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  Systems and methods for evaluating the appearance of a gemstoneUSPTO Application #: 20070043587Title: Systems and methods for evaluating the appearance of a gemstone Abstract: Of the “four C's,” cut has historically been the most complex to understand and assess. This application presents a three-dimensional mathematical model o study the interaction of light with a fully faceted, colorless, symmetrical round-brilliant-cut diamond. With this model, one can analyze how various appearance factors (brilliance, fire, and scintillation) depend on proportions. The model generates images and a numerical measurement of the optical efficiency of the round brilliant-called DCLR—which approximates overall fire. DCLR values change with variations in cut proportions, in particular crown angle, pavilion angle, table size, star facet length, culet size, and lower girdle facet length. The invention describes many combinations of proportions with equal or higher DCLR than “Ideal” cuts, and these DCLR ratings may be balanced with other factors such as brilliance and scintillation to provide a cut grade for an existing diamond or a cut analysis for prospective cut of diamond rough. (end of abstract) Agent: Dla Piper US LLP - San Francisco, CA, US Inventors: Ilene M. Reinitz, Mary L. Johnson, James E. Shigley, Thomas S. Hemphill USPTO Applicaton #: 20070043587 - Class: 705001000 (USPTO) Related Patent Categories: Data Processing: Financial, Business Practice, Management, Or Cost/price Determination, Automated Electrical Financial Or Business Practice Or Management Arrangement The Patent Description & Claims data below is from USPTO Patent Application 20070043587. Brief Patent Description - Full Patent Description - Patent Application Claims
PRIORITY [0001] This application is a divisional application of U.S. patent application Ser. No. 09/687,759, filed Oct. 20, 2000. BACKGROUND OF THE INVENTION [0002] The quality and value of faceted gem diamonds are often described in terms of the "four C's": carat weight, color, clarity, and cut. Weight is the most objective, because it is measured directly on a balance. Color and clarity are factors for which grading standards have been established by GIA, among others. Clamor for the standardization of cut, and calls for a simple cut grading system, have been heard sporadically over the last 27 years, gaining strength recently (Shor, 1993, 1997; Nestlebaum, 1996, 1997). Unlike color and clarity, for which diamond trading, consistent teaching, and laboratory practice have created a general consensus, there are a number of different systems for grading cut in round brilliants. As described in greater detail herein, these systems are based on relatively simple assumptions about the relationship between the proportions and appearance of the round brilliant diamond. Inherent in these systems is the premise that there is one set (or a narrow range) of preferred proportions for round brilliants, and that any deviation from this set of proportions diminishes the attractiveness of a diamond. However, no system described to date has adequately accounted for the rather complex relationship between cut proportions and two of the features within the canonical description of diamond appearance--fire and scintillation. [0003] Diamond manufacturing has undergone considerable change during the past century. For the most part, diamonds have been cut within very close proportion tolerances, both to save weight while maximizing appearance and to account for local market preferences (Caspi, 1997). Differences in proportions can produce noticeable differences in appearance in round-brilliant-cut diamonds. Within this single cutting style, there is substantial debate--and some strongly held views--about which proportions yield the best face-up appearance (Federman, 1997). Yet face-up appearance depends as well on many intrinsic physical and optical properties of diamond as a material, and on the way these properties govern the paths of light through the faceted gemstone. (Other properties particular to each stone, such as polish quality, symmetry, and the presence of inclusions also effect the paths of light through the gemstone). [0004] Diamond appearance is described chiefly in terms of brilliance (white light returned through the crown), fire (the visible extent of light dispersion into spectral colors), and scintillation (flashes of light reflected from the crown). Yet each of these terms cannot be expressed mathematically without making some assumptions and qualifications. Many aspects of diamond evaluation with respect to brilliance are described in "Modeling the Appearance of the Round Brilliant Cut Diamond: An Analysis of Brilliance." Gems & Gemology, Vol. 34, No. 3, pp. 158-183 (which is hereby incorporated by reference). [0005] Several analyses of the round brilliant cut have been published, starting with Wade (1916). Best known are Tolkowsky's (1919) calculations of the proportions that he believed would optimize the appearance of the round-brilliant-cut diamond. However, Tolkowsky's calculations involved two-dimensional images as graphical and mathematical models. These were used to solve sets of relatively simple equations that described what was considered to be the brilliance of a polished round brilliant diamond. (Tolkowsky did include a simple analysis of fire, but it was not central to his model). [0006] The issues raised by diamond cut are beneficially resolved by considering the complex combination of physical factors that influence the appearance of a faceted diamond (e.g., the interaction of light with diamond as a material, the shape of a given polished diamond, the quality of its surface polish, the type of light source, and the illumination and viewing conditions), and incorporating these into an analysis of that appearance. [0007] Diamond faceting began in about the 1400s and progressed in stages toward the round brilliant we know today (see Tillander, 1966, 