GIA to Ideal Cutters: Back to the 3-D Drawing Board

The first and largest installment of the Gemological Institute of America’s study of diamond cuts subverts the long-held belief in the supremacy of the Ideal cut. The report confirms the opinion of many diamond cutters that there’s more than one “Ideal” for a round brilliant. Among other findings, the study demonstrates that the classic Tolkowsky model does not in fact yield the most brilliance. The study could have a far-reaching impact on labs issuing top grades for Ideal cuts.

Published in the Fall 1998 issue of Gems & Gemology, the report analyzes how proportion affects brilliance, the amount of white light returned through the crown of a diamond. Its authors are GIA research associate T. Scott Hemphill; Dr. Ilene M. Reinitz, manager of research and development at GIA’s Gem Trade Laboratory in New York; Dr. Mary L. Johnson, manager of research and development at GIA’s Gem Trade Laboratory in Carlsbad, Calif.; and Dr. James Shigley, director of GIA research.

The authors selected brilliance for the first installment of their series because it’s the most important factor in a diamond’s appearance. It’s also the least subjective and the easiest to quantify. Future articles will analyze fire – light that’s visibly dispersed into spectral colors – and other properties of a diamond’s “performance.”

Weighted Light Return. The GIA researchers began their ray-tracing experiments in 1990 to track exactly how light travels through a diamond. The aim was to determine which proportions of a round diamond yield the most brilliance, fire, and scintillation (brilliance and fire in motion).

The researchers devised a measurement unit called Weighted Light Return (WLR) that gauges light returned through the crown from various angles. The highest value, 1.00, pertains to light flowing straight up through the table. Scores decline as the angles are reduced, so that light exiting horizontally through the crown is rated 0. The most brilliant diamonds range between 0.285 and 0.30. The Tolkowsky Ideal has a WLR of 0.2814, while “average” commercial cuts fall in around 0.270 to 0.275.

The authors say their results will render obsolete the cut grades currently used in the United States, Japan, and elsewhere. “Our results disagree with the concepts on which current grading systems appear to be based – in particular they do not support the idea that all deviations from a narrow range of crown angles and table sizes should be given a lower grade.” In short, there are a great many “Ideals.”

Virtual diamonds. Because it was not economically feasible to cut thousands of diamonds, the researchers turned to computer models. Working with more than 20,000 variations of the most critical proportion factors – crown angle, table size, and pavilion angle – they traced rays of light through computer representations of round brilliant. The images reproduced the patterns of light and dark seen in actual round diamonds under similar lighting.

The researchers’ reference point was an Ideal cut of 56% table, 34º crown, and 40.5º pavilion. From that base they varied the table percentages in 1% increments down to 50% and up to 75%. They adjusted crown angles in 1º increments between 1º and 50º and pavilion angles in 0.25º increments between 38º and 43º. The researchers also studied the effect of girdle facets, girdle thickness, star facet extensions, lower girdle facet extensions, and culet size. They checked their work against a pool of grading reports from 67,621 diamonds in GIA’s Gem Trade Lab archive.

The sheer volume of calculations made it impossible to measure every possible variation of these proportion factors. So the researchers limited their study mostly to the crown, table, and pavilion. They also evaluated supposedly superior proportions advocated by other researchers and found that few qualified as “very bright”; some even fell into the dark category.

The virtual diamonds did have some differences from actual stones. They were completely colorless, had perfect finish and symmetry, and were inclusion-free. The researchers acknowledge that these differences affect the results but defend their findings based on the data from the GIA Gem Trade Lab files. Besides, all researchers, including Marcel Tolkowsky, have based their work on a theoretical model instead of working with actual stones.

The trouble with Tolkowsky. The mathematician known as the father of the modern Ideal cut did his work in 1919 using a two-dimensional model with a knife-edge girdle. Tolkowsky measured the angles needed to reflect a ray of white light entering the table back out through the crown and thereby determined a single set of optimal proportions. He assumed that all light would be refracted out of the diamond after bouncing off the pavilion facets. The GIA researchers say this assumption is too simplistic; in fact, light within a diamond takes many bounces, and some gets lost in the process. Others since Tolkowsky have arrived at proportions they believe to be superior to all others.

The GIA study found that the “best” sets of proportions are all over the map. It refutes previous notions of a single or limited set of proportions that produce the best-looking diamonds. These results offer more options for diamond manufacturers trying to balance maximum yield with beauty.

