A binary printer can generate only two solid colors, black and white. Any other gray levels between them are simulated by halftone techniques and shown as the result of spatially averaging neighbor pixels. In the recently proposed 2x2 centering printer model, the conventional coordinates, which specify the location of all pixels, are redefined by shifting the entire grid by half-pixel distance in both the horizontal and the vertical directions. So, we claim that any binary printer can generate seven, instead of only two, “solid” colors. Here, the word “solid” means that all pixels within a large patch of the printout are microscopically identical, at least in the statistical sense. The seven “solid” colors, or gray levels, can be directly measured macroscopically. The 2x2 centering modeling can interpret any output of a binary printer as a seven-level gray image with the same spatial resolution as the binary input. To accurately predict the appearance of any combination of the seven gray levels, we use a modified Yule-Nielsen equation for non-linear spatial averaging. Applications of this 2x2 centering model to halftone screen design and calibration are also presented.
Shen-ge Wang, "Two-by-Two Centering Printer Model with Yule-Nielsen Equation" in Proc. IS&T Int'l Conf. on Digital Printing Technologies (NIP14), 1998, pp 302 - 305, https://doi.org/10.2352/ISSN.2169-4451.1998.14.1.art00074_1