CN116804624A - Gravure extinction film spectrum prediction method based on branched Clapper-Yule prediction model - Google Patents
Gravure extinction film spectrum prediction method based on branched Clapper-Yule prediction model Download PDFInfo
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Abstract
The invention discloses a gravure extinction film spectrum prediction method and a preparation method based on a branched Clapper-Yule prediction model, and sample design and output; measuring spectral reflectance data of the monochromatic chromatograph; establishing a spectrum prediction model suitable for an extinction film based on a Clapper-Yule model and a branch theory, and determining model parameters and a branch coefficient corresponding to a known dot area rate; and determining a branch coefficient corresponding to the area rate of the mesh point to be predicted by using an interpolation method, and applying the branch coefficient to the spectrum reflectivity predicted by the established branch Clapper-Yule prediction model. Due to the phenomenon of multiple internal reflection of light between the extinction film and the printing ink, the invention adjusts and optimizes the characteristics of the extinction film, establishes a branched Clapper-Yule prediction model suitable for the spectrum prediction of the extinction film printed matter, and provides a theoretical basis for the color spectrum prediction of the gravure extinction film.
Description
Technical Field
The invention belongs to the technical field of gravure extinction film spectrum prediction, and particularly relates to a gravure extinction film spectrum prediction method based on a branched Clapper-Yule prediction model.
Background
The extinction film has the advantages of good visual effect, strong stereoscopic impression and the like when used as a printing material, and can improve the grade of packaging printed products, so the extinction film is popular with consumers in recent years. The diffuse reflection phenomenon exists on the surface of the extinction film, and when the color spectrum prediction model of the printing material based on the surface reflectivity is applied to predicting extinction film prints, the problems of large chromatic aberration, low precision and the like exist, so that the production needs of printing enterprises are difficult to meet. Therefore, the invention aims to realize the requirements of reducing chromatic aberration and improving color accuracy by establishing an extinction film spectrum prediction model.
Disclosure of Invention
The invention aims to provide a gravure extinction film spectrum prediction method based on a branched Clapper-Yule prediction model, which solves the problem of low color spectrum prediction precision of gravure printing on an extinction film at present.
The technical scheme adopted by the invention is that the gravure extinction film spectrum prediction method based on a branched Clapper-Yule prediction model comprises the following specific operation steps:
step 1, uniformly sampling any single color within the area ratio of 0-100%, generating a single color spectrum, and printing the single color spectrum on a extinction film by using gravure printing;
step 2, measuring spectral reflectance data of the monochromatic chromatograph;
step 3, establishing a branched Clapper-Yule prediction model applicable to the extinction film based on a Clapper-Yule model and combining a branched theory, and determining a branched coefficient corresponding to model parameters and known dot area rate;
step 4, determining a branch coefficient b corresponding to the dot area rate y to be predicted by using an interpolation method and the branch coefficient corresponding to the known dot area rate y And (lambda) and applying the lambda to the established fractional Clapper-Yule predictive model to predict the spectral reflectivity corresponding to the area ratio of the mesh point.
The present invention is also characterized in that,
in the step 1, the specific generation steps of the monochromatic chromatograph are as follows: selecting any single color, and uniformly sampling and designing to obtain a single color spectrum by taking a dot area rate of 10% as a step length from 5% of dots, wherein the single color spectrum comprises 0% of dots and 100% of dots; and the printing mode of the inner printing is adopted for proofing output.
The step 3 is a branched Clapper-Yule prediction model suitable for spectrum prediction of the extinction film printed matter, which is shown as a formula (10):
wherein R is the color spectrum reflectivity to be predicted, K is the proportion of specular reflection light which can be detected, R s For the reflectivity at the air-print interface, r m To extinction film base and reflectivity at ink interface, T x T is the transmittance of the extinction film w Backing white Mo Toushe rate for inner print, T Y For the color ink transmittance to be predicted, a represents the dot area rate; b represents a part-way coefficient;
backing white Mo Toushe rate T of inner print w Color ink transmittance T to be predicted Y The specific calculation is as follows:
wherein R0 is the spectral reflectance of 0% dot area;
wherein R100 is the spectral reflectance of 100% dot area.
In step 3, the calculation of the part-distance coefficient corresponding to the known dot area rate is specifically as follows:
the corresponding part-range coefficients are solved for the known dot area ratios a=5%, 15%, 25..95% and the corresponding spectral reflectance data in step 2.
