4. Ways to control gray balance
1. The guide for gray balance and copy reproduction
The Rochester Institute of Technology (RIT) developed a gray balance and tone reproduction guide (Tone reproduction and Nentral Determination; TRAND for short) used to obtain the neutral concentration value of gray balance. TRAND has six color blocks, of which five color blocks, each color block contains dozens of color circles. The printing staff can select the color circle closest to the original gray from the guide table, and compare the dot value of each version of the color circle, so that the gray balance dot value of its three primary colors can be obtained.
Its characteristic lies in the convenience of estimation, with the neutral color block in the visual selection to get the demand of gray balance. Because the human eye is used to estimate gray, there may be errors or conditions such as color due to light sources with different color temperatures. Therefore, it must be fixed to the same light source for estimation to get a more correct value.
Second, the screen line number to get a better gray balance
In the article "Research on Screen Line Number vs. Gray Balance", its purpose is to seek the chromaticity changes of four screen and three color overlays for different screen lines, and analyze the four-color overlay and three-color overlay. The difference of neutral color degree in printing (taking 85, 120, 150, 175, 200 screen lines as the experimental range).
After printing, the printed proofs are tested for full plate density and the quality meets the requirements, and the measurement is started. Using a colorimeter as a measurement tool, the D50 light source and a 2 ° viewing angle are used to measure the color change of the progression of the sample sheet. The measurement items are the a * value and b * value of the CIELAB color space. After measurement, it is converted into C * ab value and chroma (Chroma) in CIELCH color space. The formula for another chroma value is converted to:
After statistical calculations, analysis results are available.
Conclusion: The correlation of the chroma values ​​between the lines of three-color overprinting is only the 25th-order correlation is large, and the correlation is negative, which means that the higher the screen line number, the smaller the chroma value, the gray balance The better the condition value. The four-color overlay printing is similar to the three-color overlay printing, only the 25th order chroma value can be known, 175 lines can get better neutral color. As for the chroma value comparison between three-color overprinting and four-color overprinting, as a whole, the 150-line and 200-line black editions have improved neutral color rendering with improved three-color ink overprint.
Third, the formula for color correction:
The color correction equation is a linear linear equation, which is as follows:
C, M, and Y represent the amounts of cyan, yellow, and magenta inks required for copying, and Dr, Dg, and Db are the concentrations measured by the original with red, green, and blue color filters. a11 to a33 are coefficients related to specific inks and specific printing conditions. Due to the non-additive nature of the ink, the replication effect of this formula is not very satisfactory, so the empirical equation derived from the color correction equation is proposed. (Note: Li Taijiong, Discussion on the Mathematical Model of Gray Balance in Lithography, P16)
4. The empirical equation:
Clapper (1961) and Pobboravsky (1962) both published empirical equations in TAGA. The formula is as follows:
Cr, Mg, Yb represent the amount of cyan ink, yellow ink and magenta ink (density measured by color filter) required for copying. Dr, Dg, Db are the density (chromaticity density value) measured by the color filter of the original, and a11 ～ a39 are the correlation coefficients. The difference between the empirical equation and the color correction equation is that it considers the ink density to be disproportionate and non-additive. The square term in the formula is used to correct the disproportionate characteristics of the ink, and the cross product term is used to correct the non-additive characteristics of the ink.
Because the empirical equation is based on the measurement of halftone samples, but as printing is developing in the fields of colorimetry and spectrophotometry, the value of empirical equations based on density is also relatively reduced. (Note: Li Taijiong, Discussion on Gray Balance Mathematical Model in Lithography, P16-P17)
5. Neugebauer Equation:
The Nokber equation uses full-color patch data to predict halftone values. The Nokber equation is as follows:
The three primary colors are overprinted into eight replicate primary colors, which are:
C, M, Y ... primary colors R, G, B ... secondary colors Bk ......... tertiary colors W ............... quadruple colors
The greater the percentage of the dot area of ​​the eight primary colors, the greater the color effect on the human eye. X, Y, Z in the Nokber equation are the tristimulus values ​​of the copied color, and X1, Y1, Z1 ～ X8, Y8, Z8 are the tristimulus values ​​of the eight primary colors, and f1 ～ f8 are the respective proportions of the eight primary colors Dot area percentage. The method of obtaining the gray balance by the Nokber equation is as follows:
First assume the dot area (c, m, y) of the three-color version of C, M, and Y, and then use the Demichel Equation to find the percentage of the dot area occupied by each of the copied primary colors.
Demecci's equation format:
After calculating f1 ～ f8, use a colorimeter or spectrometer to measure the tristimulus values ​​(X1, Y1, Z1 ～ X8, Y8, Z8) of the copied eight primary colors, and substitute the two equations into the Nocker equation to find the copied three The stimulus value (X, Y, Z), and then convert the tristimulus value to the chromaticity coordinate value (X, Y) and compare it with the chromaticity coordinate value of the observation light source. Neutral gray.
