Theory of Human Tetrachromatic Color Experience and Printing

Abstract

Genetic studies indicate that more than 50% of women are genetically tetrachromatic, expressing four distinct types of color photoreceptors (cone cells) in the retina. At least one functional tetrachromat has been identified in laboratory tests. We hypothesize that there is a large latent group in the population capable of fundamentally richer color experience, but we are not yet aware of this group because of a lack of tetrachromatic colors in the visual environment. This paper develops theory and engineering practice for fabricating tetrachromatic colors and potentially identifying tetrachromatic color vision in the wild. First, we apply general d -dimensional color theory to derive and compute all the key color structures of human tetrachromacy for the first time, including its 4D space of possible object colors, 3D space of chromaticities, and yielding a predicted 2D sphere of tetrachromatic hues. We compare this predicted hue sphere to the familiar hue circle of trichromatic color, extending the theory to predict how the higher dimensional topology produces an expanded color experience for tetrachromats. Second, we derive the four reflectance functions for the ideal tetrachromatic inkset, analogous to the well-known CMY printing basis for trichromacy. Third, we develop a method for prototyping tetrachromatic printers using a library of fountain pen inks and a multi-pass inkjet printing platform. Fourth, we generalize existing color tests - sensitive hue ordering tests and rapid isochromatic plate screening tests - to higher-dimensional vision, and prototype variants of these tests for identifying and characterizing tetrachromacy in the wild.