Evaluation of brilliance, fire, and scintillation in

round brilliant gemstones

Jose Sasian, FELLOW SPIE

University of Arizona

College of Optical Sciences

1630 East University Boulevard

Tucson, Arizona 85721

E-mail: [email protected]

Jason Quick

8881 West Sahara Avenue

Las Vegas, Nevada 89117

Peter Yantzer

American Gem Society Laboratories

8917 West Sahara Avenue

Las Vegas, Nevada 89117

Abstract. We discuss several illumination effects in gemstones and

present maps to evaluate them. The matrices and tilt views of these

maps permit one to find the stones that perform best in terms of illumi-

nation properties. By using the concepts of the main cutter’s line, and the

performance.

© 2007 Society of Photo-Optical Instrumentation Engineers.

关DOI: 10.1117/1.2769018兴

Subject terms: gemstone evaluation; gemstone grading; gemstone brilliance;

gemstone fire; gemstone scintillation; gemstone cuts; round brilliant; gemstones;

diamond cuts; diamonds.

Paper 060668R received Aug. 28, 2006; revised manuscript received Feb. 16,

2007; accepted for publication Apr. 10, 2007; published online Oct. 1, 2007.

1 Introduction

Craftsmanship of gemstones that produce appealing illumi-

planar surfaces called facets. The top facets form the crown

and the bottom facets form the pavilion of the stone. The

facets themselves are polygonal in their boundary. Facets in

the crown capture light and facets in the pavilion reflect

light by total internal reflection. This light capturing and

redirection function makes a gem appear illuminated and

there are several illumination effects produced that make a

stone appealing. The main illumination effects are bril-

liance, fire, and scintillation. There is a limited set of cuts

that favor the simultaneous presence of these effects that

partitioned by the stone facets into a plurality of beams that

are totally internally reflected and then refracted out of the

stone. The refracted beams, through Fresnel splitting, create

second and higher-order generations of beams that in turn

are refracted out of the stone. Each beam generation carries

less and less energy according to the Fresnel coefficients, to

light absorption in the bulk of the gemstone material, or to

light scattering by material inclusions. Light that exits the

gemstone may reach the eyes of an observer creating a

plurality of illumination effects that significantly impact the

appearance of the gemstone. Among the most important

stone to redirect light to the eyes of an observer so that the

gem’s crown appears illuminated. The effect of fire refers

to the rainbow-like colors with which light exits a gem’s

facet as seen by an observer. Fire occurs because white

light entering or exiting a stone is dispersed into its con-

stituent colors. The effect of scintillation refers to flashes of

light, white or colored light, that are produced when the

gem, the observer, or the illumination source move. Scin-

tillation is a dynamic and rich effect. The effect of leakage

refers to light that exits the stone through the gem pavilion

have been traditionally evaluated with the unaided eye and

with the aid of magnifiers. The first device to be recognized

as an effective tool to aid in the cutting of stones is the

FireScope

, which was invented in Japan in 1984

about gemstone symmetry and brilliance, and the Angular

show critical directions from which a gem captures light.

Previous studies

have been fruitful in understanding

illumination effects in gemstones but have been limited in

Fred,

LightTools,

TracePro,

there has also been progress in understanding the illumina-

Fig. 1 Nomenclature of the round brilliant cut.

Fig. 2 Light rays can enter the gem and be redirected to the eye

from different directions.

Fig. 3 Nomenclature to indicate ray directions. Normal to the gem

0 deg.

Fig. 4 Angular spectrum of a round brilliant as projected in the

hemisphere. Each dot represents a ray direction that can make a

virtual facet appear illuminated. Several ray refractions, including

the primary, are included.

Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones

Fig. 6 ASET Map of a round brilliant gem coded by colors on the

gem’s crown according to angular ranges.

scintillation. Regardless of the illumination, each illumina-

tion distribution will have associated an angular spectrum

and the product of the angular spectrums of the illumina-

tion and the gemstone will determine the stone’s appear-

ance. The concept of angular spectrum is helpful to de-

couple the contributions to a gem’s appearance from the

illumination conditions and its cut. It would be possible to

arrange the illumination conditions to make many gems

appear with the attributes of brilliance, fire, and scintilla-

tion. In practice the illumination conditions are not ideal

fire or scintillation attributes has little appeal. To produce

brilliance, fire, and scintillation the illumination must be

structured and this can be achieved in three manners. The

first is by the illumination conditions of the environment

where the stone is observed; the second is by the partial

obscuration of the gem’s angular spectrum by the observer,

and the third manner is by the intrinsic properties of the cut.

