[0065] The present invention will be described in detail below with reference to the drawings and specific embodiments.
[0066] The present invention provides a color matching method for printing spot colors based on absorption spectrum. The process is as follows figure 1 As shown, follow the steps below:
[0067] Step 1. Choose a white printing material as the printing base of primary color ink for standardization of primary color ink;
[0068] Step 2. Standardization of primary color ink:
[0069] Primary color ink standardization is to calibrate and convert primary color ink into primary color ink used for formula calculation and color matching. The specific method of primary color ink standardization is:
[0070] Dilute the n primary color inks and diluents according to a certain ratio, print the color sample scales with different dilution rates of the primary color ink on the printing material selected in step 1, and measure the L* of the different dot area ratios under different dilution ratios a*b*chromaticity value, and then construct the 3D model of the primary color ink in the L*a*b* coordinate system, and select the dilution ratio with the dot area ratio at the starting position of the linear trend as 100% as the primary color ink for color matching, namely Obtain n kinds of base color inks.
[0071] Ideally, as the diluent increases and the dot area ratio of an ink decreases, the brightness, hue, and saturation of the color are linearly transformed, and the distribution of chromaticity coordinate points in the 3D model is straight. The more diluent or dot area The lower the rate, the closer the color is to white. Such as figure 2 Shown. In actual operation, because the ink concentration is too high, the hue will have a non-linear change, which directly affects the color matching accuracy. In order to avoid this effect, the dilution ratio with the dot area ratio at the starting position of the linear trend is selected as 100%. Base color ink for color matching.
[0072] Step 3. Print the n base color inks obtained in step 2 on the black and white two-color substrate, and measure the spectral reflectance of the black and white substrate and the solid color blocks of the n primary color inks under the black and white substrate. The spectral reflectance of 2n+2 groups is obtained.
[0073] Step 4. Use the 2n+2 set of spectral reflectance in step 3 to calculate the spectral reflectance and spectral transmittance of the primary color ink. The specific calculation method is:
[0074] When light propagates in two layers of media, the propagation path is like image 3 Shown. Define the reflectivity of the upper medium as R p , The transmittance is T p , The absorption rate is A p , The reflectivity of the underlying medium is R q , The transmittance is T q , The absorption rate is A q , Considering the multi-layer internal reflection of light in the medium, there are:
[0075] When incident light enters the upper medium, the upper medium will first reflect the light once, which is R p , The remaining light entering the upper medium and the light transmitted into the lower medium is T p , Part of the light reaching the underlying medium is transmitted out to form T p T q , Another part of the light is reflected back to the upper medium, which is T p R q , Enter the upper medium T p R q The light is divided into the upward transmission to form T p R q T p And T downstream into the underlying medium p R q R p Two parts, T into the underlying medium p R q R p Light or downward transmission forms T p T q R q R p , Or continue upward to enter the upper medium, the light entering the upper medium is T p R q 2 R p , The amount of light transmitted through the surface of the medium is T p T p R q 2 R p , And the light traveling downward in the medium continues, and so on.
[0076] Due to the absorption and influence of light by substances in the medium, reflectance and transmittance can be calculated indirectly by the following formula:
[0077] Define the total reflectance of the incident light on the same side as R pq , The total transmittance of the opposite side is T pq , Then:
[0078] R pq =R p +R q T p T p (1+R p R q +…) (1)
[0079] Among them, (1+R o R q +...) is the common ratio R p R q The geometric sequence of, the sum can be:
[0080]
[0081] The same can be obtained,
[0082] T pq = T p T q (1+R p R q +…) (3)
[0083] which is
[0084]
[0085] Combining formula (2) and formula (4) can get:
[0086]
[0087]
[0088] Putting the spectral reflectance of the black and white printing material measured in step 3 and the field printing spectral reflectance data of a certain base color ink on different black and white bases into formula (2), we can get:
[0089]
[0090]
[0091] In printed matter, the upper medium is printing ink, and the lower medium is the printing material. In the formula, R p Is the ink spectral reflectance, T p Is ink transmittance, R w Is the spectral reflectance of the ink under the white substrate, R uw Is the spectral reflectance of the white printing material, R s Is the spectral reflectance of the ink under the black substrate, R us It is the spectral reflectance of the black substrate.
