The Clapper-Yule model is a physically based model describing the reflection of spectral light fluxes by a printed surface and enabling the prediction of halftone prints on diffusing substrates . The model relies on a closed-form equation obtained by describing the multiple transfers of light between the substrate and the print-air interface through the inks. Physical parameters are attached to the inks, the diffusing support, and the surface. The model assumes that the lateral propagation distance of light within the substrate, due to scattering, is much larger than the halftone screen period. Most photons therefore cross different ink dots while traveling in the print. The reflections and transmissions of light at the surface are explicitly taken into account depending on the print’s refractive index, as well as the considered illumination and measuring geometries.
The Clapper-Yule Equation
Fresnel Terms and Measuring Geometries
Calibration of the Model and Prediction
Improved Ink Spreading Assessment Method
In order to assess the prediction accuracy of the model, predicted and measured spectra may be compared on sets of printed colors. As comparison metric, one generally uses the CIELAB ΔE94, obtained by converting the predicted and measured spectra first into CIE-XYZ tristimulus values, calculated with a D65 illuminant and in respect to a 2° standard observer, and then into CIELAB color coordinates using as white reference the spectral reflectance of the unprinted paper illuminated with the D65 illuminant.
Because it assumes that the lateral propagation of light is large compared to the halftone screen period, the Clapper-Yule model is theoretically restricted to halftones with high screen frequency. For example, the model tested on two sets of 729 CMY colors printed with the same offset press on the same paper but at different frequencies, respectively, 76 and 152 lines per inch (lpi), provides better predictions for the highest frequency (average ΔE94 of 0.98 unit) than for the lowest one (average ΔE94 of 1.26 unit). Nevertheless, the experience shows that the model may also perform well for middle and low frequencies: For a set of 40 CMY colors printed in ink-jet at 90 lpi on supercalendered paper, the model achieves a fairly good prediction accuracy, denoted by the average ΔE94 of 0.47 unit. Note that the average ΔE94 is 0.70 unit when the ink superposition conditions are not taken into account in the ink spreading assessment.
Despite the simplicity of its base equation, the Clapper-Yule model is one of the most accurate prediction models for halftone prints. Its main advantage compared to other models such as the Neugebauer model or the Yule-Nielsen-corrected Neugebauer model is the fact that physical parameters are attached to the different elements composing the print (inks, paper, and surface). The Fresnel terms can be adapted to the considered measuring geometry, which is particularly interesting when predictions are made for a geometry different from the one used for calibration. The model also enables controlling ink thickness at printing time by comparing the colorant transmittances in various halftones, whose log is proportional to the ink thickness . Recent improvements and extensions have been proposed which enable predicting both reflectance and transmittance of halftone prints thanks to extended flux transfer model relying on similar physical concepts as the Clapper-Yule model [6, 7].
- 3.Rossier, R., Bugnon, T., Hersch, R.D.: Introducing ink spreading within the cellular Yule-Nielsen modified Neugebauer model. In: IS&T 18th Color Imaging Conference, San Antonio, TX, USA, pp. 295–300 (2010)Google Scholar