1995). In his early mathematical model of the behavior of light in fashioned diamonds, Tolkowsky (1919) used principles from geometric optics to explore how light rays behave in a prism that has a high refractive index. He then applied these results to a two-dimensional model of a round brilliant with a knife-edge girdle, using a single refractive index (that is, only one color of light), and plotted the paths of some illustrative light rays. [0008] Tolkowsky assumed that a light ray is either totally internally reflected or totally refracted out of the diamond, and he calculated the pavilion angle needed to internally reflect a ray of light entering the stone vertically through the table. He followed that ray to the other side of the pavilion and found that a shallower angle is needed there to achieve a second internal reflection. Since it is impossible to create substantially different angles on either side of the pavilion in a symmetrical round brilliant diamond, he next considered a ray that entered the table at a shallow angle. Ultimately, he chose a pavilion angle that permitted this ray to exit through a bezel facet at a high angle, claiming that such an exit direction would allow the dispersion of that ray to be seen clearly. Tolkowsky also used this limiting case of the ray that enters the table at a low angle and exits through the bezel to choose a table size that he claimed would allow the most fire. He concluded by proposing angles and proportions for a round brilliant that he believed best balanced the brilliance and fire of a polished diamond, and then he compared them to some cutting proportions that were typical at that time. However, since Tolkowsky only considered one refractive index, he could not verify the extent to which any of his rays would be dispersed. Nor did he calculate the light loss through the pavilion for rays that enter the diamond at high angles. [0009] Over the next 80 years, other researchers familiar with this work produced their own analyses, with varying results. It is interesting (and somewhat surprising) to realize that despite the numerous possible combinations of proportions for a standard round brilliant, in many cases each researcher arrived at a single set of proportions that he concluded produced an appearance that was superior to all others. Currently, many gem grading laboratories and trade organizations that issue cut grades use narrow ranges of proportions to classify cuts, including what they consider to be best. [0010] Several cut researchers, but not Tolkowsky, used "Ideal" to describe their sets of proportions. Today, in addition to systems that incorporate "Ideal" in their names, many people use this term to refer to measurements similar to Tolkowsky's proportions, but with a somewhat larger table (which, at the same crown angle, yields a smaller crown height percentage). This is what we mean when we use "Ideal" herein. [0011] Numerous standard light modeling programs have also been long available for modeling light refractive objects. E.g., Dadoun, et al., The Geometry of Beam Tracing, ACM Symposium on Computational Geometry, 1985, p. 55-61; Oliver Devillers, Tools to Study the Efficiency of Space Subdivision for Ray Tracing; Proceedings of Pixlm '89 Conference; Pub. Gagalowicz, Paris; Heckbert, Beam Tracing Polygonal Objects, Ed. Computer Graphics, SIGGRAPH '84 Proceedings, Vol. 18, No. 3, p. 119-127; Shinya et al., Principles and Applications of Pencil Tracing, SIGGRAPH '87 Proceedings, Vol. 21, No. 4, p. 45-54; Analysis of Algorithm for Fast Ray Tracing Using Uniform Space Subdivision, Journal of Visual Computer, Vol. 4, No. 1, p. 65-83. However, regardless of what standard light modeling technique is used, the diamond modeling programs to date have failed to define effective metrics for diamond cut evaluation. See e.g., (Tognoni, 1990) (Astric et al., 192) (Lawrence, 1998) (Shor 1998). Consequently, there is a need for a computer modeling program that enables a user to make a cut grade using a meaningful diamond analysis metric. Previously, Dodson (1979) used a three-dimensional model of a fully faceted round brilliant diamond to devise metrics for brilliance, fire, and "sparkliness" (scintillation). His mathematical model employed a full sphere of approximately diffuse illumination centered on the diamond's table. His results were presented as graphs of brilliance, fire, and sparkliness for 120 proportion combinations. They show the complex interdependence of all three appearance aspects on pavilion angle, crown height, and table size. However, Dodson simplified his model calculations by tracing rays from few directions and of few colors. He reduced the model output to one-dimensional data by using the reflection-spot technique of Rosch (S. Rosch, 1927, Zeitschrift Kristallographie, Vol. 65, pp. 46 -48.), and then spinning that computed pattern and evaluating various aspects of the concentric circles that result. Spinning the data in this way greatly reduces the richness of information, adversely affecting the aptness of the metrics based on it. Thus, there is a need for diamond evaluation that comprises fire and scintillation analysis. SUMMARY OF THE INVENTION [0012] According to one embodiment described herein, a system models interaction of light with a faceted diamond and analyzes the effect of cut on appearance. To this end, computer graphics simulation techniques were used to develop the model presented here, in conjunction with several years of research on how to express mathematically the interaction of light with diamond and also the various appearance concepts (i.e., brilliance, fire, and scintillation). The model serves as an exemplary framework for examining cut issues; it includes mathematical representations of both the shape of a faceted diamond and the physical properties governing the movement of light within the diamond. [0013] One mathematical model described herein uses computer graphics to examine the interaction of light with a standard (58 