
Three different approaches are now used for grading the cut quality of a diamond. The first is based on analyzing the set of cut parameters (proportions and angles). The second involves instrumental detection of the light returned by the diamond. The third is based on 3D modeling of the diamond. Below, we analyze the advantages, drawbacks, and limitations of the abovementioned approaches.
1. Parameterbased description of a diamond. Two principal problems arise when using this approach. First, the parameter set presently used in laboratories describes an ideally symmetric diamond and, therefore, does not completely describe the shape of a real diamond. Moreover, this parameter set does not completely describe even a symmetric stone, because it does not include the coordinates (angles and azimuth) of the upper and lower girdle facets. The second problem is that different cut parameters of a diamond are interdependent in the sense of their combined influence on the optical effects demonstrated by the stone. In the existing gemological grading systems, the cut parameters are usually considered as independent. Therefore, the zone of highquality diamonds, plotted in the "crown angle  pavilion angle" coordinates, looks like a rectangle. However, it is known that such parameters as the crown and the pavilion angle are interdependent. Therefore, it is easy to find such combinations of the parameters, which conflict with the conventional grading. Cutting diamonds with different combinations of the crown and pavilion angles would allow one to draw a corrected "quality map". However, all the other cut parameters should be fixed in such a case. This means that the corrected "map" will not be valid for a stone with a deviation in any of these parameters (for example, in the table size, star facet length, lower girdle facet length, or upper girdle facet azimuth). Considering each extra parameter leads to exponential growth of the possible cases, and the problem of building a parameterbased database that describes all these cases becomes more and more complicated, and even unsolvable (starting from a certain number of the considered parameters, which yields an enormously large number of cases to classify). Therefore, when the parametric approach is used in practice, some of these parameters are anyway fixed (their influence on the stone appearance is deliberately neglected). However, this influence does actually exist. As a result, this fixing leads to building such a cut grading system that sometimes conflicts with real cases. It is clear that the abovediscussed limitation is fundamental for the parametric approach (database approach).
For example, the results of recent diamond cut studies carried
out at GIA show that "every facet matters". Probably, the GIA grading
system does not reproduce the errors peculiar to the "quality rectangle"
approach. However, similar errors may occur due to neglecting some
other cut parameters. This is a direct consequence of the fact that
the GIA system, though considering slightly more parameters with
respect to the preceding systems, still employs the same approach.
The approach remains parametric.
Figure 1
The problem of taking into account the interdependent parameters is illustrated in Fig. 1. The left end of the segment corresponds to the situation when all the parameters are independent (which does not reflect the actual state of things). The right end of the segment corresponds to the situation when all the parameters are considered along with their interdependence (such a database is almost impossible to construct, due to an enormously large number of cases to classify). The dots correspond to the grading systems developed in different laboratories, such as AGS, HRD, and GIA.
Figure 2
2. Cut grading based on optical measurements.
Examples of instruments that use the second approach are the Brilliancescope, Firescope, Hearts and Arrows Viewer, Idealscope, and Isse2. The design of these devices is based on the use of fixed types of structural illumination. If it's a priori known that some stone is "good", it is always possible to choose such an illumination type, for which this stone will be clearly distinguishable from the others. As a result, such a device will check how the diamond under study is close to (or far from) the initial etalon (which is usually called a Masterstone). All these instruments allow one to reject those stones looking different from the Masterstone. So, all such stones will be graded as "bad", even if some of them look quite good when viewed by the observer.
It is important to understand the difference between the method of looking for bad stones and the method of looking for good stones (see Fig. 2).
3. Cut grading based on 3D modeling.
An accurate 3D model of a diamond completely describes the shape of the stone and allows one to synthesize photorealistic images of the stone under different lighting conditions and to calculate the individual optical coefficients for every stone. A cut grading system can be built on the basis of the 3D model. On this way, it is important to adequately model the illumination, the diamond, and the observer, as well as to properly choose the coefficients to compute. The main drawback of this approach is the need for system verification using real diamonds (including those having nonstandard cut proportions) supplemented with expert grading data for these stones. However, it is worth noting that this drawback is peculiar to all the approaches considered.