Structured lighting is a key concept for understanding and

producing illumination effects in gemstones and it is em-

phasized in this paper.

Gray areas represent light leakage.

a cut that shows little brilliance.

Fig. 11 The phenomenon of dynamic contrast shown in a series of tilt positions ranging from −30 to

30 deg in 5-deg intervals.

Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones

the angular spectrum of the primary refraction. The dis-

reference to indicate ray directions. The axis of the stone

passes through the center of the hemisphere and ray direc-

tions are measured with respect to the plane of the table.

Thus a direction of 90 deg coincides with the axis of the

stone and hemisphere as shown in Fig. 3.

One way to acquire the angular spectrum of a gem is

through computer modeling and ray tracing. Rather than

forward illuminating the gem, a reverse ray trace starting at

the observer’s eye will indicate the ray directions that ac-

tually can bring light to the observer’s eye. If these ray

the Fresnel ray split. In comparison, Fig. 5 shows the an-

gular spectrum contributed only by the primary refraction.

In this later case there is a one-to-one mapping between the

direction and the point where a ray exits the gem’s crown in

its path to the observer’s eye.

Although reverse ray tracing can easily display a precise

representation of the angular spectrum in the hemisphere, it

is more insightful to actually show regions in the gem’s

crown that contribute to specific angular spectrum ranges.

We have defined three angular ranges in relation to the

that leaks through the pavilion and therefore do not contrib-

ute to brilliance or fire. This representation of the angular

spectrum by ranges and zones on a gem’s crown is useful

because it directly relates ray directions to crown zones and

therefore can be easily interpreted. We call this graphical

representation of the angular spectrum an ASET map.

The choice of the angular ranges to acquire the angular

spectrum reflects practical considerations. The high angles

an average observer can block this angular range. Thus

tion of gemstones is naturally done with light arriving ei-

ther from the back or above the head of the observer, third

is the structured lighting that is created in the gemstone due

to the obscuration of the head and body when the stone is in

movement, and fourth is that in realisitic environments il-

lumination frequently occurs at angles greater than 45 deg.

does not contribute significantly to brilliance or structured

lighting. There is some simplification in the ranges selected

that intends to account for common illumination and obser-

purposes of the characterization approach presented in this

paper. Given the eightfold symmetry of the round brilliant

cut there is no need to further subdivide the angular ranges

in the hemisphere with respect to azimuth. Some fancy cuts

with reduced symmetry, however, would require further

subdivision of the hemisphere to acquire more detailed in-

formation about their angular spectrum.

5 Illumination Effects

The main goal of this paper is the evaluation of the illumi-

nation effects of brilliance, fire, and scintillation. However,

tribution and variety of colors in the maps as commented

map shows the added blue regions with a darker hue.

Fig. 13 Brilliance of a round brilliant stone as the illumination over the hemisphere increases in 30-deg

sectors. Note that by 180 deg the crown is substantially illuminated and exhibits positive contrast

properties.

Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones

facets. This occurs because as a beam of light enters a

gemstone it is divided into a plurality of beams resulting

from the projection of the entering beam on the gemstone

facets as shown in Fig. 7. These perceived facets are known

as virtual facets and their number depends on the number of

actual facets the stone has and on the number of times light

is partitioned as it propagates in the stone. Within the round

shape there are cut geometries that include more facets than

the standard round brilliant cut such as the Gabrielle

Fig. 15 A large facet can appear multicolored since it can redirect to

obscuration. The fact that the Tolkowsky cut retains a well-

balanced contrast pattern in these two views indicates su-

periority in creating structured lighting. Thus characterizing

gem contrast is essential in assessing the visual appeal of

gemstones.

Fig. 17 Angular spectrum of a gemstone as projected in the hemisphere upon −15, − 10, −5, 0.0, 5,

10, and 15 deg tilts. This sequence shows that upon tilting a stone the probability of intersecting a

source by the angular spectrum is essentially one.

