How to calculate color from spectra of uniaxial gemstones

Abstract

Color is the most important quality for colored stones, one that is widely discussed and studied by gemologists. Understanding the color characteristics of a gemstone can provide a scientific basis to guide its cutting. This study uses visible spectroscopy to determine the unpolarized spectra of a uniaxial material from the polarized spectra (o-ray and e-ray) in order to predict the color of a uniaxial gem material when viewed in any direction. A seemingly intuitive way of doing this, by adding weighted amounts of the o-ray and e-ray absorption spectra, does not actually work for estimating the unpolarized spectra. The mathematically and physically correct way to reconstruct these unpolarized spectra is to add weighted polarized transmittance spectra and then to convert back to absorption if desired. This method allows color to be accurately predicted for a material when viewed in any direction as long as the polarized spectra and the viewing angle relative to the c-axis are known. This method has been verified by comparison with a synthetic V-bearing sapphire and a synthetic Cr-bearing sapphire cut into wafers (not faceted gemstones) at various angles relative to the optic axis.