Determining a path-division coefficient b corresponding to the dot area rate y to be predicted in step 4 y The calculation of (λ) is specifically as follows:
in order to predict the spectral reflectivity of a certain dot area rate y, firstly, finding out two known dot area rates closest to the dot area rate in the measured data, and marking as x and z;
in step 3, the corresponding part-range coefficients of the known dot area rate have been solved, and the part-range coefficients b according to the two known dot area rates x and z x (lambda) and b z (lambda) calculating the path-division coefficient b of the dot area ratio to be predicted by interpolation y (lambda) is as in formula (6):
the path-division coefficient b obtained by interpolation y And (lambda) is applied to the established fractional Clapper-Yule prediction model, so that the spectral reflectivity corresponding to the area ratio of the mesh point can be predicted.
Step 6, verifying the accuracy of the branched Clapper-Yule prediction model; the established branched Clapper-Yule prediction model is used for predicting the spectral reflectances of other single-color dots, the spectral values obtained by the prediction model are converted into Lab values through a colorimetry formula, and compared with the actual Lab values, the accuracy of a color difference test model is calculated, and the method is specifically as follows:
lab values are calculated using a correlation colorimetry formula, shown in formulas (12) (13), and a CIE1976 LaBcolor difference formula, shown in formula (14):
wherein X, Y, Z is the tristimulus value of the color sample, k is the normalized coefficient,is the tristimulus value of standard chromaticity observer, < >>Lambda is the wavelength, 380-780nm, as a function of spectral power distribution.
Wherein the method comprises the steps of
Wherein X is n 、Y n 、Z n Is CIE standard illuminant tristimulus value, L * For psychometric lightness, a * 、b * Is psychometric in chromaticity.
Wherein DeltaL * 、Δa * 、Δb * Respectively two colors are in L * 、a * And b * The difference in the three channels, Δe, represents the color difference between the two colors.
The invention has the beneficial effects that the gravure extinction film spectrum prediction model is built based on the branched Clapper-Yule prediction model, the multiple internal reflection of light between the extinction film and the printing ink is explored, the branched coefficient is connected with the dot area rate, the gravure extinction film spectrum prediction model with simple operation is provided, and a theoretical basis is provided for extinction film spectrum prediction.
Drawings
FIG. 1 is a single color chromatograph employed in the present invention;
FIG. 2 is a graph showing an example of multiple internal reflections of light between a matting film substrate and ink in accordance with the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
Example 1
The gravure extinction film spectrum prediction method based on the branched Clapper-Yule prediction model provided by the invention is implemented according to the following steps:
step 1, sample design and output:
uniformly sampling from 5% of the dots with the dot area rate of 10% as a step length to generate monochromatic chromatograms in the dot area rate of 0% -100%, as shown in figure 1; the printing material is a extinction film, the printing mode is gravure printing, and the printing is performed to print a sample and output monochromatic chromatograph;
step 2, measuring chromatographic spectral reflectance data:
and obtaining monochromatic chromatographic spectral reflectivity data by using a desk-top spectrophotometer under the condition of a D65 light source and a 10-degree view field.
Step 3, establishing a spectrum prediction model suitable for the extinction film based on a Clapper-Yule model, and determining model parameters;
the phenomenon of multiple internal reflection of light between the extinction film and the ink was analyzed, and based on the conventional Clapper-Yule model, the characteristics of the extinction film were adjusted and optimized as shown in fig. 2:
a beam of light is transmitted through the extinction film (T is set x For the transmittance of the matting film) into the ink layer, let a denote the dot area ratio of the monochromatic ink, the probability of light passing through the monochromatic ink into the priming white ink is a, and the probability of light directly entering the priming white ink is (1-a).
