Yule-Nielsen based recto-verso color halftone transmittance prediction model Mathieu Hébert, Roger D. Hersch To cite this version: Mathieu Hébert, Roger D. Hersch. Yule-Nielsen based recto-verso color halftone transmittance pre- diction model. Applied optics, Optical Society of America, 2011, 50 (4), pp.519-525. hal-00559756 HAL Id: hal-00559756 https://hal.archives-ouvertes.fr/hal-00559756 Submitted on 26 Jan 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Yule–Nielsen based recto–verso color halftone transmittance prediction model Mathieu Hébert1,* and Roger D. Hersch2 1Université de Lyon, Université Jean Monnet de Saint-Etienne, CNRS UMR5516 Laboratoire Hubert Curien, F-42000 Saint-Etienne, France 2School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland *Corresponding author: mathieu.hebert@univ‐st‐etienne.fr Received 20 September 2010; accepted 19 November 2010; posted 8 December 2010 (Doc. ID 135363); published 27 January 2011 The transmittance spectrum of halftone prints on paper is predicted thanks to a model inspired by the Yule–Nielsen modified spectral Neugebauer model used for reflectance predictions. This model is well adapted for strongly scattering printing supports and applicable to recto–verso prints. Model parameters are obtained by a few transmittance measurements of calibration patches printed on one side of the paper. The model was verified with recto–verso specimens printed by inkjet with classical and custom inks, at different halftone frequencies and on various types of paper. Predictions are as accurate as those obtained with a previously developed reflectance and transmittance prediction model relying on the multiple reflections of light between the paper and the print–air interfaces. Optimal n values are smaller in transmission mode compared with the reflection model. This indicates a smaller amount of lateral light propagation in the transmission mode. © 2011 Optical Society of America OCIS codes: 100.2810, 120.7000. 1. Introduction fitted according to the considered printing technology, Color prediction for halftone prints has been an active dithering method, paper, and inks. The second ap- subject of investigation for more than 60 years. For col- proachis based on the Clapper–Yuleequation,derived or management purposes, the relationship between from an optical model accounting for the reflectance of printed colors and surface coverages of inks deposited the paper substrate and the absorbance of the inks [4]. on paper needs to be established. This is achieved by Recent extensions provide very good predictions for a measuring the reflectance spectra of many printed wide range of diffusing supports and printing patches, or by predicting them thanks to an appropri- technologies [5]. ate model. For accurate prediction, the model must By definition, these reflectance models apply when take into account the “optical dot gain,” i.e., due to the light source and the observer are located on the light scattering, the lateral propagation of light be- same side of the print. But some printed objects are illuminated from behind such as advertisement light tween the different colorant areas of the halftone panels, neon signs, or lampshades. The prediction of [1]. Two types of models can be used. The first is based the resulting colors requires a transmittance model. on the Yule–Nielsen equation [2,3]. In order to model Recently, we developed a first reflectance and trans- the effect of optical dot gain, the halftone reflectance is mittance prediction model as an extension of the given by a sum of fulltone print reflectances raised to a Clapper–Yule model, also valid for recto–verso prints power 1 n. The n parameter is an empirical parameter = [6,7]. It describes the multiple reflections of light be- tween the paper and the print–air interfaces (Fig. 1). 0003-6935/11/040519-07$15.00/0 The angle-dependent attenuation of light within the © 2011 Optical Society of America colorants followed the approach of Williams and 1 February 2011 / Vol. 50, No. 4 / APPLIED OPTICS 519 (cyan and magenta), and black (cyan, magenta, and yellow). The paper coated with colorant k on the recto side has a transmittance spectrum TkðλÞ, which can be measured with a spectrophotometer in transmit- tance mode, e.g. the X-Rite Color i7 instrument in to- tal transmittance mode (d:0° geometry). In classical clustered-dot or error diffusion prints, the fractional area occupied by each colorant can be deduced from the surface coverages of the primary inks according to Demichel’s equations [13]. For cyan, magenta, and yellow primary inks with respec- tive surface coverages c, m, and y, the surface cov- erages of the eight colorants