Clapper-Yule Model Research Articles

Simulating the composition and structuration of coloring layers in historical painting from non-invasive spectral reflectance measurements

Reflectance spectroscopy is a powerful non-invasive technique for determining the material composition of historical polychromies, since the measurement is fast, simple, and contactless. However, reflectance spectra of complex color mixtures can sometimes be hard to interpret from a compositional point of view. In these cases, theoretical optical simulations can provide useful additional data. The main issue is the choice of the optical model that must be adapted to the measurement protocol and the material structure of the coloring layer, this latter being generally unknown. Simple models based on analytical formulas are preferred, as they can be easily inversed to deduce the optical and structural properties of the materials from the measured spectral reflectance of the object. In this paper, we address this issue to investigate the material composition of the colors of the Codex Borbonicus, a 16th-century Mesoamerican manuscript. Two models dedicated to two different types of material structures are presented: the Kubelka–Munk model with Saunderson correction, suitable for one homogenous layer, and the Clapper–Yule model used for continuous colorant layer, suitable when a weakly scattering paint is on top of a diffusing support. The results of the simulation provide new insights into the way the coloring materials were combined in the document, either as mechanical mixture before application or as superimposition. La spectroscopie de réflexion diffuse est une technique non invasive très pratique pour l'étude des polychromies historiques, puisque sa mise œuvre est rapide, simple et sans contact. Toutefois, les spectres de réflexion de mélanges colorés complexes peuvent parfois être difficiles à interpréter d'un point de vue compositionnel. Dans ces cas, des simulations optiques théoriques peuvent fournir des données supplémentaires pertinentes. La problématique principale concerne le choix du modèle optique, qui doit être adapté au protocole de mesure et à la structure matérielle (généralement inconnue) des couches colorées étudiées. Les modèles simples basés sur des formules analytiques sont préférés, puisqu'ils peuvent facilement être inversés pour déduire les propriétés optiques et la structure des matériaux à partir de leur réflectance spectrale. Dans cet article, cette problématique est abordée pour l'étude de la composition des peintures du Codex Borbonicus, un manuscrit mésoaméricain du XVIe siècle. Deux modèles sont appliqués pour deux types de structure matérielle : le modèle de Kubelka–Munk avec la correction de Saunderson, adapté à une couche colorée homogène, et le modèle de Clapper–Yule pour des couches continues de colorants, adapté à une peinture faiblement diffusante superposée à un support diffusant. Les simulations apportent une nouvelle compréhension quant à la façon dont les matériaux colorants ont été associés dans le document, soit par mélange mécanique avant application, soit par superposition.

Two-flux transfer matrix model for predicting the reflectance and transmittance of duplex halftone prints.

We introduce a model allowing convenient calculation of the spectral reflectance and transmittance of duplex prints. It is based on flux transfer matrices and enables retrieving classical Kubelka-Munk formulas, as well as extended formulas for nonsymmetric layers. By making different assumptions on the flux transfers, we obtain two predictive models for the duplex halftone prints: the "duplex Clapper-Yule model," which is an extension of the classical Clapper-Yule model, and the "duplex primary reflectance-transmittance model." The two models can be calibrated from either reflectance or transmittance measurements; only the second model can be calibrated from both measurements, thus giving optimal accuracy for both reflectance and transmittance predictions. The conceptual differences between the two models are deeply analyzed, as well as their advantages and drawbacks in terms of calibration. According to the test carried out in this study with paper printed in inkjet, their predictive performances are good provided appropriate calibration options are selected.

Improving Clapper–Yule model of the reflectance prediction by the path branching factor depending on the screen frequency of color halftone imaging

The new path branching Clapper–Yule prediction model of spectral reflectance based on the traveling probability and the path branching factor depending on the characteristic parameter of paper and spatial distribution of imaging dots is proposed. Our numerical results show that the new spectral reflectance model is more close to the experimental data than the basic Clapper–Yule model and the reflectance is a nonlinear function of the dot percentage coverage of the halftone imaging.

