We have shown some of the complexities that we have discovered in our studies. As a result of these and other discoveries not shown, we now believe it is now possible to develop a system for grading the quality of diamond cut of any individually scanned stone using 'Basic Light Responses' (BLR) information in conjunction with formalized criteria established by experts. The idea is discussed in our article in these proceedings titled 'A Strategy for Development'. This expert cut quality assessment system will also be applicable to any diamond irrespective of its shape or symmetry.

The validity of the computer software BLR output will be based on a comparison of data from scanned 3 Dimensional models of the diamonds under consideration using the flow chart below:

OctoNus tools for these tasks:

HELIUM software for precise 3D model building for polished diamonds and semi-polished diamonds.

• Symmetry evaluation on the base of 3D model
• ReCut option

• BLR calculations: Light Return, Leakage, Contrast, FishEye for every cut style.
• Ray tracing abilities.
• Parameterization of scanned diamonds. Calculation of optical features with some cut parameters changing.
• Changing of lighting/observing conditions including known structural lighting.
• Movie recording with stereo ability - scintillation study.
• Changing absorption spectra - ability to work with colored diamonds and other gemstone materials.

Beginning with a set of Master Stones and following the strategy outlined above, it is possible to define a set of Basic Light Responses (BLR) for human observation of diamonds. It would then be possible with those BLR features to grade any diamond.

Correlation between two clusters (groups) of diamonds can be established with help of fuzzy logic technology.

ETAS

A part form Basic Light Responses that are strongly dependant on illumination conditions we introduce a new type of BLR not dependent on illumination but describing fundamental cut properties - the possibility of a cut diamond to increase the visible part of space.

A diamond is an optical instrument that redirects light from illumination sources and distributes it into surrounding space. A diamond splits a light beam into several smaller (secondary) beams; their effective total angular size (ETAS) may be greater or smaller than that of the primary one.

An increment in number of virtual facets can result in an increase or a decrease of ETAS. While the number of facets is small enough, ETAS grows with the number.

A decrease of ETAS begins when the size of virtual facets becomes so small that blinding reduces the brightness of primary source to the level comparable to that of secondary sources.

It is important to evaluate light response of diamonds as they are perceived by the human mind. Two important effects are that light rays are not simple parallel beams, the simplification used by scientists and most ray tracing software (see fig. 7). Secondly, as we have shown, the eye is not an objective measuring device. But not only does it suffer (or enjoy) perceptual variations, it also has its own geometry of lens and receptors.

Figure 7. The light source is in focus

See more detales at "The importance of the relationship between the pupil of a human eye, a light source, and the size of diamonds virtual facet" and "ETAS - part of space visible trough moving diamond".

Virtual diamond facets

A virtual facet of diamond can be explained by the overlapping the crown and pavilion facets.

A good diamond should have two types of virtual facets: small facets guarantee that at least one sparkle is always visible, and big facets reveal bright sparkles.

The virtual diamond facets modeled in DiamCalc after second internal light reflection (see fig. 8).

Figure 8. The virtual diamond facets modeled in DiamCalc after second internal light reflection.

It is apparent that this actual diamond has even more virtual facets than that shown in the wire model; these result from the next level of internal reflections, the third, forth and so on. There comes a point where the virtual facets become too small for us to observe them and this brings us to issues like what size should the virtual facets be for diamonds of different sizes? The size of a diamonds virtual facets can be related to their number and the stones geometry; for instance princess cut appear to have more and smaller virtual facets than a round brilliant which has more facets. Another factor that affects the size and quantity of virtual facets is diamond symmetry. We believe it is possible to improve the appearance of larger diamonds with certain planned asymmetry, where as better symmetry has good validity in smaller sized stones.

The methodology described here, in our opinion, is an optimal way to develop a reliable and useful diamond cut grading system. For the proper modeling of diamond appearance it is important to adequately model not only diamond itself but also lighting and viewing conditions. It is important to move grading from proportions and parametrical approach to the optical appearance of diamond.
Basic Light Responses of diamond can be evaluated from precise 3-dimensional diamond models, and diamond cut grading based on these Basic Light Responses makes it possible to range diamonds by their cut quality. The diamond characteristic ETAS (Effective Total Angular Size) introduced here is a parameter showing the sparkle (scintillate) possibility for each particular diamond.
This methodology applies the same approach to all cuts. It is distinctive from all other approaches because it allows verification of grading systems and grading of fancy cuts and other (non diamond) materials.
We believe that implementation of described methodology to diamond industry will led to creation of more beautiful diamonds and new beautiful cuts. The diamond trade also can benefit from cut grading system with increasing profit selling more beautiful diamonds.

1. The Results of Diamond Cut Studies Carried out in MSU, 1999
2. On the problem of grading the quality of diamond cut: an analysis of some aspects of the problem, March 2002
3. Collection of various "movies" generated with the DiamCalc Software, 2002

Sergey Sivovolenko, OctoNus, Moscow, Russia
Yuri Shelementiev, Gemological Center MSU, Moscow, Russia