[0092] Combining formula (7) and formula (8), we can get the ink spectral reflectance R p for:
[0093]
[0094] Ink transmittance T p for:
[0095]
[0096] According to the above formulas (9) and (10), the spectral reflectance and spectral transmittance of n primary color inks can be calculated respectively.
[0097] Step 5. Select the sample color sample EX as the target spot color, measure the spectral reflectance of the target spot color and its substrate, and mark them as R ex , R 0;
[0098] Step 6, use the spectral reflectance of the n primary color inks obtained in step 4 to construct the calculated formula color TH, and establish a color matching model with the target spot color spectral reflectance in step 5:
[0099] In order to match the target spot color, it is necessary to calculate the spectral reflectance R of the formula color sample (TH) under the same lighting conditions th Spectral reflectance R with target spot color (EX) ex It is equal under the corresponding wavelength in the visible spectrum, namely:
[0100] R th (λ)-R ex (λ)=0 (11)
[0101] In analytical calculations, the residual sum of squares W is a quantity that evaluates the difference between the corresponding positions of the discrete data points and the regression points. The smaller the residual sum of squares of a set of data, the better the fit, that is, the best in a certain sense Approximately or fit the known data. When R th With R ex When the sum of the squares of the difference at each wavelength is the minimum value min, it can be considered that the spectral reflectance of TH is the closest to the spectral reflectance of EX, and the matching degree is the best, then there is
[0102] W=∑[R th (λ)-R ex (λ)] 2 =min (12)
[0103] Where W is the residual sum of squares of the spectral reflectance of EX and TH, R th (λ) is the spectral reflectance of the calculated formula color at wavelength λ, R ex (λ) is the spectral reflectance of the target spot color at wavelength λ.
[0104] When n kinds of base color inks are mixed to obtain the calculated formula color, considering the absorption characteristics of the base color, the mixed absorption of the base color inks has a proportional additive property:
[0105] a th =a 0 +c 1 a 1 +c 2 a 2 +...c n a n (13)
[0106] Where a th To calculate the absorption rate of the formula color, a 0 Is the absorption rate of the substrate, a 1 , A 2 ,..., a n Is the corresponding absorption rate of n primary color inks, c 1 , C 2 ,..., c n For the corresponding concentration when the n kinds of primary color inks are mixed, the formula (12) can be simplified as:
[0107]
[0108] Where c i Is the concentration of the i-th base color ink, a i Is the absorption rate of the i-th primary color ink.
[0109] According to the law of energy, the sum of transmitted, reflected and absorbed radiant flux must be equal to the incident radiant flux. Then the light irradiates the surface of the object, and the sum of the spectral reflectance R, transmittance T and absorptance A is 1, that is:
[0110] R+T+A=1 (15)
[0111] When the printing substrate is an opaque material, the influence of the transmission of the substrate on the color of the color material can be ignored, and the combination of formulas (14) and (15) can become:
[0112]
[0113] Where R 0 Is the spectral reflectance of the printing material measured in step 5, R i Is the spectral reflectance of the i-th base color ink, T i Is the transmittance of the i-th primary color ink.
[0114] Considering that the sum of the concentration of each primary color in the ink is 1, the simplified formula (16) can be obtained:
[0115]
[0116] Putting formula (17) into formula (12), the final form of the color matching model becomes:
[0117]
[0118] Using the spectral reflectance and spectral transmittance values of the base color ink calculated in step 4 and the spectral reflectance values measured in step 5, the formula (18) is solved for the minimum value, and the unique solution K=(c 1 , C 2 ,..., c n ), which is the best ratio of each primary color ink required to obtain the target spot color.
[0119] Since the premise of color matching is based on standardized base color inks, this method is not limited to a specific printing ink, but can be made into a new standard base color with differentiated ink raw materials for different manufacturers, thereby reducing production errors For the influence of formula calculation, the error caused by the viscosity and pigment concentration of the ink itself is eliminated at the same time. With the increase of the dilution rate of the base color ink, the higher the hue linearization rate, the higher the linearity of the mixed ink and the more accurate the formula. On the other hand, this method is not limited to the commonly used overprint primary colors cyan, magenta, yellow, and black when mixing inks. The base colors can be selected for color matching, which can better expand the color gamut of ink color matching.
