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1. Kubelka-Munk theory and its limitations
The KM theory was proposed as early as 1931, but it was not until 1958 that it was successfully used in the textile printing and dyeing industry. The application of this theory in the printing industry began in the 1970s. Computer color matching systems developed in countries such as the United States and Japan still use this theory.
By deriving a series of KM theories, the simplest form and derivative form of the function for the color matching calculation are given:
K/S=(1-r)2/2r
r=K/S+1-[(K/S+1)2-1]1/2
In the formula, r represents the reflectivity at the wavelength; K is the absorption coefficient, which represents the absorptivity of the micro-thick dielectric layer after the diffuse illumination light is incident in an infinitely thick planar medium; S is the scattering coefficient and represents the thickness of the microelement. The scattering rate of light.
So far, the basic principle of computer color matching (CCM) still follows KM theory. For example, spectral visual matching methods, computer reflectance spectroscopy color matching, and computer color matching approximation algorithms are all based on KM theory. However, in the practical application of KM theory, there are often differences between its theoretical calculations and specific practices. The reasons can be summarized as two factors.
The 1K-M theory itself is deduced under certain assumptions.
Firstly, the thickness of the tint layer is x. When the light falls on any of the micro element layers dx, the reflection caused by the interface is not considered. The result must lead to the application of the theory that the color layer is immersed in the medium of the same refractive index. An algorithm that simplifies the problem and ignores different refractive indices on the interface may cause errors.
Second, dx is any microelement layer within the thickness x of the color layer. The absorption coefficient and the scattering coefficient determined in this way are considered to be the same throughout the use of the color layer, but this assumption is difficult to apply to extinction or semi-extinction Oiled material.
Third, the colorant particles in the color layer are disorderly arranged, so that the illumination in the color layer becomes a diffuse diffusion form, and the particles are completely submerged in the diffusion effect, resulting in two upper and lower channels. However, in practical applications, when particles are present in the oily film in the form of thin sheets, most of them are arranged in the horizontal direction, causing the assumption of the destruction of the luminous flux of the two channels.
Fourth, on the thin layer, the light does not have time to scatter into the interior of the color layer. In the dark shades, a considerable amount of light has been absorbed before scattering, so the light beams entering the color layer do not diffuse, resulting in experimental results Big difference.
2 The printing industry must consider the interaction between light and pigment particles and the physical properties of the ink when describing the ink overlay effect. In practical applications, it should be said that the KM theory contains two double constants, the absorption coefficient K and the scattering coefficient S, and the scattering ability of the ink to the light is negligible compared to the scattering ability of the matrix. Therefore, the principle of ink coloration is mainly The ink selectively absorbs light, and the ink's ability to absorb incident light is affected by the thickness of the ink layer and the ink concentration. KM theory is based on the premise of non-transparent media, and the ink used in printing is transparent or translucent. Therefore, KM theory has a great shortage.
2. Using computer color matching with tristimulus values
(1) Tristimulus color matching
At present, the mathematical models used by computer color matching systems at home and abroad are mainly K/S functions. In view of the limitation of K/S and the characteristics of the printing industry, this paper proposes a color matching method using tristimulus values. This method does not use color-to-color indexes such as K/S value and reflectivity, and uses only tristimulus value as a color index.
On the basis of K/S theory, tristimulus values ​​can also be used for color matching, but a database of K/S values ​​and concentrations needs to be established in stages to study the relationship between tristimulus values ​​and concentration, ie between tristimulus values ​​and the percentage of dots. Relationship. In printing, the method of converting the tristimulus value and the dot percentage is mainly useful for the conversion of the Newcastle equations, the transformation using the matrix transformation method, and the use of the lookup table transformation. This paper selects the chromatography to establish the lookup table for conversion.
(to be continued)
Computer ink color matching method and principle analysis (2)
Third, computer color matching principles and systems