Figures 2–4 display chromaticity diagrams of individual R, G and B primaries for angles of incidence from 30∘ to 70∘ for varying angles of observation. To demonstrate angularly changing color characteristics, we plot x and y values distinguishing between angles of incidence. Coordinates measured in specular directions are connected with a red line. As can be seen from the displayed data, specular reflections are concentrated in the part of the diagram closest to the saturated R, G and B in the xy-diagram. At the same time, specular reflection at 30∘ incident direction provides the most saturated primary color. On the other hand, observation in normal direction to the surface normal will result in grayish color.

Halftoned patches were prepared with stochastic 50% area coverage for combinations of each two primaries, and with three primaries at 33% each (totally 100% area coverage). Given the color coordinates for individual primaries shown above, we demonstrate measured and predicted appearance of stochastic dot off dot combinations (on a black paper) at 30∘ illumination and viewing directions. We calculated predicted color coordinates and halftoned patches using the simple Neugebauer formula [5] and considering no interaction of the inks with the substrate. Figure 5 demonstrates resulting colors of individual patches and predicted color with a straightforward approach based on spectral reflectance of individual primaries. The measured colors appear darker due to the physical screen printed negative dot gain on the black substrate. Color difference values according to the CIEDE2000 standard [6] are demonstrated in Table I. Closer look into obtained color difference values suggest good estimation of LAB a∗ and b∗ values, and discrepancies are observed mainly in the lightness coordinate. We attribute this difference to the negative physical dot gain and slight misalignment of the individual screen printed dots, which is common for screen printing process in general.

After capturing BRDF of individual patches filled with primary color inks, we simulated color coordinates under the conditions of diffuse illumination. The values were computed by cosine weighted average of reflectance values obtained under corresponding incident illumination directions. Figure 6 demonstrates appearance of individual primaries under diffuse illumination in RGB color space representation. For the demonstration purposes, RGB values are displayed in rectangular images corresponding to the observation directions 0∘ (top of the image) to 70∘ (bottom of the image). Figure 7 shows chromaticity diagram of three primaries under diffuse illumination. For all three primaries xy-coordinates located closest to the saturated R, G and B correspond to the observation direction with angle 30∘ with the surface normal (marked with a filled circle in the figure). Based on the measured BRDF data, we conclude that the optimal angle for observing the colors produced by interference RGBW inks is around 30∘ with the surface normal. Solid black lines in Fig. 7 connectxy-coordinates of individual primaries demonstrating the gamut that is possible to obtain by employing such primaries. The only missing points are the colors of the Red primary ink under observation directions above 30∘. These values, however, lay farther away from the sRGB red primary. Numerical calculations for the ideal thin film of titanium dioxide and incidence angle [7, 8] do not suggest more saturated colors for angles of incidence below 30∘. Taking into account missing measured data, we conclude that optimal observation direction is between 20∘ and 30∘. As in the previous example, we also demonstrate appearance of halftoned patches under diffuse illumination and predicted appearance based on the individual reflectance spectra of the primaries, as shown in Figure 8. We compare measured color coordinates to the simulated based in terms of CIE dE2000 standard [6] for each observation direction, as shown in Figure 9. Increasing values of color difference between measured and calculated values most likely result from specular reflections from the substrate and edges of printed dots and are approached in the next section on the example of one primary printed with different area coverage and can be treated as angular-dependent dot gain.

In the case of blue primary ink, we estimated the angle-dependent dot gain. While during printing we could observe negative physical dot gain from the normal direction of observation, optical dot gain can propagate in a form of brighter appearance of the inks from oblique illumination and observation directions due to the present physical height of individual dots. We therefore estimate angle-dependent total dot gain expressed as effective area coverage by the blue ink. Here, we use CIEZ-value for the blue primary Zprimary obtained from reflectance values of the 100% covered patch, where the contrast between the printed primary and black paper is the highest (for red and green primary one should choose X and Y respectively). Comparison of Zmeasured measured and expected value of Zprimary coordinate is expressed as an effective area aeff (that in this case turns out to be higher than the nominal) [9] as: where Zbp corresponds to the Z-coordinate of the black paper.

We compared patches filled with 10–90% area coverage with simulated results under diffuse illumination. The comparison between measured results and calculated values in terms of spectral mixing is displayed in Figure 10.

As can be seen in the Fig. 10, the calculation results match the measurements really well for larger coverage of blue (patches on top) and not that well otherwise. The reason is that we have used the Z-values to estimate the effective coverage, corresponding to the shorter wavelength of the visible wavelength interval. One suggestion to improve the estimation is that instead of using only one dot gain characteristic curve based on Z-values, we use three different curves based on CIE X, Y and Z, as suggested in Ref. [10] or more rigorous estimation of angle-dependent reflectance properties based on the knowledge of surface micro- and macro roughness alignment of the pigments, and taking into account specular reflection from the print surface.