GIA’S SYMMETRY GRADING BOUNDARIES FOR ROUND BRILLIANT CUT DIAMONDS Ron H. Geurts, Ilene M. Reinitz, Troy Blodgett, and Al M. Gilbertson ations during planning and cutting. Likewise, mak- ers of non-contact optical scanners have been inter- Grade boundary limits are presented for 10 ested in guidelines for how measurable symmetry symmetry parameters of the round brilliant cut parameters affect the GIA symmetry grade. The diamond. Starting in early 2012, these values grade boundaries presented here offer a substantive will be used to support and constrain visual estimate of the symmetry grade for any round bril- symmetry grading on GIA diamond reports. liant cut diamond. For manufacturers, the boundaries provide In GIA’s laboratory, polished diamonds are mea- useful predictions of symmetry grades. Other sured with a non-contact optical scanner early in the symmetry features of faceted diamonds will grading process. Later, polish and symmetry are eval- continue to be evaluated visually. uated visually at 10× magnification, using a standard procedure. As described in Gillen et al. (2005), specif- ic parameter- and facet-related features are consid- ered in grading symmetry. This article presents numerical grade limits for 10 important symmetry ince 2006, GIA has used certain proportion mea- parameters that can be measured accurately enough surements obtained with non-contact optical to support visual symmetry grading. Although mea- Sscanners to grade the cut of round brilliant dia- sured values have been available to graders as a guide monds. Improvements in the operation and accuracy for several years, beginning in 2012 GIA will use of these instruments now enable us to also measure measured values and apply these boundary limits some symmetry parameters during the grading pro- strictly when grading symmetry for round brilliant cess. Although both Excellent and Very Good sym- cut diamonds. Facet-related symmetry features, and metry grades meet GIA’s criteria for an Excellent cut the manner in which multiple features combine, grade (Moses et al., 2004), there is a premium for may also affect the symmetry grade, and these what the trade calls a “triple Excellent”: an aspects will continue to be evaluated visually, as Excellent grade for cut, polish, and symmetry. they are presently beyond reproducible instrument Therefore, many diamond manufacturers would like measurement. to be able to predict GIA symmetry grades from Compared to visual assessment, instrumental measurement data, so they can apply these consider- measurements provide a more consistent way of establishing a symmetry grade, especially when a dia- mond has very subtle symmetry deviations. Figure 1 shows a diamond with several symmetry flaws: a See end of article for About the Authors. wavy and uneven girdle (resulting in an uneven GEMS & GEMOLOGY, Vol. 47, No. 4, pp. 286–295, http://dx.doi.org/10.5741.GEMS.47.4.286. crown height), a table not parallel to the girdle, and © 2011 Gemological Institute of America uneven bezel facets. In the past, the only means of 286 SYMMETRY GRADING FOR ROUND BRILLIANTS GEMS & GEMOLOGY WINTER 2011 Figure 1. This 0.69 ct standard round bril- liant cut diamond displays several obvious symmetry features that can be quantified. Photo by Robert Weldon. determining this diamond’s symmetry grade would measure crown angle to three decimal places, but if have been the judgment and experience of the grader. repeated measurements demonstrate an uncertainty Quantifying these features by instrumental measure- in the first decimal place, the two additional digits ment provides a more consistent basis for symmetry offer no meaningful precision (Reinitz et al., 2005). grading, and gives cutters the details needed to Even detailed knowledge of the uncertainty does improve their diamonds’ symmetry. not tell us whether measurements are accurate. Accuracy can only be determined relative to the mea- BACKGROUND surement of a known standard, such as an object The repeated measurement of any attribute, such as with NIST-traceable values and reported uncertain- weight or size, is accompanied by a certain degree of ties. Box A describes some basic metrology concepts, uncertainty. For example, the repeated measurement including measurement uncertainty. of a diamond’s weight, or its total depth, yields The proportion values used to determine a dia- results that vary slightly within a certain range. For mond’s cut grade are normally the average of eight the most accurate results, the measured value itself measurements; these are not greatly affected by a sin- and the variation in repeated measurements—the gle outlying value. In contrast, symmetry parameters uncertainty of that value—are both important. examine the range (the largest and smallest) of those The U.S. National Institute of Standards and values, and they are much more affected by a single Tech nology (NIST) notes that “a measurement result poor measurement. This means a higher level of con- is complete only when accompanied by a quantita- fidence in the reproducibility and accuracy of