GIA Sets to Work on Cut Question
By Ilene M. Reinitz, Mary L. Johnson, James E. Shigley, and Thomas M. Moses
The quality and value of faceted gem diamonds are often described in terms of the “four C’s”: carat weight, color, clarity, and cut. Carat weight can be directly measured, while grading standards for color and clarity, largely based on systems first developed by the Gemological Institute of America in the 1950’s, are widely used and accepted in the jewelry trade.
Evaluation of cut is much more complex. Many factors affect the appearance of a polished gem diamond, but little is understood about just how these various properties improve diamond appearance, even within a single cutting style, the 58-facet round brilliant. Without a sound theoretical basis (or else a means of directly measuring brilliance, fire and/or scintillation), the assessment of what constitutes better appearance is a subjective judgment that varies with individual and market preferences.
Despite this lack of understanding, there exists in the trade today a growing interest in a simple grading system for cut. Several grading systems are in use for round brilliants, each based upon certain assumptions about the relationship between proportions and appearance. Although there is a general perception that diamond appearance has been extensively studied, relatively little scientific information exists. Most widely known is the analysis published 80 years ago by Marcel Tolkowsky, in which he found a single set of proportions that he believed would produce the best possible appearance in a round brilliant diamond. A number of other researchers since then have made their own analyses and proposed “superior” proportions. Although several of them use the term “Ideal” to describe these proportions, it is surprising how dissimilar many of them are.
A modified version of Tolkowsky’s results has been used as the basis for most of the cut-grading systems currently used, with the added assumption that any deviation in any proportion diminishes the attractiveness of a diamond. While this simplification allows for establishment of simple cut grading categories, it is contrary to the experience of diamond manufacturers who recognize that there are various proportions that produce attractive diamonds.
GIA’s Diamond Study
Recognizing that modern computer tools could be used to investigate diamond appearance more thoroughly than had been done so far, GIA researchers began a study of this complex subject several years ago. Our initial step was to develop a precise theoretical model of the interaction of light with a faceted diamond, in order to work toward our overall goal: a comprehensive understanding of how cut affects diamond appearance. In this article, we describe our model, and summarize the first results of this long-term study. A complete report of these results is presented in the Fall 1998 issue of GIA’s quarterly journal, Gems & Gemology (Hemphill et al., 1998, “Modeling the Appearance of the Round Brilliant Cut Diamond: An Analysis of Brilliance,” Gems & Gemology Vol. 34, No. 3, pp. 158-183).
Our Model
Our work uses modern computer graphics simulation techniques to investigate diamond appearance. (Such techniques are employed to produce many of the realistic computer images that we see today in the media.) For our study, we created mathematical representations of both the three-dimensional shape of a faceted diamond, and the physical properties governing the movement of light within the diamond. This “virtual” diamond we modeled is completely colorless and flawless (figure 1), is fully faceted including the girdle, and has perfect symmetry and polish. At present, the shape we analyzed is a round brilliant, but this can be generalized to almost any shape.
Diamond appearance is described in terms of brilliance, fire, and scintillation. To compare these concepts for various round brilliant proportion combinations, we first needed to develop mathematical expressions for each concept, that is, some quantitative measure. Calculating values for a concept, like brilliance, also requires choosing lighting and observing conditions. By tracing the paths of millions of light rays from our chosen source, our model produces both realistic images and numerical results for round brilliants with different proportion combinations. Because we can separately control all relevant factors, computer modeling allows us to investigate the influence of thousands of possible proportion combinations on appearance, a nearly impossible task using actual diamonds.
Modeling of Brilliance
For this first phase of our study, we focused on an analysis of brilliance. When looking at a diamond, this aspect of appearance is the one most immediately noticed. It is the aspect for which the desired outcome is obvious—bright appearance is good, and dark appearance is not. Brilliance has also been the subject of most previous investigations. We developed a numerical value, which we call weighted light return (WLR), as a representation of brilliance. WLR is a single number that is a weighted sum of the amount of light returned through the crown of the virtual diamond to all positions of observation above the girdle. This number quantifies the amount of light (excluding glare) returned from our virtual diamond for averaged illumination and viewing conditions. While other illumination and viewing conditions are possible, we developed WLR to best represent the way an experienced observer sees a diamond, especially when mounted in jewelry, with diffuse lighting that illuminates the diamond from all directions above the girdle. By use of WLR, we can directly compare the efficiency of various proportion combinations of the round brilliant to yield virtual diamonds with high light return. The next phase of this study will investigate fire.
We used eight parameters to define the shape of our virtual diamond, and looked in general at how WLR varied as we changed one parameter at a time. However, direct observations of actual diamonds show that the overall shape of the round brilliant is primarily determined by three parameters—crown angle, pavilion angle, and table size. Thus, we examined in detail how WLR varies as these three parameters were changed together, while the others were held constant at a specific set of reference proportions. During our study, we calculated WLR values for over 20,000 proportion combinations covering large ranges for crown angle, pavilion angle, and table size. From observations of actual diamonds, large differences in WLR values correlate to visible differences in overall brightness.
WLR Results
We first examined how WLR changed as crown angle, pavilion angle, or table size varied individually, while keeping the remaining parameters constant. Then we looked at WLR as all three parameters were varied together.
Of these three parameters, changing the crown angle alone produced the greatest variation in WLR. In general, WLR increases as crown angle decreases, with some noteworthy features. WLR decreases sharply for crown angles greater than 35°, and although very shallow crown angles are generally impractical, at crown angles of 15° or 23°, round brilliants show significantly higher WLR than at other, similar angles (e.g., 17°, 20°, or 25°).
