A simplified method of predicting the colorimetry of spot color overprints

Although methods exist for predicting the color of a spot color ink when it overprints another ink, there is a need for a simplified model for the purpose of previewing that can be used during document creations. The proposed model characterizes each spot color individually and predicts the color of overprinting solids and halftones by linearly combining the reflectances of two colors. Each ink is defined separately in terms of its opacity, and relatively few measurements are required to predict the resulting color of the overprint. The model was evaluated for three different substrates. A 6color test chart, containing a total of 4550 patches of different combinations of C, M, Y, K and two spot colors, was printed using the offset printing process. The overprint model was applied to predict the resulting colors. Model predictions were compared to the measured data in terms of ∆L*, ∆a*, ∆b* and CIEDE2000. Average CIEDE2000 values between the measured and predicted colors were found to be below 3, for both the spot colors on all papers. Introduction Printing uses four process inks, CMYK. In some industries, additional inks are used, for example to print critical brand colors. These are known as spot colors or special inks. Colors printed by a combination of process inks and spot colored inks can be characterized by means of an ICC profile. However, it is not practical to print a profile target and generate an ICC profile for all inks in combination. This makes it difficult to predict the effect of overprinting spot colors onto process inks or other spot colors, whereas in a color reproduction workflow it is important to have a preview or proof of the anticipated color. Spectral printer models are available for characterizing the four-color printing system. These models try to depict the complex interaction between light, paper and ink. Some of these models include: Kubelka-Munk model, Yule-Nielsen modified Neugebauer model [1], Van De Capelle and Meireson model patented by EskoArtwork [2][3], Enhanced Yule-Nielsen modified Neugebauer (EYNSN) model to account for ink spreading in different ink superposition conditions [4][5]. Although these models were not developed for spot colors, they can be used to predict the color of ink combinations of spot colors. Some of these models require extensive number of inputs and optimization process. Furthermore, these are relatively complex models and they cannot be easily integrated into the existing standards like ICC profiles and PDF/X. YNSN model requires to print all combinations of primary inks. For a 6-ink printing system, it needs 64 color patches. The packaging industry uses a large number of spot colors. For example, one sample library contains 1114 spot colors, and it is not practical to print and measure all possible combinations of these inks. Here a simple numerical method for estimating the colorimetry of spot color overprints is described. This method does not necessarily generate a more accurate prediction than existing methods, but simply provides a simplified method that can be easily implemented and that is free of existing intellectual property. Method A 6-color test chart (Fig.1) was designed to evaluate the model, which is described in the next section. The Basic set of the IT8.7/3 CMYK chart,, consisting of 182 color patches, was selected to represent the background objects. Two spot colors, Pantone 157C and Pantone 330C, were printed in addition to Cyan, Magenta, Yellow and Black inks. On each of the 182 patches of CMYK, different combinations of spot colored inks (0%, 25%, 50%, 75% and 100%) were printed. Thus, for each CMYK basic color, there were 25 combinations resulting in a total of 4550 patches. Figure 1. Fraction of the 6-color test chart To define each spot colored ink individually, an ink characterization chart was used. This consists of ramps of inks from 0% to 100% printed over the substrate, over the grey backing (50% black ink) and over the black backing (solid black ink). Figure 2. Ink characterization chart for Spot Colour2 (Pantone 330C) Thus there were three similar ramps consisting of 11 steps, printed over white (i.e. Substrate), grey and black backings. This is similar to Van De Capelle's method [2]. Spectral measurements of 18th Color Imaging Conference Final Program and Proceedings 213 the ink characterization chart provide ink reflectance characteristics transparency. Printing process used in this study was the Offset printing process on three different substrates: Mitsubishi Paper MYU Coat NEOS, Hokuetsu Paper Pearl Coat N and Nihon Paper Be-7. Toppan standard inks were used with the following sequence: K – C – M – Y – Spot Colour1 (PMS 157C) – Spot Colour2 (PMS 330C). The test charts and ink characterization charts were measured according to ISO 13655:2010 measurement condition M0 using an X-Rite SpectraScan. The ink characterization chart is used to calculate the coefficients of the model. Model predictions were compared to the measured tristimulus values of color patches. The proposed model is compared to following existing models: Kubelka-Munk with Saunderson correction, YNSN model, Van De Capelle model. These models were applied for the above mentioned 6-ink printing system. Proposed Overprint Model The overprint model is used to predict colors resulting from combinations of special inks, which includes solid overprints