The Development and Color Matching Principle of Computer Ink Color Matching System (2)

Second, computer color principle and system

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.

(2) Principle of color matching with tristimulus values

According to the CIE standard colorimetry system, any natural color can be represented by spectral tristimulus values ​​X, Y, Z. At present, most advanced colorimetric instruments use this colorimetric system, ie the color of any object can be represented by the tristimulus values ​​X10, Y10, Z10. The principle of computer color matching is to use the principle of metamerism, that is, if the tristimulus values ​​X10, Y10, and Z10 of the two color samples are equal, the two are the same color.

A chromatogram-created look-up table describes the relationship between tristimulus values ​​and the percentage of each color ink dot. Let a color sample be overprinted by three types of inks a, b, and c. The dot percentages of the three inks are l, m, and n. The ratio of inks a, b, and c is l:m:n, and white ink. Take (1-l)+(1-m)+(1-n). This color matching system uses CIE standard light source D65 and 10° field of view data for calculation, while using CIELAB color difference formula: ΔEab=[(ΔL)2+(Δa)2+(Δb)2]1/2 to calculate the standard color The color difference between the sample and the color matching sample.

We can see that using computer color matching with the tristimulus value can make the color of the color sample to be matched with a specific light source expressed by data. There is a corresponding relationship between the tristimulus value of the color sample and the ink ratio, and the color difference can be used. Check to see if the recipe meets the requirements.

(3) Three stimulus color matching methods

The tristimulus value of each color patch of the chromatogram and the percentage of dots of each ink were input into the computer to establish a basic database. In color matching, the tristimulus value of the target color sample is input into the system, the system calculates the mixed ink and its proportion, and outputs the formula prediction result. When the ink color matching result is dry, the tristimulus value is measured again, and the computer calculates the difference in color according to the color difference formula, and further correction instructions are made to promptly formulate the high-quality homochromatic color.

In terms of the quality requirements of color reproduction, according to the national standards for the clear requirements of the color difference ΔE*ab of the same batch of color decorating prints, this paper selects ΔE*ab≤3.

Chromatography includes most of the common colors. For the colors in the chromatogram, you can directly find the ratio of the ink, not the color in the chromatogram. You can first find the color with the smallest color difference in the chromatogram, and then use linear interpolation. Solution.

3. Computer color matching system

(1) Function of color matching system

The computer color matching system is a modern device that integrates a colorimeter, a computer, and a color matching software system. The basic role of computer color matching is to pre-store the color data of the ink used in color matching in a computer, and then calculate the mixing ratio of the color of the sample draft with these inks in order to achieve the purpose of the predetermined formula.

(2) The composition of the color matching system

1 hardware part of computer color matching system

Computer: Use Windows operating system, hard disk storage space at least 20MB; Spectrodensitometer; Chromatography.

2 computer color matching software system

The software main menu: displays the program directories in the color matching system software, so that the operator has a general understanding of the color matching software, so that the operator selects and invokes the programs displayed in the directory according to his own purpose.

Basic data files: Use Microsoft's Access to create database files, including two-color overprinting, three-color overprinting, and spot color overprinting.

The document includes the establishment, management, data processing part and recipe storage program of the basic data file.
3 Formula calculation and correction

Call this program to calculate the color difference between the color match sample and the standard sample, select the recipe based on the color difference, and correct the recipe.

The color matching system software has a strong human-machine dialogue function. The operator can input the corresponding parameters and data according to the prompt on the computer screen to obtain the required ink formulation.

Color matching is a complex technical project involving light color theory, ink, paper, process, etc. The use of chromatography to perform tristimulus color matching overcomes the limitations of KM theory and is suitable for the characteristics of the printing industry, reducing the burden on the color matching staff. , Improve the color quality of the product, color matching speed, accuracy, and increase economic efficiency. Although there are still many places to be improved, such as different color differences calculated by the tristimulus value matching under different light sources, the color matching accuracy has a great relationship with the accuracy of the chromatogram. However, with the constant updating of computers, the more sophisticated instruments, the constant emergence of various mathematical methods, and the gradual standardization and dataization of materials, computer color matching will inevitably show unparalleled superiority.