When a beam of light with the intensity of unit energy is incident on the interface between the air and the printed matter, the first surface reflectivity at the interface between the air and the extinction film is set as r s Let K denote the part of the reflected light that reaches the spectrometer, the light reflected by the front surface is:
R 0 ＝K·r s (1)
only (1-r) s ) The light transmittance of (2) is T x Let a denote the area ratio of the single-color ink dots, the probability of light passing through the single-color ink to enter the priming white ink is a, the probability of directly entering the priming white ink is (1-a), the sum of the two light is the light entering the ink layer for the first time, and the size is:
r 1 ＝(1-r s )·T X ·[a·T w ·T Y +(1-a)·T w ] (1)
after the light continues to be reflected off the substrate, a portion of the light enters the matting film from the ink layer and a portion is reflected offOil is injected back to the ink, and the reflectivity at the interface of the extinction film and the ink is r m There are (1-r) m ) Part of light enters the extinction film from the ink layer and finally exits, and r is the number m Part of the light is reflected back. The light intensity of the first light emitted from the surface of the printing product is as follows:
R 1 ＝(1-r s )·(1-r m )·T X 2 ·[a·T w ·T Y +(1-a)·T w ] 2 (2)
r m after part of the light is reflected back, the propagation process of the light entering the ink for the first time is repeated, and the light intensity emitted from the printing product for the second time can be obtained by the same method as the following:
R 2 ＝(1-r s )·(1-r m )·T X 2 ·[a·T w ·T Y +(1-a)·T w ] 2 ·r m ·[a·T w 2 ·T Y 2 +(1-a)·T w 2 ] (3)
the light intensity emitted from the surface of the printing product for the nth time can be obtained by the same method:
R n ＝(1-r s )·(1-r m )·T X 2 ·[a·T w ·T Y +(1-a)·T w ] 2 ·r m (n-1) ·[a·T w 2 ·T Y 2 +(1-a)·T w 2 ] (n-1) (4)
considering light 0,1, 2..after n internal reflections, the spectral reflectance can be obtained by combining all reflected light:
R＝K·r s +R 1 +R 2 +…+R n (5)
the properties of the array of equal ratios can be used to obtain:
wherein R is the spectral reflectance of the color to be predicted, a is the area ratio of the dots of the ink, K is the proportion of specular reflection light which can be detected, and R s For the reflectivity at the air-print interface, r m To extinction film base and reflectivity at ink interface, T x T is the transmittance of the extinction film w Backing white Mo Toushe rate for inner print, T Y To the color ink transmittance that needs to be predicted.
Bringing the spectral reflectances R0 of a=0 and 0% dot area ratio into formula (1), calculating the transmittance T of the priming white ink w 。
Bringing the spectral reflectances R100 of a=1 and 100% dot area ratio into equation (1), calculating the predicted color ink transmittance T Y 。
Step 4, combining the path theory with a Clapper-Yule model to establish a path Clapper-Yule prediction model, and calculating the value of a path coefficient b (lambda);
in order to improve the prediction precision of the model, a separation theory is introduced into the established Clapper-Yule model, the incident light with the probability of b enters and exits from the same ink dot region or enters and exits from the same non-dot region through one or more internal reflections, and the short-range propagation of the incident light can be described by the formula (9):
while the incident ray with probability (1-b) still proceeds in length Cheng Chuanbo in the halftone print in the manner described by the classical Clapper-Yule model. A branched Clapper-Yule prediction model suitable for the spectrum prediction of the extinction film printed matter is established in this way, and the model is shown as a formula (10):
wherein the partition coefficient b is between 0 and 1.
The corresponding coefficients of the pass were solved for by spectral reflectance data corresponding to other known dots (a=5%, 15%, 25%..95%).
Step 5, determining a path-dividing coefficient b (lambda) corresponding to the area rate of the net point to be predicted by using an interpolation method, and applying the path-dividing coefficient b (lambda) to an established path-dividing Clapper-Yule prediction model;
in order to predict the spectral reflectance of a certain dot area rate y, first, two dot area rates closest to the dot area rate in the measured data are found and marked as x and z.
The path-division coefficient b according to the two dot area ratios x and z x (lambda) and b z (lambda) calculating the path-division coefficient b of the dot area ratio to be predicted by interpolation y (lambda) is as in formula (21):
the path-division coefficient b obtained by interpolation y And (lambda) and the area rate y of the mesh point to be predicted are brought into an established branched Clapper-Yule prediction model, so that the spectral reflectivity corresponding to the area rate of the mesh point can be predicted.
Example 2
The method also comprises a step 6 of verifying the accuracy of the spectrum prediction model;
and predicting the spectral reflectivities of other single-color dots by using the established prediction model, converting the spectral value obtained by the prediction model into a Lab value by using a colorimetry formula, and comparing the Lab value with the actually measured Lab value to calculate the accuracy of the color difference test model.
Lab values are calculated using a correlation colorimetry formula, shown in formulas (12) (13), and a CIE1976 LaBcolor difference formula, shown in formula (14):
wherein X, Y, Z is the tristimulus value of the color sample, k is the normalized coefficient,is the tristimulus value of standard chromaticity observer, < >>The bit is wavelength, 380-780nm, as a function of spectral power distribution.
Wherein the method comprises the steps of
Wherein X is n 、Y n 、Z n Is CIE standard illuminant tristimulus value, L * For psychometric lightness, a * 、b * Is psychometric in chromaticity.
Wherein DeltaL * 、Δa * 、Δb * Respectively two colors are in L * 、a * And b * The difference in the three channels, Δe, represents the color difference between the two colors.