New Algorithm for Ink Trapping Ratio Based on Transmittance

To reflect the relationship between the trapping effect and colorimetric value of prints, this paper establishes an algorithm to calculate the ink trapping ratio. The new algorithm assumed that the second ink of two-color overprint solid forms an evenly distributed and thinner ink layer by keeping the total ink volume as constant and it employed the transmittance of single solid ink and overprint solid to compute the ratio of the thickness of the second ink layer printed on the first ink layer and on the blank paper on basis of Lambert's law. Because of the difficulties of measuring the transmittance of prints, it used the Clapper-Yule model to calculate them. To evaluate it, the ink trapping ratio computed by the densitometry method and the new algorithm for two sets of two-color overprint solid were adopted to predict the spectral reflectance of them. By comparing the CIELAB color difference between the calculated and measured value of spectral reflectance, the proposed new algorithm is precisely defined and it improves the calculation accuracy of ink trapping.

Study on Optical Dot Gain Model Based on Point Spread and Probability Methods

Optical dot gain is the key point of halftone reconstruction study, and has always been a meaningful topic of theoretical study. The Yule–Nielsen formula is by far the most widely used research method of optical dot gain. However, solving the Yule–Nielsen parameter n remains a difficult problem. This paper disregards solving for the Yule–Nielsen parameter n, analyzes the light scattering and osmotic effect of halftone presswork, deduces the exact expressions of blank area of presswork, and determines the reflectivity of the dot part and halftone presswork according to the point spread function and probability method. Furthermore, this paper analyzes how the optical dot gain depends on the dot area coverage of presswork, ink layer transmittivity, and paper-based spectral reflectivity. In addition, a new algorithm model for optical dot gain is established. By employing the Clapper–Yule Model to calculate the spectral transmittance of printing ink and comparing it with the practical measured spectral reflectivity of the halftone presswork proof, the accuracy of the model established in this paper is fully verified.

Theoretical Research of Color Reproduction on Concentric Dot

Concentric dot is a new shape of ink dot, which subdivides dot of AM screening into ring and space. Concentric dot has morphological characteristics and reproduction characteristics of AM dots and FM dots, also has excellent color reproduction characteristics. Compared with traditional solid dot, high saturation of concentric dot has been proven. However, the mechanism of this phenomenon is rarely reported. Taking AM dots as reference, this paper try to explain the high saturation of concentric dot theoretically from several aspects, and aims to reveal the mechanism of the color reproduction characteristics of concentric dots. Due to the low amount of ink, the surface of concentric dots is smoother, and achieves better reproduction of color. The distribution characteristics of ring and space result in dot gain both inside and outside of concentric dots, which have a positive impact on the color reproduction. Establishing the relationship of optical dot area and saturation, the difference of color reproduction characteristics between concentric dots and AM dots can be analyzed as the result of the different microstructure of two dots. Using the improved Clapper-Yule model and the law of Lambert-Beer, the conclusion above can be analyzed theoretically. On this basis, experiments are designed and carried out to prove the correctness of theoretical analysis. According to the research, several conclusions are made. The conclusions can be list as follow: different saturations of concentric dots and AM dots lead to different color reproduction, when optical dot area stays the same; different saturations of concentric dots and AM dots is mainly caused by the microstructures of the tow dots; Under the same condition of incident light, concentric dots of monochrome ink reflect more of the visible spectrum than AM dots after absorption, which reasonably explains the high saturation of concentric dots. The study is to reveal the principle of color reproduction of concentric dots with high saturation, providing a theoretical basis for the application of concentric screening technology.

Reflectance prediction model of frequency modulation halftone image copied by variable dot-volume press

Based on thickness extended Clapper–Yule model, the volume extended and accurate volume extended Clapper–Yule reflectance model are developed for the ink film thickness variable of halftone image copied by variable dot-volume ink jet press. Our numerical simulations show that in the case of same ink coverage area ratio, the change of droplet-volume affects the transmittance of image. So the transmittance of ink need adjust to fit the droplet-volume change or need adjust the droplet-volume of ink and the numerical density of frequency modulation screening dot to give the suitable transmittance.