are, respectively, Fig. 1. Physical model of the interaction of light with a recto– verso print on paper accounting for the multiple reflections aw ¼ð1 − cÞð1 − mÞð1 − yÞ; between the paper bulk and the print–air interfaces. ac ¼ cð1 − mÞð1 − yÞ; 1 − 1 − Clapper [8] and the spreading of the inks was ac- am ¼ð cÞmð yÞ; counted for according to the method proposed in [9]. a ¼ð1 − cÞð1 − mÞy; The parameters used by that model were the reflec- y 1 − tance and the transmittance of the paper substrate, amþy ¼ð cÞmy; the transmittance of the colorant layers, the surface a ¼ cð1 − mÞy; coverages of the colorants, and the Fresnel coeffi- cþy 1 − cients corresponding to the reflection and transmis- acþm ¼ cmð yÞ; sion of light at the print–air interfaces. That first model illustrated the ability to extend a reflectance- acþmþy ¼ cmy: ð1Þ only model to transmittance. In a similar manner, we now propose as a trans- Let us assume, as a first approximation, that the mittance model [10] an extension of the Yule–Nielsen transmittance of the halftone print is the sum of λ modified spectral Neugebauer model [3]. In order to the colorant-on-paper transmittances Tkð Þ weighted verify its prediction accuracy, we tested the proposed by their respective surface coverages ak. We obtain a model with recto–verso halftones printed by inkjet transmittance expression similar to the spectral with classical cyan, magenta, and yellow (CMY) as Neugebauer reflectance model [3,14] well as with custom inks, at different halftone fre- quencies and on various types of paper. Before intro- 8 λ λ ducing the model, let us recall that the transmittance Tð Þ¼ ajTjð Þ: ð2Þ of a diffusing layer or multilayer does not change Xj¼1 when flipped upsidedown with respect to the light source. This property, that Kubelka called “nonpolar- However, the linear Eq. (2) does not predict correctly ity of transmittance” [11], remains valid when the the transmittance of halftone prints due to the scat- strongly scattering layer is coated with inks and tering of light within the paper bulk and the multiple – bounded by interfaces with air, provided the geome- reflections between the paper bulk and the print air tries of illumination and of observation are identical, interface, which induce lateral propagation of light for example, directional illumination at 0° and obser- from one colorant area to another. This phenomenon, vation at 0°[12]. When the two geometries are differ- known for reflectance as the “Yule–Nielsen effect” ent, flipping the print may induce a small variation [3,15], also occurs in the transmittance mode (see of its transmittance spectrum. Nonpolarity of Fig. 1). In order to account for this effect, we follow transmittance applies for single-sided as well as the same approach as Viggiano [3] by raising all the for recto–verso prints. There is no equivalent in the transmittances in Eq. (2) to a power of 1=n. We obtain reflectance mode. the Yule–Nielsen modified Neugebauer equation for the transmittance of a color halftone printed on the 2. Yule–Nielsen Model for Transmittance recto side: A halftone is a mosaic of juxtaposed colorant areas obtained by printing the ink dot layers. The areas 8 1 n with no ink, those with a single ink layer, and those TðλÞ¼ a T =nðλÞ : ð3Þ j j with two or three superposed ink layers are each con- Xj¼1 sidered a distinct colorant (also called Neugebauer primary). For three primary inks (e.g., cyan, magen- A second phenomenon well known in halftone print- ta, and yellow), one obtains a set of eight colorants: ing is the spreading of inks on the paper and on no ink, cyan alone, magenta alone, yellow alone, red the other inks [9]. In order to obtain accurate spec- (magenta and yellow), green (cyan and yellow), blue tral transmittance predictions, effective surface 520 APPLIED OPTICS / Vol. 50, No. 4 / 1 February 2011 coverages need to be known. They are deduced from and yellow, are halftoned, with the respective nom- the measured transmittance spectra of a selection of inal surface coverages c0, m0, and y0. Before being printed halftones, called calibration patches. able to use Demichel’s Eqs. (1) to calculate the effec- tive surface coverages of the eight colorants, we need 3. Effective Surface Coverages to compute the effective surface coverages c, m, y of The amount of ink spreading is different for each ink the inks, accounting for the superposition-dependent and depends on whether the ink is alone on paper or ink spreading. Effective surface coverages of an ink superposed with other inks. Effective surface cov- halftone are obtained by a weighted average of the erages are therefore computed for all ink superposi- ink spreading curves.