Mathieu Hébert

Reflectance and transmittance model for recto-verso halftone prints

We propose a spectral prediction model for predicting the reflectance and transmittance of recto-verso halftone prints. A recto-verso halftone print is modeled as a diffusing substrate surrounded by two inked interfaces in contact with air (or with another medium). The interaction of light with the print comprises three components: (a) the attenuation of the incident light penetrating the print across the inked interface, (b) the internal reflectance and internal transmittance that accounts for the substrates intrinsic reflectance and transmittance and for the multiple Fresnel internal reflections at the inked interfaces, and (c) the attenuation of light exiting the print across the inked interfaces. Both the classical Williams-Clapper and Clapper-Yule spectral prediction models are special cases of the proposed recto-verso reflectance and transmittance model. We also extend the Kubelka-Munk model to predict the reflectance and transmittance of recto-verso halftone prints. The extended Kubelka-Munk model is compatible with the proposed recto-verso reflectance and transmittance model. In the case of a homogeneous substrate, the recto-verso models internal reflectance and transmittance can be expressed as a function Kubelka-Munks scattering and absorption parameters, or the Kubelka-Munks scattering and absorption parameters can be inferred from the recto-verso models internal reflectance and transmittance, deduced from spectral measurements. The proposed model offers new perspectives both for spectral transmission and reflection predictions and for characterizing the properties of printed diffuse substrates.

Extension of the Williams-Clapper model to stacked nondiffusing colored coatings with different refractive indices

We propose a model for predicting the reflectance and transmittance of multiple stacked nonscattering coloring layers that have different refractive indices. The model relies on the modeling of the reflectance and transmittance of a bounded coloring layer, i.e., a coloring layer and its two interfaces with neighboring media of different refractive indices. This model is then applied to deduce the reflectance of stacked nonscattering layers of different refractive indices superposed with a reflecting diffusing background that has its own refractive index. The classical Williams-Clapper model becomes a special case of the proposed stacked layer model.

Compositional reflectance and transmittance model for multilayer specimens

We propose a compositional model for predicting the reflectance and the transmittance of multilayer specimens composed of layers having possibly distinct refractive indices. The model relies on the laws of geometrical optics and on a description of the multiple reflection-transmission of light between the different layers and interfaces. The highly complex multiple reflection-transmission process occurring between several superposed layers is described by Markov chains. An optical element such as a layer or an interface forms a biface. The multiple reflection-transmission process is developed for a superposition of two bifaces. We obtain general composition formulas for the reflectance and the transmittance of a pair of layers and/or interfaces. Thanks to these compositional expressions, we can calculate the reflectance and the transmittance of three or more superposed bifaces. The model is applicable to regular compositions of bifaces, i.e., multifaces having on each face an angular light distribution that remains constant along successive reflection and transmission events. Kubelkas layering model, Saundersons correction of the Kubelka-Munk model, and the Williams-Clapper model of a color layer superposed on a diffusing substrate are special cases of the proposed compositional model.

Yule-Nielsen based recto-verso color halftone transmittance prediction model

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.

Reflectance and transmittance model for recto-verso halftone prints: spectral predictions with multi-ink halftones

We extend a previously proposed spectral reflectance and transmittance prediction model for recto-verso prints to the case of multi-ink halftones. The model takes into account the multiple reflections and the lateral propagation of light within the paper substrate (optical dot gain) as well as the spreading of the inks according to their superposition conditions (mechanical dot gain). The model accounts for the orientation of the incident and exiting lights when traversing the halftone ink layers, which enables modeling the measuring geometry. The equations for the calibration of the model and for the predictions are presented in detail. Several experiments with inkjet prints show that the multi-ink halftone transmittance model is as accurate as the actually most performing reflectance models for halftone prints.

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.

Dichroic colored luster of laser-induced silver nanoparticle gratings buried in dense inorganic films

This paper deals with the colorimetric properties of silver nanoparticle gratings buried in a dense titania film that result from a continuous wave laser-induced self-organization process. The samples exhibit shining colors in the direction of the specular reflection, which are very sensitive to polarization. We show that a large color gamut and a tunable dichroism can be reached by varying the exposure conditions. We also discuss the physical meaning of the observed variations in the dichroism. This laser process produces a single pass marking with a micrometer resolution and could be useful for developing innovative solutions in fields like active color displays, security, polarization imaging, or design.

Spectral prediction model for piles of nonscattering sheets

The present paper investigates the reflection and transmission properties of piles of nonscattering sheets. Using a spectral prediction model, we perform a detailed analysis of the spectral and color variations induced by variations of the number of superposed sheets, the absorbance of the sheet material, the refractive index of the medium between the sheets, and the reflectance of the background. The spectral prediction model accounts for the multiple reflections and transmissions of light between the interfaces bounding the layers. We describe in detail the procedure for deducing model parameters from measured data. Tests performed with nonscattering plastic sheets demonstrate the excellent accuracy of the predictions. A large set of predicted spectra illustrate the different evolutions of reflected and transmitted spectra as well as the corresponding colors for various types of piles.

Correspondence between continuous and discrete two-flux models for reflectance and transmittance of diffusing layers

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelkas layering model describes the multiple reflections and transmissions of light taking place between various superposed diffusing layers (discrete two-flux model). The compatibility of these two models is shown. In particular, the Kubelka–Munk reflectance and transmittance expressions are retrieved, using Kubelkas layering model, with mathematical arguments using infinitely thin sublayers. A new approach to the Kubelka–Munk expressions is thus obtained, giving, moreover, new details for physical interpretation of the Kubelka–Munk theory.

Color calibration of an RGB camera mounted in front of a microscope with strong color distortion.

This paper aims at showing that performing color calibration of an RGB camera can be achieved even in the case where the optical system before the camera introduces strong color distortion. In the present case, the optical system is a microscope containing a halogen lamp, with a nonuniform irradiance on the viewed surface. The calibration method proposed in this work is based on an existing method, but it is preceded by a three-step preprocessing of the RGB images aiming at extracting relevant color information from the strongly distorted images, taking especially into account the nonuniform irradiance map and the perturbing texture due to the surface topology of the standard color calibration charts when observed at micrometric scale. The proposed color calibration process consists first in computing the average color of the color-chart patches viewed under the microscope; then computing white balance, gamma correction, and saturation enhancement; and finally applying a third-order polynomial regression color calibration transform. Despite the nonusual conditions for color calibration, fairly good performance is achieved from a 48 patch Lambertian color chart, since an average CIE-94 color difference on the color-chart colors lower than 2.5 units is obtained.