Thus, we have shown that the coefficients used at GIA absolutely do not correlate with the BR coefficient defined intuitively. Moreover, in our imaginary experiment these coefficients almost do not change, while BR changes strongly (first increases and then falls down to almost zero). This example illustrates that the WLR coefficient principally differs from the brilliance, and that WLR measurements do not allow one to study the brilliance. This experiment also shows that the LR_MSU coefficient does not correlate with the brilliance as well. However, a multiplicative function of the image contrast and the LR_MSU coefficient can be used as a good approximation of the brilliance.

The example considered above is not abstract or far-fetched. It describes rather adequately the brilliance phenomenon perceived by a man looking at a diamond. When no dispersion occurs in the diamond (for example, if the illumination is monochromatic), it acts like a plurality of tiny mirrors. Thus, although the split mirror model is quite simple, it allows us to introduce a correct and adequate definition of primary brilliance.

Accordingly, the following question arises: What are the optimum source size, distances between the objects, and the diamond cut, which make the observer see many bright and colored images of the source? (The brightness corresponds to the brilliance of the diamond, while the coloration corresponds to its fire).

Fig.6. Diamond facet as additional diaphragm for light source
Click to enlarge picture

The sizes of the elementary prisms depend on their quantity, the size of the stone, and the arrangement of its facets. Studying this problem allows one to determine the optimum combination of a light source and facet dimensions by numerical calculations. The interrelation between the source, one of the facets, and the eye pupil is illustrated at Fig. 6. In other words, if the light emitted by the source falls on a stone with few large facets, the stone produces few intense light beams; and if the light falls on a stone with many small facets, the stone produces many weak beams. When the number of the facets is large enough, the intensity of each of these beams tends to zero.

It is important to make a diamond grading model adequate not only from the viewpoint of geometrical optics but also from the viewpoint of the psychophysiological features of human perception. When studying the fire, the GIA group uses the following steps:

Empirical determination of a threshold for the intensity of the minimum signal (page 184 of "Modeling the Appearance…").

The use of an intensity smoothing function (let me cite a phrase contained on page 183 of "Modeling the Appearance…": "…Thus, rather than use the intensity directly, we "smoothed" it with an "S-shaped" function…" )

We think that at this stage of their studies the GIA group faced the problem of mathematically modeling such phenomena as «subjective brightness» and «subjective size of a highlight». These phenomena are due to the fact that a man perceives light intensity as subjective brightness and subjectively senses the size of a highlight. Some studies on the subjective brightness can be found in literature (section 6.3 «Brightness and Lightness scales», pp. 493-499, in "Color Science. Concepts and Methods, Quantitative Data and Formulae" by G. Wyszecki and W.S. Stiles, 2000).

The GIA group uses the area of a highlight as a measure of its subjective size, while the human brain primarily responds to the linear size of an object.
Of course, these problems have not been completely solved in the literature cited, but the material published there convinces one that the experimental data can be fitted by functions that are essentially different from those used at GIA.