MSU Diamond Cut Study

The detailed model description

To study diamond cut, a group of researchers from Moscow State University have developed specialized software called "Brill". The software employs a mathematical model that consists of the following parts:

Model parts :


1. Illumination sources.	5. Absorption.
2. Diamond.	6. Coefficients.
3. Ray tracing.	7. Tolkowsky diamond.
4. Observer.

1. Illumination sources.

The illumination model involves a set of up to 100 virtual Lambertian sources of white light. Each of the sources has its own position and angular size. To determine the fire of a diamond, 60 randomly positioned light sources are used. The angular size of these sources is small (2-10°) - to model "Chandelier" light source. To model diffuse illumination, from 2 to 5 separate sources are used, each of these having an angular size of 20-40° - light source "Office" - type. The sources are located at a semi-sphere, from which the contour of the observer is excluded. The positions of the sources are selected so that they do not illuminate the pavilion of the diamond when the latter is inclined by an angle of no more than 30°. The software is capable of modeling not only Lambertian sources, but also light sources with non-uniform directional patterns.

2. Diamond.

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to enlarge

The diamond under study is chosen to have a standard round brilliant cut with a pointed culet and faceted girdle, with ideal symmetry and ideally polished flat facets. The computer builds up a complete 3D parametric model of diamond cut, the shape of which is determined by the following parameters:

А (crown angle)	The angle (measured in degrees) between the bezel facets and the girdle plane
B (pavilion angle)	The angle (measured in degrees) between the pavilion mains and the girdle plane
Dp (table size)	The width of the table (in % of the girdle diameter)
q (lower girdle facet size)	The length of the lower girdle facet divided by the distance between the center of the culet and girdle edge
h (minimum girdle thickness)	The distance between upper and lower girdle facets (the narrow part of the girdle), measured in % of the girdle diameter
Gd (maximum girdle thickness)	The girdle thickness in the thick part of the girdle, measured in % of the girdle diameter

The software allows the user to model other common fancy shapes as well. The calculations use the following fixed parameters: h=1% (at the narrow part) and q=0.82. The pattern of the crown facets is maintained so that the table and the star facets form two squares when the diamond is viewed in face-up position.

3. Ray tracing.

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to start ray-trace modeling

The calculations deal with multiple ray tracing with taking into account Fresnel reflections at facets. Partial polarization of light (as it is refracted and reflected in the diamond) is not considered. The maximum number of the multiple reflections of a single ray in round brilliant cut considered as 20. If the intensity of a ray decreases 1000 times, it is no longer traced. To simulate the facet polishing imperfection, the model includes separate light scattering coefficient for all the facets of the modeled gem. The value of the coefficient can be varied from zero to unity.

4. Observer.

The software models the angular size of the observer's pupil (the linear size of the pupil divided by the distance between the pupil and the diamond). It is taken into account that the observer's head screens some of the illumination sources. The angular size of the head can be varied from 5 to 20°. The screening of illumination sources by the observer's body is kept in mind when arranging the sources. Color computations match the standard colorimetric observer CIE 1931.

5. Absorption.

When modeling a colorless diamond, light absorption inside the crystal is neglected. For colored diamonds, the absorption is determined by a stepwise-approximated absorption spectrum of the real diamond. Color computations needed for determining the fire of the gem and the color of a separate ray match the ordinates of the composition curves of the standard colorimetric CIE 1931.