The study demonstrated that there are numerous peaks and troughs when the crown angle, pavilion angle, and table size are varied against each other. For example, enlarging the table size may at first reduce the WLR but eventually increases it as the table widens. More telling is that Tolkowsky’s classic “Ideal” cut – 53% table, 34.5º crown angle, 40.75º pavilion angle – warranted only a “moderately bright” rating. A diamond with a 61% table, 26.3º crown angle, and 42.5º pavilion angle was rated “very bright.” Brightest of all was a diamond with a 54% table, 27.3º crown, and 42.4º pavilion.

The researchers found that diamond brilliance is based on complex relationships among all proportion factors of a diamond. In fact, diamonds with widely varying proportions can produce very similar brilliance.

The study determined that changing the crown angles resulted in the biggest variations in brilliance and that shallower crown angles delivered the most light. There were “peaks,” however. A 23º crown angle proved brightest when the table size and pavilion were kept at the reference points. Pavilion angles reached a brilliance peak at 40.7º when the table size and crown were kept at the reference values. Brilliance diminished when pavilion angles exceeded 40.7º.

Table size is somewhat more complex, with brightness varying considerably depending on the crown and pavilion angles. In general, smaller tables usually provided more brilliance when the crown and pavilion were kept at reference points. As the table size reaches 60%, the choices of crown and pavilion angles become more limited. If the table exceeds 62%, the diamond will exhibit high brilliance only if the crown angles are below 29.3º – which is rare in commercial cuts. As table size increases, the crown angle must be reduced to maintain brilliance.

There were some surprises. For example, a 65% table delivered more brilliance than the basic Ideal reference stone when combined with a 23º crown and 40.5º pavilion. The study also found that the WLR decreased in proportion to an increase in girdle thickness, though it remained constant as the number of girdle facets increased from 32 to 144. Fewer facets yielded less brilliance. Surprisingly, however, culet size made little difference in a diamond’s brilliance unless enlarged well beyond what most cutters regard as attractive. The study also found that elongating the star extension facets yields more brilliance, while shortening the girdle extensions can also increase brilliance.

A new paradigm? Although the subject of diamond brilliance, fire, and other diamond “performance” criteria has generated considerable controversy over the years, there’s been little hard research up to now. Although Tolkowsky and others worked only on paper with a simplistic, two-dimensional model, their work has been used to justify many different cut-grading systems.

The GIA report cites numerous examples of high-brilliance diamonds that would not earn high cut grades under most current grading systems. The researchers concede there’s still too little evidence to base such grades on the balance of fire and brilliance. The authors undercut the argument that the Ideal cut offers the best such balance, since Tolkowsky “did not consider the possible dependence of fire on pavilion angle” – though it can make a critical difference in a diamond’s appearance.

The study is also critical of computer-aided cut-grading services and machines that purportedly measure a diamond’s light output. “They use a considerably less sophisticated set of starting assumptions than are employed [in this study],” according to the report.

Forthcoming research. The authors acknowledge that their brilliance study is not the last word on the subject. Measuring brilliance in terms of WLR is only the “first piece of a puzzle.” Ongoing research will focus on how to measure brilliance under different lighting conditions and which proportions deliver the most fire. Devising measurements for these factors will be “the greatest challenge,” say the researchers. Many variables have to be considered when measuring fire, such as the amount and distribution of colored light rays exiting throughout the crown, the colors observed, and how they recombine into “sparkle,” or scintillation.

“Our results disagree with the concepts on which current grading systems appear to be based,” the study’s authors wrote.

Once the fire scale is developed, the researchers will devise a measurement for scintillation. That may prove equally difficult. The researchers will then explore how symmetry and diamond color affect a diamond’s performance. “From our efforts and observations of actual diamonds in this study, we suspect that symmetry deviations may produce significant variation in brilliance,” says the report. To measure the performance of diamonds with noticeable body color, the research team must use a formula for absorption (the amount of light soaked up by the color) and for distribution of the body color (even or zoned).

The research team has set no timetable for these forthcoming studies. The authors say that in the end it may be easier to issue negative grades for poorly cut diamonds, because it’s easier to predict the worst proportions than to assign grades for the best. The ultimate aim of the study is to map out proportion ranges that “clearly fail to bring out the attractive properties of a diamond,” and then to examine the remainder for the best balances between brilliance, fire, and scintillation.

“Only then can an intelligent, fact-based discussion take place of what diamonds produce superior appearance,” say the authors. Taken in this light, they argue, “any [existing] cut grading system is premature.”


The study’s ultimate aim is to map out proportion ranges that “clearly fail to bring out the attractive properties of a diamond” and then to examine the remainder.