Prediction Algorithm of Spectral Reflectance of Spot Color Ink Based on Color Parallel and Superposition Model

Spectral prediction of spot color ink has always been a difficult problem in the field of color research. The current paper adopted color parallel and superposition models to deal with the Clapper-Yule model and to simplify the prediction model of spectral reflectance of spot color ink. respectively. Based on the experimental verification. the simplified method has a certain practical application value. and the spot color prediction of general presswork can meet the requirements fully. The most important consideration is that the simplification can largely reduce the computational difficulty. Moreover. the current paper compared the accuracy of color parallel model with the superposition model to simplify the spectral prediction model of spot color ink. The result showed that the color superposition model has higher accuracy in simplifying the spectral prediction model of spot color ink.

Spectral Prediction Model for Halftone Prints by Enhanced Clapper-Yule Model

The classical Clapper-Yule model and its improved models will both introduced the extended application which supports rough printing and halftone color fluorescent imaging. The characteristics of the new model were analyzed and the prospect of the Clapper-Yule mode was discussed. We proposed a new model, which was an enhancement of the classical Clapper-Yule model, which simulate optical dot gain of halftone prints by taking into account lateral scattering within the paper bulk and multiple internal reflections. The model we propose also takes into account the reflectance of inks at surface of the specific colors at specific rates. The model opens the way towards color separation of images to be reproduced. Several designs printed on an offset press demonstrate their applicability and their benefits.

Spectral Prediction Model for Halftone Prints by Enhanced Clapper-Yule Model

The classical Clapper-Yule model and its improved models will both introduced the extended application which supports rough printing and halftone color fluorescent imaging. The characteristics of the new model were analyzed and the prospect of the Clapper-Yule mode was discussed. We proposed a new model, which was an enhancement of the classical Clapper-Yule model, which simulate optical dot gain of halftone prints by taking into account lateral scattering within the paper bulk and multiple internal reflections. The model we propose also takes into account the reflectance of inks at surface of the specific colors at specific rates. The model opens the way towards color separation of images to be reproduced. Several designs printed on an offset press demonstrate their applicability and their benefits.

Probabilistic spectral model of color halftone incorporating substrate fluorescence and interface reflections

A spectral model incorporating three major physical phenomena, lateral light scattering, substrate fluorescence, and interface reflections governing light-print interaction is presented. In the model, light scattering inside a paper substrate is described by probabilities applicable for any degree of light diffusion. The concept of fluorescence enhanced transmittance has been proven very useful for extending the probability approach to prints on fluorescent substrates. The contribution of multiple internal reflections is accounted for by series expansion of fast convergence. Previously developed models like the Neugebauer equation and the Clapper-Yule model can easily be obtained as special cases of the present model.

Spectral prediction model for color prints on paper with fluorescent additives

I propose a model for predicting the total reflectance of color halftones printed on paper incorporating fluorescent brighteners. The total reflectance is modeled as the additive superposition of the relative fluorescent emission and the pure reflectance of the color print. The fluorescent emission prediction model accounts for both the attenuation of light by the halftone within the excitation wavelength range and for the attenuation of the fluorescent emission by the same halftone within the emission wavelength range. The model's calibration relies on reflectance measurements of the optically brightened paper and of the solid colorant patches with two illuminants, one including and one excluding the UV components. The part of the model predicting the pure reflectance relies on an ink-spreading extended Clapper-Yule model. On uniformly distributed surface coverages of cyan, magenta, and yellow halftone patches, the proposed model predicts the relative fluorescent emission with a high accuracy (mean DeltaE(94)=0.42 under a D65 standard illuminant). For optically brightened paper exhibiting a moderate fluorescence, the total reflectance prediction improves the spectral reflectance prediction mainly for highlight color halftones, comprising a proportion of paper white above 12%. Applications include the creation of improved printer characterization tables for color management purposes and the prediction of color gamuts for new combinations of optically brightened papers and inks.

