Optimal color scheme design for opaque products
The colorful opaque colored products in daily life are dyed by colorants. Therefore, the color matching of opaque products plays an important role in its appearance and market competitiveness. However, traditional artificial color matching has certain limitations, such as strong subjectivity and low efficiency. Therefore, it is of great significance to study how to realize the color matching of opaque products by computer methods.
Light propagates through objects in three ways: absorption, reflection, and transmission. For opaque articles, most of the light is absorbed or reflected by the surface. The absorbed and reflected light is decomposed into different color components according to wavelength after correction such as transparency, forming a spectral map. The spectrogram is usually composed of various colors of light in the 400--700nm band. To simplify the calculation, the reflectance of the color after the final color matching is represented by the spectral data at intervals of 20nm. For opaque materials, there is a certain relationship between the ratio of absorption coefficient K/scattering coefficient S and reflectivity R. For details, please refer to the KM optical model in [1] "Research on Computer Color Matching Theory and Algorithms".
The color parameters obtained based on the optical model can be applied to the calculation of color difference. Usually, the color difference (no more than 1) is used as the standard for the color matching effect. Color difference calculation method references [2] The total color difference calculation method of CIELAB color space in "Research on Color Measurement of Blended Fabrics Based on CIELAB Uniform Color Space and Clustering Algorithm". The calculation method of the tristimulus value XYZ appearing in the calculation of the color parameters L* (lightness), a* (red-green degree) and b* (yellow-blue degree) is as follows:
The problem of color matching of opaque products is to design the color matching model of opaque products based on the optical model. Compared with manual color matching, it saves a lot of manpower, material resources and financial resources, which is of great significance to reduce energy consumption.
For an opaque product, the K/S values of red, yellow and blue colorants at different concentrations and different wavelengths and the K/S values of base materials at different wavelengths are known, see Annex 2. Wherein, concentration=colorant gram weight/substrate weight. The ratio of the absorption coefficient K/scattering coefficient S of each colorant is additive, please refer to the KM single constant theory in [1] "Research on Computer Color Matching Theory and Algorithm" for details. See Appendix 3 for the R values of 10 target samples (made by mixing two to three colorants). Please keep 4 decimal places for the result display.
Please build a mathematical model to solve the following problems:
Question 1: Please calculate the relationship between K/S and concentration of the three colorants in Appendix 2 at different wavelengths, and fill in the relationship formula and fitting coefficient in the table.
Question 2: Please establish an optimization model for the color matching of opaque products. On the premise of knowing the R value of the target sample (Appendix 3), based on the spectral tristimulus value weighting table (Appendix 1) and the colorant K/S basic database (Appendix 2), use the optimization model to calculate the color difference with the target sample The closest 10 different formulations require a color difference of less than 1.
Question 3: On the basis of question 2, consider cost control and batch color matching, and improve the color matching model. Perform color matching on 2kg of the base material, and find 10 different formulas with the closest color difference to the target sample (Appendix 3), and the color difference is required to be less than 1. See Appendix 4 for the price per gram of masterbatch.
Question 4: In actual production, the less coloring agent required for color matching, the better. Based on this, on the basis of Question 3, find the optimal color scheme for the first 5 samples in Appendix 3, and require each sample to be formulated 5 different formulations with less than 1 color difference.
Data and information provided:
1. Attachment 1 (spectral tristimulus value weighting table)
2. Attachment 2 (K/S values of different concentrations and different wavelengths)
3. Attachment 3 (R value of 10 samples)
4. Attachment 4 (dye price)
5. References [1] Jiang Pengfei. Research on computer color matching theory and algorithm [D/OL]. Zhongyuan Institute of Technology, 2016.
6. References [2] Wang Linji. Research on color measurement of blended fabrics based on CIELAB uniform color space and clustering algorithm [D]. Zhejiang Sci-Tech University, 2011.
References Follow the official account at the end of the article and reply "Reference B" to get it!