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The appearance of a gemstone depends in part on illumination
conditions: diffuse illumination favors brilliance; localized illumination, such as
spot lighting, favors fire. Regardless of the type of illumination, each illumination
distribution has an associated angular spectrum; the product of the angular
spectrums of the illumination and of the gemstone determines the stone’s
appearance. One goal of optical design is therefore to increase the angular spectrum of
the gem. In a sense, the multiple facets and their projections through internal
reflections in a gemstone act like little windows that permit light to reach the
observer. It is the distribution and variation in brightness from each of these
windows that create contrast. The angles blocked by the observer’s head and by
light leaking through the pavilion may help to create contrast. In the Tolkowsky
cut, in fact, if the facets are aligned properly, the lack of the high angles blocked
by the observer’s head produces eight arrowlike radial obscurations that
enhance contrast. In a “nail-head” diamond, on the other hand, the observer’s
head makes most of the table appear dark and unattractive.
Geometrical angular spectrum is a useful concept for understanding gem-stone
appearance. For purposes of optical design, it allows the contributions of
illumination conditions to be differentiated from the contributions of cut
proportions. Angular spectrum analysis can be used to study fancy-shape cuts (a current
pursuit of the American Gem Society). Figure 5, for example, shows a rendering
of a heart cut and its integrated angular spectrum, characterized by an increased
content of low angles as compared to a round brilliant gemstone.
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Geometrical ray analysis of a gem-stone can be a complex matter because it
involves nonsequential, polarization, splitting and birefringent ray tracing. It
can be time consuming as well, given the large number of rays that need to be
traced and graphically displayed. The gemstone industry uses basic and
advanced programs such as GemCad8 and DiamCal9 to assist in calculating the precise
weight and cut proportions of gemstones. Professional optical design
software such as ASAP,10 FRED,11
LightTools,12 TRACEPRO13 and
ZEMAX14 are capable of performing
sophisticated analysis of gemstones. In some cases, however, in the analysis of
gemstones custom programming may be required to properly display useful
information.
The analysis of a gemstone involves several steps. First, a CAD file in DXF,
IGES or another format that contains the gem geometry must be generated. This
file is imported into an optical design program where sources and detectors are
defined. Next, rays are traced and the ray coordinates and detector information are
processed and displayed as needed. Figure 6 shows the rendering of a round
brilliant diamond by FRED. Since the design and analysis of gems is not a
standard practice, the optical designer faces the tasks of display construction and of
defining metrics for gemstone performance. The optical design of gemstones
is still in its infancy. With the advent of optimization algorithms in illumination
optics, however, it is foreseeable that automatic optimization of gems will
become a reality in the near future. When that time comes, it will be possible to
select a material such as cubic zirconium, to choose a cut shape such as the princess
and to optimize a cut to ensure the strongest brilliance, fire and scintillation.
Historically, this work has been done though trial and error.
One useful criteria in the optical design of gemstones is the goal of
bringing to the observer’s eye the maximum amount of light, while at the same time
producing variations in light intensity to create contrast. To achieve this goal, light
from the low, medium and high ray angles must be distributed evenly and
thoroughly though the gem crown, table and bezel, so that the absence or presence
of one of these angular ranges will contribute to creating contrast. In a superior
cut gem, the blockage of the high angles to produce contrast. Light leakage
through the pavilion is minimized. Fire is maximized by increasing ray deviation
and minimizing leakage through the crown bezel.
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©
2003 Copyright Optical Society of America
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