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| Metrics for beauty | ||
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Recently, members of the gemstone industry have engaged in efforts to
produce metrics for a diamond’s beauty that measure appearance attributes such as brilliance, fire and scintillation. Notable are the studies by the Gemological Institute of America (GIA)3,4 and a group of professionals at Moscow State University.5,6 To identify and quantify which cuts produce the best appearance, as well as to contribute to the establishment of a system to grade gems, the two organizations have independently defined metrics and made parametric studies of the proportions of the round brilliant diamond. It is well known, for example, that a decrease in the angle of the pavilion can be compensated by an increase in the angle of the crown. This concept is similar to that of lens bending in lens design. It should be noted, in any case, that for fancy-shape cut gem-stones — such as the marquise, oval and heart — the understanding of light propagation and its link to optimal design is still somewhat of an open question. Figure 3. (a) Representation of the angular spectrum, (b) integrated angular spectrum (relative collected energy vs. angle), (c) change of integrated angular spectrum with color. Figure 4. (a) Effect of facet illumination in producing contrast, (b) multiple light sources accentuating fire. James Caudill (a) (b) to the gem and collected on the hemisphere. |
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One insightful approach to analyzing light propagation in gems is to use the
concept of geometrical angular spectrum. Here angular spectrum refers to the
set of ray-angle directions that can make a gem’s facet bright. Rather than
forward illuminating a stone, a reverse ray trace indicates the ray directions that
can actually bring light to the observer’s eye (see Fig. 2). If these directions are
projected into a hemisphere (as described by Meinel and Meinel 7 ) and centered on the
gem, a two-dimensional map can be obtained that shows the directions
or angles that can contribute to brilliance and fire [see Fig. 3(a)]. The observer’s head can block some of the central angles, so one goal of the optical design of gems is to control how much angular range can be blocked in this way. Some diamonds, called “nail heads,” lack brilliance because the pavilion has nearly a 45° angle that makes the stone act as a retroreflector and prevents ambient lighting from reaching the observer’s eye. The summation of the ray energy over concentric rings that are equally spaced on the hemisphere permits quantification of the angular spectrum [see Fig. 3(b)]. For the Tolkowsky cut — 34.5° crown angle, 40.7° pavilion angle, 53% table-to-diameter ratio — which has become a standard, about 75% of the energy reaches the hemisphere, about 17% corresponds to reflection on the crown which is not taken into consideration because it represents glare and about 9% is light leakage through the pavilion. In the hemisphere, high angles are from 76° to 90° (observer head), medium angles are from 45° to 75° and low angles are from 0° to 44°. In the Tolkowsky cut, about 15% of the energy is directed to the high angles, 51% to the medium and 8% to the low angles. Other cut proportions produce different angular spectrums and have different light proportions in the low, medium and high angles. An angular spectrum can be considered a gem signature because it intrinsically carries the cut proportions. The change of angular spectrum with color (blue and red) gives a measure of the dispersion and ray directions that can produce fire [see Fig. 3(c)]. When a stone is tilted, the angular spectrum increases in the low angles and the energy that reaches the hemisphere decreases. The directions that can produce fire are increased and fire may decrease toward the low angles as well. This suggests that for the analysis of a gemstone, it is sufficient to consider a normal view with respect to the gem’s table. Analysis of the Tolkowsky cut shows that the majority of light, 51%, comes from the medium angles, as does the fire. The facets of a stone that are brilliant have the potential to produce fire. Brilliance is a combination of lighted on and off facets. A stone that evenly returns light, with no dark facets, appears lacking in life. It is the distribution and number of dark and bright facets that produce brilliance in a gemstone, as shown in Fig. 4 (a). For comparison, Fig. 4 (b) shows fire as enhanced by a plurality of localized light sources. |
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©
2003 Copyright Optical Society of America
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