.B., and Wyszecki, G., "Color in Business, Science and Industry", 3rd edn, John Wiley, New York, 1975.
25.
Allen, E., Colorant Formulation and Shading, in "Optical Radiation Measurements ", Grum, F. and Bartleson, C. J. (eds), Academic Press, New York, 1980.
26.
Ciba Specialty Chemicals Inc., CIBACRON® C Active Dyestuffs Pad Dyeing, in "Ciba Specialty Chemicals Products Instruction", Ciba Specialty Chemicals Inc., Shanghai, 2002.
27.
Jin, X.R. , "Experiments on Dyeing and Finishing", China Textile Press, Beijing, 2000 .
28.
Yang, H.Y., Zhu, S.K., Zuo, L., et al., Study on Optical Absorption Behavior of Dyestuff in Fabric . Journal of Donghua University (Eng. Ed.), 25(2), 58-61 (2008).
29.
Wang, N.N., "Optical Measure Technology for Particle Size and its Application", AtomicPower Press, Beijing, 2000.
30.
Rundlof, M. , and Bristow, J.A., A note concerning the interaction between light scattering and light absorption in the application of the Kubelka-Munk equations, J. Pulp Paper Sci., 23(5), 220-223 (1997).
