The gonio-chromatic attributes of optically variable ink (OVI) lead to its extensive applications in anti-counterfeit printing, such as confidential documents, banknotes, and packaging products. Products printed with this ink exhibit a notable color-changing effect when observed from various angles. Although current color measurement standards specify a large number of measurement geometries, there is a lack of research on assessing the efficacy of these conditions for OVI. Consequently, manufacturers rely on subjective evaluations for determining the color-changing effects of OVI, resulting in substantial uncertainty in the quality control of anti-counterfeit products. Thus, it is imperative to conduct a systematic study on the color measurement methods of OVI to accurately capture the color-changing effects of OVI.

We employ different color measurement instruments to test measurement geometries on 22 OVI samples, supplied by ink manufacturers. The employed measurement geometries are extensively adopted for gonio-apparent object characterization, following the notation stipulated in the ASTM E2539-14. Initially, the OVI microstructure is observed at 400× magnification using a 3D laser confocal microscope, and images are captured by a Canon EOS 760D camera in measurement geometries of 45°:-60° (as-15°), 45°: -30° (as15°), 15°: -30° (as-15°), 15°: 0° (as15°). Then, the X-Rite MAT12 multi-angle spectrophotometer is leveraged to measure the spectral power distributions and chromaticities of the samples in 12 geometries. These results are utilized for evaluating the geometries recommended by international standards. Finally, the influence of measurement variables α and β on OVI chromaticity is investigated by customizing 28 different geometries using an R1 angle-resolved spectrometer to find the optimal measurement geometries for OVI.

Images captured in four measurement geometries using a 3D laser confocal microscope and a Canon EOS 760D are compared with the color-changing effects labeled by manufacturers (Fig. 5). Results demonstrate that the r45as45 and r45as-15 geometries in GB/T 17001.7—2023 do not correspond well with the named samples. However, the color changes between the r15as15 and r45as-15 geometries show a better correlation with their designated names. The measurement results from the X-Rite MAT12 indicate that due to the gonio-chromatic characteristics of OVI, there are notable differences in the spectral power distribution of different measurement geometries (Fig. 6). The chromaticities of the samples under multiple measurement geometries are calculated by D65/10° and compared in CIE 1976 a^*b^* diagrams (Fig. 7). The hue changes between the r15as15 and r45as-15 geometries are more obvious than r45as45 and r45as-15 in GB/T17001.7—2023. By utilizing the R1 angle-resolved spectrometer with customized α and β variables, the α angle is set at 5°/15°, β varies from 5° to 135°, and the spectral energy of eight samples is collected. The calculated chromaticities indicate that with a constant β angle, the sample saturation decreases when the α angle increases from 5° to 15°, with unchanged hue (Fig. 9). Furthermore, polynomial regression is employed to analyze the relationship between the β angle and saturation C^* (Fig. 10). The geometries 5°:0° (as5°), 45°:-40° (as5°), and 60°:-55° (as5°) best characterize the range of hue changes in OVI.

We primarily report on the color measurement results of OVI samples for a range of measurement geometries and derive three key findings. First, the colorimetric properties observed in the 15°:0° (as15°) and 45°:-60° (as-15°) measurement geometries align with the color-changing effects designated for OVI by ink manufacturers. These geometries enable to capture a more extensive range of hue variations in OVI. Second, the color measurements of OVI samples using the R1 angle-resolved spectrophotometer based on the customized α and β measurement conditions reveal that smaller α angles correspond to higher saturation levels with little effect on hue, while β angles influence both hue and saturation. Finally, the measurement geometries outlined in ASTM E2539-14 are insufficient to cover the maximum hue and saturation change ranges for OVI. The β angle ranging from 5° to 115° is identified to cover the maximum range of hue changes. Meanwhile, the highest saturation is found at measurement geometries of α=5° and β=85°. Therefore, the measurement geometries 5°:0° (as5°), 45°:-40° (as5°), and 60°:-55° (as5°) are found to effectively represent the hue and saturation changes in OVI.