Physical Interpretation of Neugebauer Equations and Applications for Achromatic Synthesis

Abstract

As Lambert-Beer's Law in density modulation images, Neugebauer Equations are basic equation for reproduction of dot modulation images. Its significance increases with advance of digital printing technology. Its' applications have been diversely enlarging to identify relationship between dot allocation and gamut', to forecast reproduced color2, and to discuss achromatic synthesis in principle 3, 4 . As well known, its principle is that color is reproduced by averaging additive mixture of basic 8 colors' area and stimulus determined statistically by Demichel's law . The significant assumption here is the independency of each area, that is, coverage and stimulus of each area are not influenced by those of neighbor. However, in an actual dot modulation image, optical diffusion and mixture occur within image as known as Yule-Nielsen's effect (Y-N effect). Therefore, former assumption cannot be adapted on actual images. Since various marking technologies have their own optical diffusion and mixture respectively due to their marking principle and image structure, it seems that an overall comprehension for reproduction of these images is required from these technologies. And besides, reconstruction of reproduction theory including density modulation images will be more necessary in future. For this purpose, new theoretical approach adding Y-N effect to Neugebauer equations might be indispensable . From viewpoint, this paper introduces full-color image structure models which quantifies optical diffusion and mixture within recorded image and mentions physical interpretation of Y-N effect in full-color image. Next, by using Neugebauer equations with Y-N effect6, we analyze achromatic synthesis and propose theoretical method for black determination applicable to all image formation, through density modulation to completely binary image.