The dot area combining this neutral gray color is the halftone dot area required. Then use Murray Davies Equation (Murray Davies Equation) to find the corresponding concentration value.
The Murray Davis equation is as follows:
In this way, the neutral gray dot area and its corresponding concentration value can be obtained. (Note: Li Taijiong, Discussion on the Mathematical Model of Gray Balance in Lithography, P17-P18)
6. Modified Neugebauer Equation:
The combined neutral color dot area of ​​the modified Nokber equation and the Nokber equation is the same. The difference lies in the equation applied to the corresponding concentration value.
Since light will be affected when passing through paper, Yule and Colt proposed a value of n in 1951 to modify the Murray Davis equation. This equation is called Yule Nelsen Equation. Its equation is as follows:
Due to the n value, the Ulniersen equation considers a (the halftone dot area of ​​each color version) in the equation as the actual dot area. The size of n value is affected by four points (n value is about 1.5 ~ 3.05):
a. Paper type b. Number of halftone screen lines c. Size of halftone dots d. Full version density (Note: Li Taijiong, Discussion on the Mathematical Model of Gray Balance in Lithography, P21-P22)
7. n-value Modified Neugebauer Equation (n-value Modified Neugebauer Equation):
This equation is a further modification of the Nocker equation, because the modified Nocker equation only considers the effect of the n value on the calculated concentration, but does not consider the scattering and reflection of light in the paper. The tristimulus values ​​of the eight primary colors produce errors.
Therefore Yule suggested to change to the following formula:
5. Comparison of control methods:
Because the control method of the screen line number is to use different screen line numbers (85 ~ 200) to compare which line number can get the better quality, which is different from the method of calculating the better gray balance by using the color copy equation. The two can't compare their pros and cons, so I first compared the control of the screen line count to the pros and cons of the three-color overlay printing and the four-color overlay printing on the different screen lines, and then compared the three-color overlay printing with the four-color overlay printing. The pros and cons of the number of lines of each screen.
1. The control method of the screen line number:
First, compare the advantages and disadvantages of three-color and four-color overlay printing on different screen lines, and then compare the advantages and disadvantages of three-color and four-color overlay printing on each screen line.
2. Comparison of color copy equations:
Compare the accuracy and applicable scope of the five formulas: a, color correction equation b, empirical equation c, Nacker-squared program d, modified Nacker-formula e, and n-value modified Nacker-squared program.
Since the printing color reproduction has been developed in the fields of chromatics and spectrophotometry, the color correction equations and empirical equations based on concentration are less practical in the future than the Nokker equations. The Nocker equation is to find the neutral gray dot area to correspond to its concentration value, but there is one thing to consider, that is, the dot expansion and the shape of the dot, whether future research can solve the problem of the Nocker equation The error caused by the expansion of the network.
6. Conclusion
The control law of gray balance is to be able to find the correct amount of ink required by equations under different conditions. The management of traditional printing quality requires data standards in order to control the stability of replicas. The early method was to establish a data-based concept by combining the gray balance and the copy of the guide table, the concentration meter, and the empirical equation. With the development of colorimetry and spectrophotometry, the current data standard is established with a colorimeter and n-value modified Nokber's equation. When the data standard is established, when printing, please pay attention to whether the printing machine It can print out the required amount of ink stably, so as to improve the printing quality. The Nokber equation is to find the neutral gray dot area to correspond to its concentration value, so there are several points to consider, that is, the dot expansion and the shape of the dot, so whether the equation can solve its error is very important.
Future printing trend "Digital printing machine" The gray balance control method should be very different from traditional printing. Traditional printing mainly controls the dot area to achieve the gray balance requirements, and the digital printing machine has a printing method. For printing and non-pressless printing, etc., the gray balance control method may be slightly different, and the color complex equation can be applied. Therefore, I hope that in the future there will be research on the relevant aspects of the digital printing standard for color printing and the future application of the color printing equation in digital printing.
References
Luo Fulin, Li Xingcai, Introduction to the Printing Industry, Seventh Edition, Luo Meijun, Publishing Department, Chinese Culture University, Printing Chromatics, Zhao Renrong, Print Technology Magazine, Principles of Color Reproduction, Li Yangshi, National Compilation Museum, Principles and Applications of Color Design, Hongda Fei , Color Printing Quality Inspection and Tools, Printing Industry Press Luo Meijun, Method of Determining Neutral Color Variation in Printing and Copying System Li Taijiong, Discussion on the Mathematical Model of Gray Balance in Lithography Huang Chuang, Research on the Influence of Expanded Screens on Color Reproduction Zhang Haohong, Number of Screens Research on the influence of gray balance Jiang Ruizhang, commonly used dot shape color and color prediction research
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