Modeling the Influence of Dye Distribution on the Perceived Color Depth of a Filament Array

Abstract

This paper presents a model of the reflection, refraction, and absorption of light rays by a dyed cylindrical filament according to classical laws of optics. Overall light transmit tance and reflectance of a single filament are then assumed to apply to a complete layer of such filaments. The optical behavior of the entire filament array is derived by adding successive filament layers with the same or different amounts and distributions of dye. Each filament contains a light-absorbing dye that may be evenly distributed throughout it, or located in a ring close to the filament periphery (ring dyed). The model also considers the case where only filaments near the surface of the array are colored, while those in the interior are not. The calculations predict how the various different distributions of the dye in the filament array influence the perceived color depth. The results are discussed in relation to previous work and to practical dyeing experience.