Example 3
The process of establishing the gravure extinction film spectrum prediction model based on the branched Clapper-Yule prediction model is specifically described by taking actual gravure extinction film spectrum prediction as an example. Take the example of printing cyan in the three primary colors.
Step 1, sample design and output:
uniformly sampling and designing monochromatic chromatograms (comprising 0% of dots and 100% of dots) by taking the dot area rate of 10% as a step length from 5% of dots, as shown in fig. 1; selecting a gravure printing mode and an inner printing process, wherein the printing material is BOPP extinction film, east ocean gravure ink is used as experimental ink, and a three positive fine machine gravure proofing machine is used for real proofing and outputting a sample.
Step 2, measuring monochromatic chromatographic spectral value data;
measuring the spectrum value of the monochromatic chromatograph by using a desk-top spectrophotometer under the condition of a D65 light source and a 10-degree view field, wherein the spectrum value is shown in a table 1;
table 1 single color ladder ruler spectrum data example
Step 3, establishing a spectrum prediction model suitable for the extinction film based on a Clapper-Yule model, and determining model parameters;
analyzing the phenomenon of multiple internal reflection of light between the extinction film and the printing ink, adjusting and optimizing the characteristics of the extinction film based on a traditional Clapper-Yule model, and establishing a Clapper-Yule model suitable for the extinction film:
where R is the color spectral reflectance to be predicted, K represents the proportion of specular reflected light that can be detected, since the measurement is performed using a bench spectrophotometer, k=1, R is taken s For reflectivity at the interface of air and printed matter, refer to the related literature and take r s ＝0.05，r m For reflectivity at the interface of the extinction film base and the ink, refer to the related literature and take r m ＝0.6，T x For the transmittance of the extinction film, the extinction film transmittance T can be obtained by measurement x Is 31-dimensional data related to wavelength, T w Backing white Mo Toushe rate for inner print, T Y To the color ink transmittance that needs to be predicted.
Bringing the spectral reflectances R0 of a=0 and 0% dot area ratio into formula (1), calculating the transmittance T of the priming white ink w 。
Bringing the spectral reflectances R100 of a=1 and 100% dot area ratio into equation (1), calculating the predicted color ink transmittance T Y 。
Step 4, combining the branch theory with a Clapper-Yule model to establish a branch Clapper-Yule prediction model, and calculating the value of a branch coefficient;
introducing a path theory into the established Clapper-Yule model, wherein incident light with the probability of b enters and exits from the same ink dot region or enters and exits from the same non-dot region through one or more internal reflections, and the short-range propagation of the incident light can be described by the following formula (9):
while the incident ray with probability (1-b) still proceeds in length Cheng Chuanbo in the halftone print in the manner described by the classical Clapper-Yule model. A branched Clapper-Yule prediction model suitable for the spectrum prediction of the extinction film printed matter is established in this way, and the model is shown as a formula (10):
wherein the partition coefficient b is between 0 and 1.
Equation (5) is a finally established prediction model, and the newly added parameters are a part-way coefficient b and a correction parameter omega of the model, wherein the part-way coefficient is obtained through the step (5), and the correction parameter omega=0.5 is obtained through multiple experiments.
Step 5, selecting 10%, 20%, 30%,. 80%, 90% dot area rate as dot area rate to be predicted, and determining a path-dividing coefficient b of dot area rate to be predicted by interpolation method (11) 10 (λ)、b 20 (λ)、b 30 (λ)、...、b 80 (λ)、b 90 (λ0。
b y (λ0 is the part-way coefficient of the dot area rate y to be predicted, x and z are the two dot area rates closest to the predicted dot area rate, the part-way coefficient b to be obtained by interpolation y By applying (lambda) to the established fractional Clapper-Yule prediction model pattern (1), the spectral reflectivity corresponding to the dot area ratio can be predicted. Table 2 is the spectral reflectance data predicted using the predictive model.
Table 2 predicted values of spectral data
Step 6, verifying the accuracy of the spectrum prediction model;
spectral values of 10%, 20%, 30%, 80%, 90% dot area rate were predicted using a predictive model, as in table 1. Then, the Lab value is calculated by a colorimetry formula, and the color difference is compared with the measured Lab value by a color difference formula, and the result is shown in Table 3:
TABLE 3 model color differences
The result shows that the color difference delta E of the prediction model is smaller than 1NBS, meets the national standard requirement, and shows that the prediction precision of the branched Clapper-Yule prediction model is higher.