[0120] The following is a specific example for description.
[0121] Step 1. Choose a white printing material as the printing base of the primary color ink for standardization of the primary color ink;
[0122] Step 2. Standardization of primary color ink:
[0123] Take the five primary color inks of cyan (C), magenta (M), yellow (Y), green (G), and orange (O) as examples. The primary color ink and thinner are respectively 100%, 68%, 47%, Dilute by 33% and 22%, print the color sample scales with different dilution rates of each primary color ink on the printing material selected in step 1, and measure the L of the 50%-100% dot area ratio under different dilution ratios * a * b * Chroma value, and then construct 5 kinds of primary color inks in L * a * b * The 3D model in the coordinate system. The dilution ratio of the dot area ratio at the starting position of the linear trend is 100% as the base color ink for color matching. In this experiment, we selected 33% cyan ink, 33% magenta ink, 47% yellow ink, 68% green ink and 68% orange ink as five basic color inks.
[0124] Step 3. Print the five basic color inks selected in step 2 on the black and white printing material, and measure the spectral reflectance of the black and white printing material and the spectral reflectance of the solid color block under the black and white printing substrate. , Get 10+2 sets of spectral reflectance. Use a spectrophotometer to collect the spectral reflectance with a wavelength of 400-700nm in the visible spectrum, with a sampling interval of 10nm.
[0125] Step 4. Calculate the spectral reflectance and spectral transmittance of the five primary color inks according to formulas (9) and (10).
[0126] The spectral reflectance curve of the base color ink is as follows Figure 4 Shown. It can be seen that different basic color inks have different reflection response areas to the spectrum, and different reflection curves can produce different color effects in the human eye. In the mixed color matching, with the change of the basic color ink addition ratio, more colors can be obtained.
[0127] Step 5. Select the sample color sample EX as the target spot color, measure the spectral reflectance of the target spot color and its substrate, and mark them as R ex , R 0; Use a spectrophotometer to collect the spectral reflectance in the visible spectrum with a wavelength of 400-700nm, with a sampling interval of 10nm.
[0128] Step 6, use the spectral reflectance of the five basic color inks obtained in step 4 to construct the calculated formula color TH, and establish a color matching model with the target spot color spectral reflectance in step 5:
[0129] Using the spectral reflectance and spectral transmittance values of the base color ink calculated in step 4 and the spectral reflectance values measured in step 5, solve the equation (18) to find the minimum value, and the boundary condition is 0≤c i ≤1 and ∑c i = 1, the only solution K = (0, 0, 0.05, 0, 0.95) can be solved, that is, yellow and orange are added in the ratio of 0.05: 0.95 to obtain the target spot color.
[0130] The matching result is like Figure 5 As shown, the figure shows the spectral reflectance curves of the base color ink yellow and orange, the formula color TH, and the target color EX under the white substrate. It can be concluded that the curve of the two colors must fall between the curves of the two primary colors. It is calculated that when the formula color and the target color are solved as K = (0, 0, 0.05, 0, 0.95), the residual sum of squares W of the two curves achieves the minimum value of 0.02. The two spectral curves are very close to a certain extent. Can express the same color on. The color difference between the two curves is calculated to be 2.13, which can meet the color matching needs.
[0131] Through the method proposed in this paper, the feasibility of using the absorption spectrum for gravure printing spot color matching is realized. In actual production, the color matching base color is not limited to 5 kinds, two or more base color formulas can be realized in the calculation. This method greatly reduces material waste, saves color matching time, and effectively improves color matching accuracy.
[0132] Due to differences in printing conditions, printing materials and light sources, two spectral reflectance curves with exactly the same color cannot be obtained. Using the spectral color matching method can reduce the influence of the light source and the substrate on the color matching, and obtain a matching spectral curve that is closest to the target curve. This method can obtain color matching inks with color differences that meet the production requirements.