Pavilion angle is often cited as the parameter that matters most in terms of brilliance, and with the other parameters fixed at the reference proportions, we found a smooth decrease in WLR away in both directions from a maximum value of pavilion angle at about 40.7°. (Note that for different choices of crown angle and table size, the optimal pavilion angle can be different as well.) Calculated images of virtual diamonds with low, medium, and high pavilion angles correspond closely with the appearances that we would expect for actual diamonds with these pavilion angles (“fish-eye”, normal, and “nail-head” appearances, respectively). WLR varied with table size, with maximum values occurring for table size percentages from about 53 percent to 59 percent and lower values outside of this range.
For the purpose of our study, however, we wanted to go further and understand how WLR changed as these parameters were varied in combination. We found that WLR has a complex dependence on how these parameters interact. Because it becomes difficult to depict on two-dimensional paper the interaction of three or more parameters, we chose to present graphs of how two parameters varied over a range of constant values for the third parameter (figure 2). We can illustrate WLR results graphically for proportion combinations from three perspectives–constant table size, constant pavilion angle, and constant crown angle. These graphs resemble topographic maps, which show the differences in elevation of an area of land.
For table sizes up to 61 percent, WLR is higher for smaller crown angles (less than 34°) with pavilion angles ranging from 38° to 43°, and it increases as crown angle decreases. Higher WLR values are found for the widest range of crown angles and table sizes as the pavilion angle tends toward 41°. (However, at higher and lower pavilion angles, lower crown angles and smaller tables still produce relatively high WLR values.) In general, WLR decreases as crown angle increases, but for most typically-seen crown angles, WLR is highest for intermediate pavilion angles and table sizes up to 60 percent.
In terms of the remaining five parameters, WLR decreases as the thickness of a faceted girdle increases, but remains constant with increasing number of girdle facets from 32 to 144. There was little change in WLR for increasing culet sizes up to as large as 12 percent. Variations in the relative sizes of star facets and lower-girdle facets also lead to small variations in WLR values.
What WLR Results Mean
The graphs of WLR results reveal the complex influence of proportions on light return in a round brilliant diamond. In these graphs, there is no simple relationship between any one proportion and light return. Our results do not support the existing categories of cut grades in several grading systems used today, where each proportion parameter is considered separately, and all deviations from a narrow range of proportion combinations are given a lower cut grade. Instead, our results suggest that there are many combinations of proportions that would yield equally “attractive” round brilliant diamonds. Because of the complex relationship between proportions, for given values of two proportions, change in a third proportion in a single direction may first result in a lower WLR value and then a higher WLR value. This makes characterization of what constitutes the best appearing diamond a great challenge.
Because many combinations of proportions yield similarly high WLR values, our results suggest that diamonds can be cut to a wider variety of proportion combinations, with the same high light return, to better utilize available rough. For example, one might choose to saw a piece of asymmetrical octahedral rough just slightly off center (through an elongated or tilted portion) to yield a bottom piece weighing 1.75 carats. From that piece, a round brilliant with a 35.5° crown angle, 40.8° pavilion angle, and 57 percent table size would earn a high grade in the existing grading systems; our calculations show a WLR value of 0.279 for these proportions, with a finished weight of about 0.93 carats. Alternatively, a round brilliant with a 32.7° crown angle, a 41.5° pavilion angle, and a 60 percent table also yields a WLR value of 0.279, but at a finished weight of 1.02 carats.
What WLR Results Do Not Mean
The WLR data presented here do not constitute a basis for a cut grading system. We have only addressed one appearance aspect, calculating weighted light return as a measure of brilliance. Our intention now is to use our same basic model to analyze fire, and then to combine these results with the WLR data. Whether or not this research project will ultimately yield results that can be translated into a practical cut grading system is unknown at this time.
A WLR value depends on the choice of illumination and viewing conditions. If either of these factors is changed, the specific numerical value may also change (and would no longer be called a WLR value, because it is not on the same scale). We calculated WLR values for a “perfect” diamond model that is colorless, flawless, and completely symmetrical, and has perfect polish. Actual diamonds can differ in many possible ways, and we have not yet taken into account all of these variables in our computer programming.
Conclusion
We have presented here a brief summary of the results obtained to date in our long-term computer modeling study of diamond appearance. To those wishing to read our complete study, we encourage you to obtain a copy of our article in Gems & Gemology. We intend to build on the results obtained so far to consider other aspects of appearance, starting with fire, so as to build a more complete understanding of faceted diamond appearance. Although we know these other aspects are important, no fashioned diamond can be considered beautiful if it lacks brilliance.
This study represents the most complete theoretical analysis of diamond appearance yet attempted. Our computer model differs from previously published work in terms of (1) being a three-dimensional analysis, (2) using the most detailed scientific data on the physical properties of diamond, (3) taking into account averaged illumination and viewing conditions that represent how actual diamonds are observed, and (4) analyzing a very large set of proportion combinations. As we gather future data, information from this research project will be reflected in our educational materials, and may be applied to our laboratory reporting and instrument development.
Cut is the most complex of diamond’s 4Cs. In this paper, we have not addressed all of the factors involved in diamond appearance. We have published the results obtained to date; future results from this study will be published as they become available. It is our opinion that any cut grading system that attempts to categorize diamond appearance is premature in absence of a more complete understanding of the factors that give rise to this appearance.
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