To reproduce color images in print, the continuous tone image is first transformed into a binary halftone image, producing various colors by discrete dots with varying area coverage. In halftone prints on paper, physical and optical dot gains generally occur, making the print look darker than expected, and making the modeling of halftone color reproduction a challenge. Most available models are based on macroscopic color measurements, averaging the reflectance over an area that is large in relation to the halftone dots. The aim of this study is to go beyond the macroscopic approach, and study halftone color reproduction on a micro-scale level, using high resolution images of halftone prints. An experimental imaging system, combining the accuracy of color measurement instruments with a high spatial resolution, opens up new possibilities to study and analyze halftone color prints. The experimental image acquisition offers a great flexibility in the image acquisition setup. Besides trichromatic RGB filters, the system is also equipped with a set of 7 narrowband filters, for multi-channel images. A thorough calibration and characterization of all the components in the imaging system is described. The spectral sensitivity of the CCD camera, which can not be derived by direct measurements, is estimated using least squares regression. To reconstruct spectral reflectance and colorimetric values from the device response, two conceptually different approaches are used. In the model-based characterization, the physical model describing the image acquisition process is inverted, to reconstruct spectral reflectance from the recorded device response. In the empirical characterization, the characteristics of the individual components are ignored, and the functions are derived by relating the device response for a set of test colors to the corresponding colorimetric and spectral measurements, using linear and polynomial least squares regression techniques. Micro-scale images, referring to images whose resolution is high in relation to the resolution of the halftone, allow for measurements of the individual halftone dots, as well as the paper between them. To capture the characteristics of large populations of halftone dots, reflectance histograms are computed as well as 3D histograms in CIEXYZ color space. The micro-scale measurements reveal that the reflectance for the halftone dots, as well as the paper between the dots, is not constant, but varies with the dot area coverage. By incorporating the varying micro-reflectance in an expanded Murray-Davies model, the nonlinearity caused by optical dot gain can be accounted for without applying the nonphysical exponentiation of the reflectance values, as in the commonly used Yule-Nielsen model. Due to their different intrinsic nature, physical and optical dot gains need to be treated separately when modeling the outcome of halftone prints. However, in measurements of reflection colors, physical and optical dot gains always co-exist, making the separation a difficult task. Different methods to separate the physical and optical dot gain are evaluated, using spectral reflectance measurements, transmission scans and micro-scale images. Further, the relation between the physical dot gain and the halftone dot size is investigated, demonstrated with FM halftones of various print resolutions. The physical dot gain exhibits a clear correlation with the dot size and the dot gain increase is proportional to the increase in print resolution. The experimental observations are followed by discussions and a theoretical explanation.

Les solutions pour lutter contre la contrefaçon permettant une sécurisation des produits dépendent des capacités de mesure à l’échelle microscopique de points imprimés. Les recherches explicitées dans ce manuscrit ont donc été consacrées au développement d’un équipement et de méthodes permettant de mesurer les imprimés à l’échelle microscopique. Un microscope en réflexion avec lumière polarisée a été associé avec un appareil photographique numérique. La matrice de Bayer a été retirée de la surface du capteur photographique et des images raw ont été enregistrées. La platine du microscope, l’appareil photographique, un photomètre et un thermomètre ont été contrôlés directement dans une interface logicielle développée en Python. Une méthode de mesure permettant d’élargir la gamme dynamique de reflectances mesurées a été proposée. L’appareil et les méthodes de mesures ont permis d’améliorer la précision et d’automatiser la mesure des points de trame à l’échelle microscopique. Les élargissements physique et optique des points de trame ont alors été séparés et analysés. Une méthode d’ajustement des pics de l’histogramme, correspondant à l’encre et au papier, avec une fonction Gaussienne a été proposée. Des algorithmes de seuillage ont été employés pour séparer l’élargissement optique et physique des points de trame. Une méthode objective d’évaluation des algorithmes de seuillage a été développée pour déterminer leurs performances sur les images de tramés. Cette méthode d’évaluation procède à une simulation des effets de la diffusion de la lumière et des défauts générés par l’imagerie afin de générer des images tests et images de référence. 30 algorithmes de seuillage de la littérature ont été évalués et ont présenté une dépendance avec le pourcentage de couverture de l’encre. Deux nouveaux algorithmes de seuillage ont alors été développés spécialement pour traiter les imprimés tramés. Le premier algorithme détermine le déplacement du pic correspondant à l’encre sur l’histogramme. Le deuxième algorithme proposé se base sur une pseudo-déconvolution permettant de prétraiter les images et se basant sur une séparation des effets de l’élargissement optique. Une caractérisation de l’élargissement optique et physique a alors été menée sur 2708 images d’imprimés tramés. Enfin, un modèle de l’élargissement physique et un modèle de l’élargissement optique des points de trame ont été proposés. Le modèle physique se base sur une génération de particules d’encre placées selon une fonction de probabilité et sur une fusion des particules d’encre. Le modèle a été évalué en considérant 43269 points de trame différents, mesurés automatiquement sur le microscope. Un nouveau modèle prédisant la réflectance des tramés a été développé, basé sur une double convolution avec deux fonctions différentes d’étalement du point. Ce modèle a permis de simuler de manière précise les effets principaux de la diffusion de la lumière dans le tramé, tout en simulant les effets de piégeage de la lumière à proximité des bords des points de trame. / Applications in the field of product security and authentication to prevent counterfeiting rely on abilities of microscale measurements of printed dots. Thus, researches described in this manuscript have been directed toward the development of measurement methods and apparatus to characterize halftone dot at the microscale. A polarized reflection optical microscope has been adapted with a commercial digital camera. The Bayer matrix was removed from the surface of the camera and raw images were retrieved. The microscope stage, the camera, the photometer and the thermometer were controlled directly in a Python graphic user interface specifically developed. A high dynamic range capture method was proposed and tuned specifically to obtain richer information on the ink and paper regions. The measurement apparatus and methods helped improve the accuracy and automate the measurements of the halftone dots at the microscale. The physical and optical dot gains were then separated and analyzed. A Gaussian fitting of the ink and paper histogram peaks was proposed to measure automatically the ink and paper region reflectance as a function of the ink coverage. Thresholding algorithms were applied to separate optical and physical dot gain. An objective threshold evaluation method was developed in order to define the best threshold algorithms for halftone images. The method was based on a simulation of the optical dot gain effects and of the microscope distortions to obtain test images and ground truth images. 30 threshold algorithms from literature were evaluated and demonstrated dependency on the ink surface coverage of the halftones. Two novel threshold algorithms were then developed specifically to process halftones. The first threshold algorithm was based on the determination of the amount of ink peak shift. The second threshold algorithm proposed a pretreatment of the images by applying a pseudo-deconvolution strategy, removing the optical dot gain from the halftones. Characterizations of the optical and physical dot gains were then conducted analyzing 2708 different halftones. Finally, a physical dot gain model and an optical dot gain model were proposed in order to predict the halftone reflectances from raster to print. The physical dot gain model was based on the generation of single ink particles placed according to a probability mask and on a fusion of the ink particles. The model was evaluated with 43269 dot morphologies that were captured automatically on the microscope. A novel halftone reflectance model was proposed based on a double convolution with two different paper point spread functions. It allowed an accurate reproduction of the main effects of the light diffusion with, at the same time, an accurate reproduction of the light entrapment near the edges of the dots.