Ink Penetration, Isomorphic ColorantMixing, and Negative Values of Yule-Nielsen <italic>n</italic>

Abstract

As the number of inks used in printers increase beyond the traditional four, the “safe” profiling paradigm of factorial sampling of the ink levels combined with multi-dimensional interpolation grows exponentially in the number of samples required. The VHM-1, also known as the spectral Yule-Nielsen-modified Neugebauer model, and its derivatives are profiling alternatives that have demonstrated accuracy and enjoyed some popularity. Undoubtedly, part of the viability of these models stem from the use of the Yule-Nielsen parameter, n, as a fitting parameter, allowing the models to adapt to numerous situations.This paper examines an aspect of this adaptability that is puzzling at best and defies reason at best, namely, negative values of n arising fromfitting the model tomeasured spectra. Such values represent behavior evenmore extreme than n going to infinity, implying complete spreading of transparent ink.Lewandowski, et al., have reported negative values of n when fitting the VHM-1 to spectra of halftones printed on ceramics, and the current author has provided the theoretical explanation of spreading of scattering ink. In this paper, the penetration of ink into the substrate is offered as an additional cause for this phenomenon. Both theoretical and empirical justification are offered to support this contention.The theoretical justification is based on the remarkable similarity between the Yule-Nielsen formula with n =−1 and the ratio K/S used in colorant formulation work. Empirical data were generated by printing rather coarse halftone patterns on fiber inkjet paper, using ink jet with dye-based inks. The fitted value of n was approximately −3.8, versus fitted n values ranging from approximately +3.8 to +5.8 for prints produced on media that do not permit penetration.The concept of isomorphic colorant mixing in briefly introduced to explain the similarity between VHM-1 with n =−1 and single-constant colorant formulation. This concept is an extension of the “linear function” introduced by Allen and mentioned by Kuehni and Tzeng. This concept is explained more completely in a separate publication.