Extending the Clapper–Yule model to rough printing supports

The Clapper-Yule model is the only classical spectral reflection model for halftone prints that takes explicitly into account both the multiple internal reflections between the print-air interface and the paper substrate and the lateral propagation of light within the paper bulk. However, the Clapper-Yule model assumes a planar interface and does not take into account the roughness of the print surface. In order to extend the Clapper-Yule model to rough printing supports (e.g., matte coated papers or calendered papers), we model the print surface as a set of randomly oriented microfacets. The influence of the shadowing effect is evaluated and incorporated into the model. By integrating over all incident angles and facet orientations, we are able to express the internal reflectance of the rough interface as a function of the rms facet slope. By considering also the rough interface transmittances both for the incident light and for the emerging light, we obtain a generalization of the Clapper-Yule model for rough interfaces. The comparison between the classical Clapper-Yule model and the model extended to rough surfaces shows that the influence of the surface roughness on the predicted reflectance factor is small. For high-quality papers such as coated and calendered papers, as well as for low-quality papers such as newsprint or copy papers, the influence of surface roughness is negligible, and the classical Clapper-Yule model can be used to predict the halftone-print reflectance factors. The influence of roughness becomes significant only for very rough and thick nondiffusing coatings.

Spectral reflection and dot surface prediction models for color halftone prints

The proposed new spectral reflection model enhances the classical Clapper-Yule model by taking into account the fact that proportionally more incident light through a given colorant surface is reflected back onto the same colorant surface than onto other colorant surfaces. It comprises a weighted mean between a component specifying the part of the incident light that exits through the same colorant as the colorant from which it enters (Saunderson corrected Neugebauer component) and a component specifying the part of the incident light whose emerging light components exit from all colorants (Clapper-Yule component). We also propose models for taking into account ink spreading, a phenomenon that occurs when printing an ink halftone in superposition with one or several solid inks. The ink-spreading model incorporates nominal-to-effective surface coverage functions for each of the different ink superposition conditions. A system of equations yields the effective ink surface coverages of a color halftone as a weighted mean of the ink surface coverages specific to the different superposition conditions. The new spectral reflection prediction model combined with the ink-spreading model yields excellent spectral reflection predictions for clustered-dot color halftones printed on an offset press or on thermal transfer printers.

Reproducing color images with embedded metallic patterns

By combining a metallic ink and standard inks, one may create printed images having a dynamic appearance: an image viewed under specular reflection may be considerably different from the same image viewed under non-specular reflection. Patterns which are either dark or hidden become highlighted under specular reflection, yielding interesting visual effects. To create such images, one needs to be able to reproduce at non-specular reflection angles the same colors, by standard inks alone or in combination with a metallic ink. Accurate color prediction models need to be established which model the underlying physical phenomena in a consistent manner. To meet this challenge, we propose two models, one for predicting the reflection spectra of standard inks on coated paper and one for predicting the reflection spectra of a combination of standard inks and a metallic ink. They are enhancements of the classical Clapper-Yule model which models optical dot gain of halftone prints by taking into account lateral scattering within the paper bulk and multiple internal reflections. The models we propose also take into account physical dot gain and ink spreading for standard inks as well as the low reflectance of metallic inks at non-specular reflection angles and the poor adherence of standard inks printed on top of a metallic ink (trapping effect). These models open the way towards color separation of images to be reproduced by combining a metallic ink and standard inks. Several designs printed on an offset press demonstrate their applicability and their benefits for high-end design and security applications.

A generalized Clapper–Yule model of halftone reflectance

A generalized Clapper–Yule model of halftone reflectance

A generalized Clapper-Yule model of halftone reflectance

The Clapper–Yule model of halftone reflectance includes the effects of light diffusion and multiple internal reflection between the ink-layer and the paper substrate. It models complete scatter—the case in which the distance a photon diffuses is much greater than the screen period. The current work generalizes this to any degree of scatter. The model is presented in terms of probability functions, and the probabilities are calculated from the paper's point spread function (PSF). Photon diffusion within paper is due to two processes: scatter and multiple internal reflection. The usually defined PSF includes both processes. Ink on the paper surface, however, alters the internal reflectance, and so the usually defined PSF depends on the percent ink coverage. The current model separates the effects of scatter from the effects of internal reflection. The PSF introduced here accounts for scatter only—it is independent of the percent ink coverage. It is shown that the generalized Clapper–Yule model corresponds to Yule–Nielsen n-values significantly greater than 2, unlike the case of no internal reflection for which the maximum n-value is equal to 2. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 402–407, 2000