Previous Research

A review of superior proportion combinations as proposed by other investigators was published in the GIA Brilliance study (Fall 1998). None of these studies noted or conformed to an inverse relationship between crown and pavilion angles.
We will review one prior and three more recent studies as well three inventions of relevance to the HCA; DiamCalc, the Fire Scope™and the GilbertsonScope.
Bruce Harding "Faceting Limits" (Gems and Gemology Fall 1975) identified the effect of an observers head blocking rays of illumination for the main facets of a number of gem materials, including diamond. The method employed was to calculate rays that should be returned to the viewer’s eye (10 per eye) but would involve illumination blocked by the viewer’s head. This was done for rays that returned to either eye, to and from each of the main facet groups; crown to table, table to crown, table to table and crown to crown. This approach led Harding in 1986 to develop perhaps the first ever ray path analysis computer software.
Like Tolkowsky’s study Harding studied the impact of crown and pavilion main facets. Harding praised Tolkowsky’s design (but not his methods) and defined many bands of good and bad crown and pavilion angle combinations based on the blockage of rays that would be refracted to a viewer’s eye.
The range of proportions Harding proposed be avoided because of table-to-crown ray path shadows include most of the proportion combinations that rate excellent on the HCA system. Bruce and I met in January 2001 and we modeled half facets ray paths using his computer software. We demonstrated that normal blockage of light by a head that causes darkness of main facets does not result in darkening of minor facets interactions with either other minor facets, or with the main facets. This holds true for all but uncommonly low combinations of crown and pavilion angles, where upon bezel to bezel ray paths begin to cause a type of nail head effect. Consequently only very small areas of a diamond suffer this head shading and this distinction can produce a pleasing black eight pointed star in diamonds with excellent symmetry.
We will show that some head shadow darkness in a diamond contributes to its beauty. Harding agrees that extinction of main facets caused by blockage by the viewer’s head is essential for ‘dynamic contrast’ to occur. He uses the term ‘snap-snap’ to describe the strong scintillation effect of contrast between black and white alternating facets. This attracts the eye as the light, viewer or the diamond moves.
The GIA Brilliance study in the Fall of 1998 issue Gems & Gemology (Hempill, et al., 1998) was based on computer modeled 'virtual diamonds'. This study considered the ‘weighted light returns or WLR (weighted to favor the ‘face up view’) for many combinations of round brilliant diamond proportions. Further studies of fire (dispersion) and scintillation are currently being undertaken.
A diffuse illumination model was chosen to emphasize the return of white light without the complications of fire or the need to consider the shadow that a viewer's head might cast on a diamond. In this lighting environment a diamond with complete light return will appear uniformly white, flooding any effects of possible fire because the brightness of the white light returned. Darkness seen in these virtual diamonds can only result from light leakage.
An analysis of data from Figure 3, plotted as a graph of the crown and pavilion angles with the highest light returns, is shown in Figure 4. That graph, plotted during the Easter break in 1999, confirmed my belief in the inverse relationship principal and led me to develop HCA.

Figure 3.

This chart is adapted from Hemphill et al., 1998, figure 11. It shows one of many views of GIA WLR data. The center points (marked by the author) on the crown angle charts between 30.5 and 36.5 represent optimum light return for those crown angles. Figure 4 shows an almost straight-line relationship of optimal light return for those crown and pavilion angle combinations. (The shallower crowns of 31.5 had a higher WLR with a small 52% tables, where as a 36.5 crown had a maximum WLR when combined with a larger 57% table.)
The GIA authors made some odd assumptions; most have been widely reported. One was to define scintillation as glare or “flashes of light reflected from the crown”. Reflected light contributes to light return; an observer does not generally identify reflected from refracted light. And since 17% to 90% of all incident light is reflected from a diamonds surface, reflected light should not be ignored. It is worth noting that a shallow crown angled diamond reflects more light back to an observer in a face up viewing position than a steeper crown diamond.
Scintillation will be covered in detail in the section following this review, where it is defined here as amount and placement of darkness in a diamond that provides contrast for brilliant white, or firey colored sparkles, making them appear brighter to the human eye.

Figure 4.

In late 1999 a group of scientists headed by Yurii Shelemetiev and Sergey Sivovolenko from Moscow State University (MSU) posted unpublished results of cut studies on a website This study includes theoretic result for light return and fire using virtual computer modelling analysis. The study employed a realistic lighting environment (described in detail at, combining results for both light return and dispersion with equal weighting to a factor Q (Fig 5).
They stress that light return should not be equated with brilliance and that these early results were arrived at before they realized the importance of human physiology (S. Sivovolenko, pers. comm., 2001) which they are now studying and taking in to account.

Figure 5. The MSU cut quality function Q combines results of theoretic studies of light return and fire. Results for light return (not to be confused with brilliance) tend to be higher in the upper left of the chart, while results for fire tend to be higher in the lower right. A Tolkowsky proportioned virtual diamond is given a value of 1.