facet) round-brilliant-cut diamond with a fully faceted girdle. For any chosen set of proportions, the model can produce images and numerical results for an appearance concept (by way of a mathematical expression). To compare the appearance concepts of brilliance, fire, and scintillation in round brilliants of different proportions, we prefer a quantity to measure and a relative scale for each concept. A specific mathematical expression (with its built-in assumptions and qualifications) that aids the measurement and comparison of a concept such as fire is known as a metric. In one embodiment, the metric for fire considers the total number of colored pixels, color distribution of the pixels, length distribution of colored segments (as a function of angular position), density distribution of colored segments, angular distribution of colored segments, the distribution of colors over both azimuthal and longitudinal angle, and/or the vector nature (directionality) of colored segments. A more preferred embodiment uses the following metric to evaluate fire: sum (over wavelength) of the sum (over the number of ray traces) of the differential area of each ray trace that exceeds a power density threshold cutoff, multiplied by the exit-angle weighting factor. This may be calculated as follows: DCLR=.SIGMA..sub.wavelengths.SIGMA..sub.rays(dArea*.sigma.*Weighting Factor). [0014] In this preferred embodiment, if the power density of a trace is greater than the threshold cutoff, .sigma.=1; otherwise .sigma.=0 and the ray (or other incident light element) is not summed. In a most preferred embodiment, comprising a point light source, the metric considers the total number of colored pixels (sum of rays), the length distribution of colored segments (because with a point source, length approximates differential area), angular distribution of colored segments (the weighting factor) and a threshold cutoff (.sigma.=0 or 1) for ray (or other incident light element) power density. Although other factors (e.g., bodycolor or inclusions) may also influence how much fire a particular diamond provides, dispersed-color light return (DCLR) is an important component of a diamond fire metric. [0015] The systems and methods described herein may further be used to specifically evaluate how fire and scintillation are affected by cut proportions, including symmetry, lighting conditions, and other factors. In addition to the cut proportions expressly including in the tables, other proportions, such as crown height and pavilion depth may be derived from the tables, and used as the basis for optical evaluation and cut grade using the methods and systems disclosed herein. Other embodiments and applications include an apparatus and system to grade a faceted diamonds, new methods of providing target proportions for cutting diamonds, new types of diamonds cuts and new methods for cutting diamonds. [0016] Within the mathematical model, all of the factors considered important to diamond appearance--the diamond itself, its proportions and facet arrangement, and the lighting and observation conditions--can be carefully controlled, and fixed for a given set of analyses. However, such control is nearly impossible to achieve with actual diamonds. The preferred model described herein also enables a user to examine thousands of sets of diamond proportions that would not be economically feasible to create from diamond rough. Thus, use of the model allows the user to determine how cut proportions affect diamond appearance in a more comprehensive way than would be possible through observation of actual diamonds. In one preferred embodiment, the system, method and computer programs use to model the optical response of a gemstone use Hammersley numbers to choose the direction and color for each element of light refracted into a model gemstone (which defines the gemstone facets) to be eventually reflected by the model gemstone's virtual facets, and eventually exited from the model gemstone to be measured by a model light detector. The gemstone is then ultimately graded for its optical properties based on the measurement of said exited light elements from the gemstone model. [0017] In another preferred embodiment, the system determines the grade of a cut using certain assumptions--best brilliance, best fire, best balance of the two, best scintillation, best weight retention, best combination--that can be achieved from a particular piece of rough. In addition, an instrument may also measure optical performance in real diamonds based on the models described. The models of light diamond interaction disclosed herein can also be used to compare and contrast different metrics and different lighting and observation conditions, as well as evaluate the dependence of those metrics on proportions, symmetry, or any other property of diamond included in the model. BRIEF DESCRIPTION OF THE DRAWINGS [0018] FIG. 1 is a drawing and table that outlines the assumptions on which a preferred model is based. Diamond model reference proportions in this patent application, unless otherwise specified, are table 56%, crown angle 34.degree., pavilion angle 40.5.degree., girdle facet 64, girdle thickness 3.0%, star facet length 50%, lower girdle length 75%, culet size 0.5%. [0019] FIGS. 2A to 2C are a plot of DCLR versus crown angle over three thresholds for a modeled round brilliant diamond along with the table of corresponding data. Continue reading... Full patent description for Systems and methods for evaluating the appearance of a gemstone Brief Patent Description - Full Patent Description - Patent Application Claims Click on the above for other options relating to this Systems and methods for evaluating the appearance of a gemstone patent application. ###  How KEYWORD MONITOR works... a FREE service from FreshPatents1. Sign up (takes 30 seconds). 2. Fill in the keywords to be monitored. 3. Each week you receive an email with patent applications related to your keywords. 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