The Optical Design T of Gemstones José M. Sasián, Peter Yantzer and Tom Tivol Peter Yantzer The best jewellers have always been 100% aware that the quality of the cut is 53% primarily responsible for making Table Bezel a stone appear brilliant and Crown 16.2% colorful, or dull and lifeless. 34.5° Today, advanced optical design software is being Girdle used to optimize gem- cutting by modeling light propagation 40.7° through stones. Pavilion
Figure 1. Tolkowsky proportions and diamond nomenclature.
here is new excitement in the gem- metrics based on light response and stone industry. Today, for the first beauty have been introduced. The gem- T time, scientific advances are allow- buying public also benefits from an ing the detailed optical design, precision understanding of light propagation in cutting and characterization metrology gemstones. The main focus of this article of beautiful jewels. Understanding how to is to describe the role of optics in gem- cut a stone to best disperse and break stone design along with related trends in light into a plurality of colorful scintilla- the gemstone industry. tions has consistently been a major focus of the gemstone industry. Diamonds, for The complexities of cut example, are marketed on the basis of the By trial and error, ancient jewelers pro- Four C’s: cut, color, clarity and carat duced cuts that refracted light to give illu- weight. Of these four attributes, "cut" is mination life to gemstones. One of the the least understood by the general public first thought-provoking studies on how and by jewelry industry professionals. to cut gems was published by M. The word is used to refer not only to the Tolkowsky1 in 1919. He systematically shape of the diamond but also to its pro- analyzed the optics of a diamond and portions, symmetry and polish. The qual- estimated the best proportions for cut- ity of the cut is primarily responsible for ting brilliant round diamonds. With making a stone appear brilliant and col- minor changes, today’s standards for orful, or dull and lifeless. It is obvious “ideal-cut” diamonds are based on that an understanding of how a gem Tolkowsky’s definitions. The round bril- manipulates light to produce the effects liant diamond shown in cross section in of brilliance (brightness), fire (disper- Fig. 1 is the best understood of all the sion) and scintillation (sparkle) is critical shapes in which diamonds are cut. It to the proper design of jewels. consists of 57 facets, 33 in the crown (one Another important reason to under- for the crown table and 32 for the crown stand the behavior of light in gemstones bezel) and 24 in the pavilion. Light enters is to establish and apply grading sys- the stone through the crown and is inter- tems.* Given the large variety of gem nally reflected until it is finally refracted materials and shapes available today, and directed to the examiner’s eye or grading systems that make use of elsewhere. It is undesirable to have light
* Professional organizations such as the American Gem Society (AGS) offer their members services that range from certifying the authenticity of gems to giving an expert opinion on quality.
Peter Yantzer April 2003 ■ Optics & Photonics News 25 1047-6938/03/04/0024/6-$0015.00 © Optical Society of America THE OPTICAL DESIGN OF GEMSTONES
José Sasián entering or leaking out through the pavil- ion or girdle because it will reduce the potential of a diamond to show its bril- liance. Thus the optical function of a José Sasián stone’s cut is to bring light to the observer’s eye from above the crown. In performing this function, light is dis- persed and colorful flashes—known in the gemstone industry as fire—can be observed. An additional objective is to create a cut by means of which a plurality of the stone’s facets are lit and others left dark, which produces a bright appear- 2 (a) ance on the crown known as brilliance. Illumination conditions and cut propor- 0° 90° tions determine whether fire or brilliance predominates. Scintillation, another attribute of gemstones, refers to their ability to produce an appearance of flashes of light when gemstone, observer or light source is moved. Gemstone beauty is a complex subject that involves (b) the human visual system, stone cut pro- 0° 90° portions and illumination conditions. Putting technical considerations aside for the moment, it is indeed breathtaking to behold the beauty of a diamond that has been optimally cut. Metrics for beauty Figure 2. Rays are back ray traced (c) Recently, members of the gemstone to the gem and collected on the hemisphere. industry have engaged in efforts to pro- Figure 3. (a) Representation duce metrics for a diamond’s beauty that of the angular spectrum, (b) integrated angular spectrum measure appearance attributes such as (relative collected energy vs. angle), brilliance, fire and scintillation. Notable (c) change of integrated angular are the studies by the Gemological spectrum with color. Institute of America (GIA)3,4 and a group of professionals at Moscow State 5,6 James Caudill University. To identify and quantify which cuts produce the best appearance, as well as to contribute to the establish- ment 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- (a) (b) stones—such as the marquise, oval and heart—the understanding of light propa- Figure 4. (a) Effect of facet illumination in producing contrast, gation and its link to optimal design is (b) multiple light sources accentuating fire. still somewhat of an open question.