each tive statement of its uncertainty” (“Uncertainty of measured value is needed to predict a symmetry measurement results,” 1998). Whatever the tool or grade, or to reinforce visual grading. GIA has method, measurement results fall within a certain achieved this confidence through advances in the allowable range of values—the tolerance. For our pur- devices used to measure polished diamonds, coupled poses, the tolerance of a measuring device describes with efforts to ensure the diamonds are thoroughly its contribution to the overall uncertainty of the mea- cleaned. For example, suppose eight crown angles are sured values (GIA Research, 2005). individually measured at 34.1°, 34.5°, 34.9°, 35.3°, Statistical examination of repeated independent 34.2°, 34.3°, 34.0°, and 34.1°. The average is measurements provides one way to estimate their 34.43°, and the difference in values (maximum uncertainty. The distribution of these measurements minus minimum) is 1.3°. A second set of measure- also reveals information about reproducibility and ments yields values of 34.1°, 34.5°, 34.5°, 34.8°, 34.2°, defensible precision. For example, a device might 34.3°, 34.0°, and 34.1°. The second average is 34.31°, SYMMETRY GRADING FOR ROUND BRILLIANTS GEMS & GEMOLOGY WINTER 2011 287 BOX A: BASIC MEASURING CONCEPTS aking several independent measurements of the of the eight individual values. In a round brilliant of Tsame characteristic illustrates the difference lower symmetry, the eight crown angle values may vary between precision and accuracy, as shown in figure by several degrees. The uncertainty of a symmetry A-1. Accuracy refers to how close the measured val- assessment for such variation among the crown angles ues are to the reference value, shown here as the center of the target. Precision refers to how close the values are to each other, and in practice this affects Figure A-1. A measurement is accurate when it how many significant figures should be used when agrees with an independently obtained reference reporting the measurement. value (here, the center of the bull’s-eye). Measure- When the difference between two measured val- ments are precise when they can be reproduced with ues is less than or equal to the measurement uncer- small uncertainties. The ideal situation is to have tainty, the values are within tolerance of each other, measurements that are both accurate and precise. and by definition not readily distinguishable from one another. Figure A-2 shows six measurements of the total depth of one round brilliant, each with an uncertainty of ±0.015 mm. The average value of those measurements is 5.015 mm. Trial 4, with a value of 5.00 mm, is just within tolerance of that average. Trial 6, with a value of 5.04 mm, is not within tolerance of the average. This is described as Not Accurate Accurate an outlying value. Not Precise Not Precise Most gemologically important parameters for the round brilliant cut diamond, such as the crown or pavilion angle, represent averages rather than single measurements. In metrology, averages of multiple measurements are used to reduce measurement uncertainty. But a quantity such as average crown angle is calculated from eight values obtained from different facets, rather than eight measurements of Not Accurate Accurate the same facet. As a result, this average has its own Precise Precise uncertainty that is no smaller than the uncertainties only 0.12° below the previous average. But the differ- grade boundary. Multiple measurements, on one ence in values is now 0.8°, considerably smaller than device or on different devices, can yield slightly dif- the 1.3° from the first set of measurements. In other ferent results. All devices have a margin of error words, the average changes less than the difference in (within the tolerance of the device) that could yield values when one or two of the eight values is marred two different grades when one or more parameters by dirt or some other measuring problem not specifi- are near a border. Since no measurement is exact, cally related to that particular diamond. prudent cut planning acknowledges measuring toler- Higher-quality measurements have a smaller ances and avoids placing parameters too close to the uncertainty, but even the best measuring systems borders. have some tolerance for each parameter. Box A shows an example of measurement uncertainty at the border between Very Good and Excellent. Even MEASURABLE SYMMETRY PARAMETERS AND measurements of clean diamonds made on devices of ADDITIONAL FACTORS proven accuracy and precision can produce one or Ten symmetry parameters are illustrated in figure 2. more values that fall within tolerance of a symmetry GIA has developed procedures to measure these 288 SYMMETRY GRADING FOR ROUND BRILLIANTS GEMS & GEMOLOGY WINTER 2011 COMPARING VALUES WITH UNCERTAINTIES UNCERTAINTY VS. A SYMMETRY BOUNDARY 1.6 5.06 1.5 5.05 ) ˚ mm) 1.4 5.04 5.03 1.3 5.02 1.2 5.01 1.1 5.00 1.0 VARIATION ( VARIATION CROWN ANGLE CROWN 4.99 0.9 TOTAL DEPTH ( TOTAL 4.98 0.8 1 2 3 456 13452 TRIAL REPEATED MEASUREMENTS OF SAME STONE Figure A-2.