Other authors have already noted many times that the GIA illumination model (illumination source; the absence of observer's profile) is inadequate for calculating the WLR coefficient. We agree with this criticism, but wish to point out an error in the GIA approach, which is more serious than it was reported by these authors. Our opinion is that the WLR coefficient will not correlate with the brilliance even if one corrects the illumination model. The error is wrong understanding of what is the brilliance of a diamond.

First, GIA identifies the brilliance with light return.

Second, the light return is determined as the light returned from the diamond into the upper hemisphere.

Without any explanation, GIA excludes any external luster when defining the light return. However, we treat this as a technical problem of GIA and further include the external luster in the definition of the light return). Further, we will use the abbreviation LRGIA to denote the total light return into the upper hemisphere, while the abbreviation LRMSU will be used to denote the light reaching the observer's eye (eyes, for a stereo-observer).

We would like to stress that we identify none of these two figures with the brilliance. The above ideas are easier to comprehend if you imagine a mirrored disco ball. It produces a lot of reflections on the walls, ceiling and floor, but a person sees just a few at once.

In its left window, the Brill software models a single mirror that swings in such a way that the mirror inclination ranges from zero to 3 degrees. You may observe the source image motion caused by this swing. One complete highlight is permanently seen while the mirror swings.

Run Brill software - Mirror example #1

- Square mirror with a size of 35x35 cm; - Observer at a distance of 60 cm from the mirror, the pupil diameter of the observer's eye being 4 mm; - One small (point-like) incandescent lamp placed at a distance of 2 m from the mirror.

Let us adjust the mirror so as to make the observer see the lamp approximately in the center of the mirror. When the mirror is viewed from the point where the lamp is located, the angular size of the mirror is about 10°, while the observer would estimate the angular size of the mirror as 32°. If we consider a light beam that originates from the lamp, reflects off the mirror, and finally enters the pupil of the observer's eye, the diameter of this beam measured in the mirror plane will be 3 mm.

Let us now analyze the light reflected by the mirror (the coefficient LR_GIA) and the light entering the observer's eye (the coefficient LR_MSU). We shall use the abbreviation LR_GIA0 to denote the coefficient LR_GIA calculated for the specific position of the lamp and the abbreviation BR₀ to denote the mirror brilliance for this case.

Now suppose that we have split the mirror into 100 equal portions (for example, squares) and randomly tilted each portion by an angle that ranges from -3° to +3°.

Now the software models splitting the original mirror into 100 portions (10x10). Each of the portions is randomly tilted by an angle ranging from zero to 2 degrees. As before, the whole object swings with an amplitude of 3 degrees. In this case, the number of highlights visible at once ranges from zero to a few ones. Some of the highlights are complete, while other are just fragments.

Run Brill software - Mirror example #2