Feature Gems & Gemology, Fall 1998, Vol. 34, No. 3

Modeling the Appearance of the Round Brilliant Cut Diamond: An Analysis of Brilliance

T. Scott Hemphill, Ilene M. Reinitz, Mary L. Johnson, and James E. Shigley

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Of the “four C’s,” cut has historically been the most complex to understand and assess. This article presents a three-dimensional mathematical model to study the interaction of light with a fully faceted, colorless, symmetrical round-brilliant-cut diamond. With this model, one can analyze how various appearance factors (brilliance, fire, and scintillation) depend on proportions. The model generates images and a numerical measurement of the optical efficiency of the round brilliant—called weighted light return (WLR)—which approximates overall brilliance. This article examines how WLR values change with variations in cut proportions, in particular crown angle, pavilion angle, and table size. The results of this study suggest that there are many combinations of proportions with equal or higher WLR than “Ideal” cuts. In addition, they do not support analyzing cut by examining each proportion parameter independently. However, because brilliance is just one aspect of the appearance of a faceted diamond, ongoing research will investigate the added effects of fire and scintillation.