as well as halftone overprints. The assumption made in this method is that at each wavelength the reflectance factor of an overprint approximates the product of the reflectance factors of the two inks measured independently. When this reflectance product is modified by a scaling constant, the approximation is often a good prediction of the actual reflectance. Since XYZ is a linear transform of reflectance, the same approach can be adopted for XYZ tristimulus values. In the overprint model, each ink is characterized separately. This is done by printing a solid ink and its tints on three backings – plane substrate (white), grey and solid black. Spectral measurements of these patches are used to derive the coefficients of the model (scaling factors and constants) for each spot colored ink by linear regression. Where a spot color is printed over another color, the firstprinted underlying color is considered as a background object and the overprinted spot color as a foreground object. The overprint model assumes that a resulting color (Xr, Yr, Zr) is correlated to the product of the background color (Xb, Yb, Zb) and foreground color (Xf, Yf, Zf). The resulting color (Xr, Yr, Zr) is predicted as follows: Xr = jx × (Xb × Xf) + kx Yr = jy × (Yb × Yf) + ky Zr = jz × (Zb × Zf) + kz (1) where [Xb Yb Zb]: tristimulus values of background color [Xf Yf Zf]: tristimulus values of foreground color [jx jy jz]: Scaling factors [kx ky kz]: Constants As seen in Eq. (1), linear regression is used to model the relationship between the resulting color (Xr, Yr, Zr) and the products of the background and foreground colors. Scaling factors and constants are calculated from the ink characterization chart using Equation (1). Color patches on all three backings (white, grey and black) are measured and used as the resulting color (Xr, Yr, Zr) in Equation (1). The foreground color for each patch is obtained from the tints of ink on white backing. Background color for each patch is extracted from the black ink characterization chart. A least squares method was sufficient to derive the scaling factors (jx, jy, jz) and constants (kx, ky, kz). In case of 2-inks overprint (say 40% Spot1 and 30% Spot2), the background color is the first color printed on the substrate (40% Spot1) and the foreground color is the second color (30% Spot2) printed after the first color. These are obtained from the ink characterization charts (tints printed on the white backing). The missing dot percentages are derived by interpolating the existing measurements. For a printing system of multiple spot inks printed on top of each other, Eq. 1 can be applied recursively to predict the resulting color of any given combinations of inks. There is no need to measure overprints of different combinations of inks; we only have to characterize each ink individually. In a color managed workflow, the tristimulus values of background color (made of C, M, Y, K ink-combinations) can be calculated using the A2B tag of the output intent ICC profile. Tristimulus values of the foreground color (i.e. Spot colored ink) can be derived from the measurements of the ink characterization chart (colors on the white backing). Tristimulus values of the resulting color (Xr, Yr, Zr) are predicted by applying Eq. 1. Finally the B2A tag of ICC profile can be used to estimate the colorant percentages. Results Figure 3 shows the relationship between the measured colors (X, Y, Z) and the variable terms in Eq. 1. Variable term products, for example (Xb * Xf ) are plotted against the measured values of X, Y and Z. This is for Nihon Paper Be-7 and combinations of CMYK (background color) + Spot Color1(foreground color). Figure 3. Linear regression between the measured X, Y, Z and the variable terms in Equation (1) 214 ©2010 Society for Imaging Science and Technology There is clearly a strong linear relationship. It means that the resulting color can be derived by a simple linear regression method. Table 1 shows the color difference values between the predicted and the measured colors for CMYK + Spot Color1 combinations on Nihon paper Be-7. All CIEDE2000 values are below 3. It can be seen that ∆a* values have contributed the most to color difference values. Table 1. Overall accuracy of the overprint model for Spot Color1 Color difference results for CMYK + Spot Color2 combinations on the same substrate are given in Table 2. Accuracy achieved is similar to that for Spot Color1. Table 2. Overall accuracy of the overprint model for Spot Color2 A histogram of CIEDE2000 values is shown in Figure 4. This is for MYU Coat Paper and combinations of CMYK and Spot Color1. Most of the values are below 5. Despite being a simple linear model, it gives relatively good accuracy. Figure 4. Histogram of CIEDE2000 for CMYK + Spot1 on Nihon Paper Be-7 Table 3 shows the scaling factors (jx, jy, jz) and constants (kx, ky, kz) for the Nihon Paper Be-7 are shown for each spot colored ink. For the given paper, scaling factors remain the same, but constants are changing. Table 3. Scaling factors and constants for Spot1 and Spot2 inks: Paper Be-7 To further investigate the robustness of scaling factors and constants, the overprint model was applied separately to different dot percentages of spot color, for example, 25%, 50%, 75% and 100%. Table 4 shows the accuracy for these dot percentages for the paper MYU coat NEOS and Spot Color1. Table 4. Accuracy of the overprint model for different dot percentages of Spot