Fig. 18 The bigger the chromatic flares are, the larger the probabil-

ity is of being captured and clipped by the eye’s pupil.

indicates obscured, low-angle light or leakage. Dark orange indi-

An alternate view to contrast properties is shown in Fig.

13 where the hemisphere increases its illumination as the

azimuth range is increased from zero to 360 deg in 30-deg

increments and upon the face-up position.

5.4 Gem Fire

The phenomenon of fire is one of the most appealing ef-

fects in transparent gemstones. Under favorable conditions

fire makes individual facets appear fully colored with the

rainbow hues.

and the angular subtend of the eye’s pupil in relation to the

facet.

To best observe fire it is required to have a localized

source of light so that its angular subtend is much smaller

than the angular dispersion produced by the gem facet, es-

sentially a point source. As different colored rays arrive to

the eye from a facet, some of them enter the eye’s pupil and

others are blocked producing a colored appearance of the

facet as shown in Fig. 14. In this process the boundary of

the eye’s pupil plays a critical role in obstructing portions

from about 2 to 8 mm in size. Therefore there is some

variability on the amount of fire perceived by different ob-

servers in different illumination conditions.

Relative to the eye’s position, the angular subtend of a

given facet determines the appearance of the facet. If the

subtend of the facet is small, then only one color would be

observed across the facet. As the angular subtend of the

facet increases, more colors would be observed, until fi-

nally the entire spectrum would be seen. Essentially, the

eye would be observing the source at different lateral loca-

fraction of a degree to a few degrees the color saturation

will decrease. Intermediate colors such as green will disap-

pear first, then only blue and red will be observed, and

finally no colors will be observed. In this process of in-

creasing the source size, ray overlap from different loca-

tions in the source takes place, washing out the colored

appearance of the facet as shown in Fig. 16.

Modeling of gem fire can be done by assuming specific

localized illumination scenarios such as spot lighting or

chandelier illumination. However, gem evaluation may fa-

in essentially a probability of one to intersect a given local-

ized light source. This observation is illustrated in Fig. 17,

which shows the angular spectrum of a gemstone that has

been tilted in the range of ±15 deg with respect to the

face-up position. The practical meaning of this observation

is that for evaluating fire one can factor out the illumination

conditions. Thus, our evaluation of fire is independent of

the source distribution. Appendix A provides further sup-

port with a study of the angular spectrum as a function of

stone cut parameters.

the medium angles. The colors used are red, green, blue, cyan,

magenta, and yellow.

Fig. 22 Glare maps of a round brilliant showing directions in the hemisphere that can contribute glare.

The maps are in tilt positions ranging from −30 to 30 deg in 5-deg intervals.

Sasian et al.: Evaluation of brilliance, fire, and scintillation in round brilliant gemstones

Then, the next important factor in the production of fire

is the amount of dispersion that rays from facets in a gem’s

crown have. Gemstones at a distance of 250 mm possess

separate the light colors across the observer’s pupil. The

amount of dispersion from each virtual facet is a significant

is not a concern due to the relatively high brightness of

localized sources that can produce fire.

Figure 19 shows what we call a fire map, which indi-

cates the potential of a stone to produce fire. It is actually a

dispersion map, coded by colors, that indicates the amount

of dispersion that a white-light ray will undergo in reaching

the observer’s eye at a distance of 250 mm in the face-up

position. Dark orange indicates a linear dispersion of

2.0 mm or less at the eye of the observer. Orange is disper-

sion between 2.0 mm and 4.2 mm, light orange is disper-

observer’s space, show the potential to observe fire. Re-

verse fire maps, produced in the source space, show the

potential to observe a source. The dispersion in the reverse

and forward fire maps is related by the anamorphic magni-

fication associated to the prism corresponding to each vir-

tual facet.

There are other factors that can determine fire in a gem-

stone, as for example the amount of light from higher-order

cantly the fire potential of a stone and are a valuable tool

for assessing gem fire.

5.5 Gem Scintillation

In the presence of brilliance and fire the most appealing

effect is gem scintillation. In this effect the fire pattern

Fig. 23 A matrix of ASET maps as a function of crown and pavilion

angles upon primary refraction. The highlighted diagonal lines rep-