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One insightful approach to analyzing light propagation in gems is to use the José Sasián concept of geometrical angular spectrum. 0° 90° 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 pro- jected into a hemisphere (as described by Meinel and Meinel7) and centered on the gem, a two-dimensional map can be (a) (b) obtained that shows the directions or angles that can contribute to brilliance Figure 5. Fancy-shape heart cut and its integrated angular spectrum. 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 bril- liance because the pavilion has nearly a 45˚ angle that makes the stone act as a retroreflector and prevents ambient light- ing from reaching the observer’s eye. The summation of the ray energy over con- centric 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-diame- ter 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 repre- sents 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 Figure 6. A round brilliant rendered by FRED software.11 is directed to the high angles, 51% to the medium and 8% to the low angles. Other cut proportions produce different angu- lar spectrums and have different light decreases. The directions that can pro- and off facets. A stone that evenly returns proportions in the low, medium and high duce fire are increased and fire may light, with no dark facets, appears lacking angles. An angular spectrum can be con- decrease toward the low angles as well. in life. It is the distribution and number sidered a gem signature because it intrin- This suggests that for the analysis of a of dark and bright facets that produce sically carries the cut proportions. The gemstone, it is sufficient to consider a brilliance in a gemstone, as shown in change of angular spectrum with color normal view with respect to the gem’s Fig. 4 (a). For comparison, Fig. 4 (b) (blue and red) gives a measure of the dis- table. Analysis of the Tolkowsky cut shows fire as enhanced by a plurality of persion and ray directions that can pro- shows that the majority of light, 51%, localized light sources. duce fire [see Fig. 3(c)]. comes from the medium angles, as does The appearance of a gemstone When a stone is tilted, the angular the fire. The facets of a stone that are bril- depends in part on illumination condi- spectrum increases in the low angles and liant have the potential to produce fire. tions: diffuse illumination favors bril- the energy that reaches the hemisphere Brilliance is a combination of lighted on liance; localized illumination, such as
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José Sasián, James Caudill 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 (a) (b) (c) 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 (d) (e) (f) program where sources and detectors are defined. Next, rays are traced and the ray coordinates and detector information are Figure 7. Sequence of images illustrating processed and displayed as needed. the effect of the three angular ranges of Figure 6 shows the rendering of a round illumination in a diamond: (a), (b) and brilliant diamond by FRED. Since the (c) are actual photographs; (d), (e) and design and analysis of gems is not a stan- (f) are ray-tracing simulations. In (g) the dard practice, the optical designer faces three angular ranges are color coded the tasks of display construction and of and combined. defining metrics for gemstone perfor- mance. The optical design of gemstones (g) is still in its infancy. With the advent of optimization algorithms in illumination optics, however, it is foreseeable that spot lighting, favors fire. Regardless of the enhance contrast. In a “nail-head” dia- automatic optimization of gems will type of illumination, each illumination mond, on the other hand, the observer’s become a reality in the near future. When distribution has an associated angular head makes most of the table appear dark that time comes, it will be possible to spectrum; the product of the angular and unattractive. select a material such as cubic zirconium, spectrums of the illumination and of the Geometrical angular spectrum is a to choose a cut shape such as the princess gemstone determines the stone’s appear- useful concept for understanding gem- and to optimize a cut to ensure the ance. One goal of optical design is there- stone appearance. For purposes of optical strongest brilliance, fire and scintillation. fore to increase the angular spectrum of design, it allows the contributions of illu- Historically, this work has been done the gem. In a sense, the multiple facets mination conditions to be differentiated though trial and error. and their projections through internal from the contributions of cut propor- One useful criteria in the optical reflections in a gemstone act like little tions. Angular spectrum analysis can be design of gemstones is the goal of bring- windows that permit light to reach the used to study fancy-shape cuts (a current ing to the observer’s eye the maximum observer. It is the distribution and varia- pursuit of the American Gem Society). amount of light, while at the same time tion in brightness from each of these Figure 5, for example, shows a rendering producing variations in light intensity to windows that create contrast. The angles of a heart cut and its integrated angular create contrast. To achieve this goal, light blocked by the observer’s head and by spectrum, characterized by an increased from the low, medium and high ray light leaking through the pavilion may content of low angles as compared to a angles must be distributed evenly and help to create contrast. In the Tolkowsky round brilliant gemstone. thoroughly though the gem crown, table cut, in fact, if the facets are aligned prop- Geometrical ray analysis of a gem- and bezel, so that the absence or presence erly, the lack of the high angles blocked stone can be a complex matter because it of one of these angular ranges will con- by the observer’s head produces eight involves nonsequential, polarization, tribute to creating contrast. In a superior arrowlike radial obscurations that splitting and birefringent ray tracing. It cut gem, the blockage of the high angles
28 Optics & Photonics News ■ April 2003 THE OPTICAL DESIGN OF GEMSTONES by the observer is used advantageously Peter Yantzer to produce contrast. Light leakage through the pavilion is minimized. Fire is maximized by increasing ray deviation Eye and minimizing leakage through the crown bezel. Figure 7 shows, in sequence, the 10X Lens appearance of a diamond as the low-, medium- and high-illumination ray angles are removed. The first row of Red Reflector images (a, b, and c) are actual pho- tographs; the second row (d, e and f) are Transparent Tray ray-tracing simulations. There is not complete agreement between the images because of a small error in acquiring the Diffused White Light Source gem’s geometry as represented by the modeling abilities of the software pack- (a) (b) age. Nevertheless, the images show how powerful ray tracing can be as a tool for Figure 8. (a) Schematic drawing of a Firescope, the study of light behavior in gems. The (b) photograph of a round brilliant through a Firescope. colorful image in Fig. 7(g) is an actual photograph that for purposes of evalua- tion combines the low (blue), medium indicate that the stone can bring differ- References 1. M. Tolkowsky, Diamond Design: A Study of the Reflection (red) and high (black) angles. Color hues ent amounts of light from a given angu- and Refraction of Light in a Diamond, Spon & are caused by the multiple ray refractions lar range. Both the spatial view of a gem Chamberlain, New York, 1919.
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