Claims (7)
1. The gravure extinction film spectrum prediction method based on the branched Clapper-Yule prediction model is characterized by comprising the following specific operation steps:
step 1, uniformly sampling any single color within the area ratio of 0-100%, generating a single color spectrum, and printing the single color spectrum on a extinction film by using gravure printing;
step 2, measuring spectral reflectance data of the monochromatic chromatograph;
step 3, establishing a branched Clapper-Yule prediction model applicable to the extinction film based on a Clapper-Yule model and combining a branched theory, and determining a branched coefficient corresponding to model parameters and known dot area rate;
step 4, determining a branch coefficient b corresponding to the dot area rate y to be predicted by using an interpolation method and the branch coefficient corresponding to the known dot area rate y And (lambda) and applying the lambda to the established fractional Clapper-Yule predictive model to predict the spectral reflectivity corresponding to the area ratio of the mesh point.
2. The gravure extinction film spectrum prediction method based on the branched Clapper-Yule prediction model according to claim 1, wherein in step 1, the specific generation step of the monochromatic chromatograph is as follows: selecting any single color, and uniformly sampling and designing to obtain a single color spectrum by taking a dot area rate of 10% as a step length from 5% of dots, wherein the single color spectrum comprises 0% of dots and 100% of dots; and the printing mode of the inner printing is adopted for proofing output.
3. The method for predicting the spectrum of a gravure extinction film based on a branched Clapper-Yule prediction model according to claim 1, wherein the branched Clapper-Yule prediction model suitable for the spectrum prediction of an extinction film print in step 3 is as shown in formula (10):
wherein R is the color spectral reflectance to be predicted, and K is the specular reflectance that can be detectedLight proportion, r s For the reflectivity at the air-print interface, r m To extinction film base and reflectivity at ink interface, T x T is the transmittance of the extinction film w Backing white Mo Toushe rate for inner print, T Y For the color ink transmittance to be predicted, a represents the dot area rate; b represents a part-way coefficient; omega is the model parameter and is 0.5.
4. The method for predicting spectrum of gravure extinction film based on the branched Clapper-Yule prediction model as claimed in claim 3, wherein the inner printing backing white Mo Toushe rate T w Color ink transmittance T to be predicted Y The specific calculation is as follows:
wherein R0 is the spectral reflectance of 0% dot area;
wherein R100 is the spectral reflectance of 100% dot area.
5. The gravure extinction film spectrum prediction method based on the branched Clapper-Yule prediction model according to claim 3, wherein the calculation of the branched coefficient corresponding to the known dot area ratio in the step 3 is specifically as follows:
the corresponding part-range coefficients are solved for the known dot area ratios a=5%, 15%, 25..95% and the corresponding spectral reflectance numbers in step 2.
6. The method for predicting spectrum of gravure extinction film based on branched Clapper-Yule predictive model as recited in claim 4, wherein a branched coefficient b corresponding to a dot area rate y to be predicted is determined in step 4 y The calculation of (λ) is specifically as follows:
in order to predict the spectral reflectivity of a certain dot area rate y, firstly, finding out two known dot area rates closest to the dot area rate in the measured data, and marking as x and z;
in step 3, the corresponding part-range coefficients of the known dot area rate have been solved, and the part-range coefficients b according to the two known dot area rates x and z x (lambda) and b z (lambda) calculating the path-division coefficient b of the dot area ratio to be predicted by interpolation y (lambda) is as in formula (6):
the path-division coefficient b obtained by interpolation y And (lambda) is applied to the established fractional Clapper-Yule prediction model, so that the spectral reflectivity corresponding to the area ratio of the mesh point can be predicted.
7. The gravure extinction film spectrum prediction method based on the branched Clapper-Yule prediction model according to claim 1, further comprising a step 6 of verifying the accuracy of the branched Clapper-Yule prediction model; the established branched Clapper-Yule prediction model is used for predicting the spectral reflectances of other single-color dots, the spectral values obtained by the prediction model are converted into Lab values through a colorimetry formula, and compared with the actual Lab values, the accuracy of a color difference test model is calculated, and the method is specifically as follows:
lab values are calculated using a correlation colorimetry formula, shown in formulas (12) (13), and a CIE1976 LaBcolor difference formula, shown in formula (15):
wherein X, Y, Z is the tristimulus value of the color sample, k is the normalized coefficient,is the tristimulus value of standard chromaticity observer, < >>Lambda is wavelength, 380-780nm, which is a spectral power distribution function;
wherein the method comprises the steps of
Wherein X is n 、Y n 、Z n Is CIE standard illuminant tristimulus value, L * For psychometric lightness, a * 、b * For psychometric chromaticity;
wherein DeltaL * 、Δa * 、Δb * Respectively two colors are in L * 、a * And b * The difference in the three channels, Δe, represents the color difference between the two colors.
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