Experimental Methods for Estimation of Jewels Suggested as Optical Division and Angle Anisotropy

Authors have been investigating experimental estimation methods for grading of diamonds as cut jewels, which are regarded as transparent polyhedral materials constructed by plane facets. Interpretation that glare of the jewels is regarded as optical scattering by polyhedrons can suggest a way to physical and statistical analysis based on optical experiments.<br> Generally, grading of some jewels is achieved as optical observation by human's sense under recommended isotropic lighting environment since their brilliance is realized as external light. If so, recognized brilliance brought to human's eye should originate in both source of external incidence (from unidentified direction) and internal path in the samples. But, it is unfortunately too complicated to search or to trace the origin of incidence and inner path. Or, isotropic external lighting might not be necessarily suitable to quantitative evaluation.<br> The authors have noticed that the sample of the cut jewel as optical scatterer is shaped as polyhedron constructed by plane facets and that it is three-dimensional materials with linear ridgelines. Therefore, if the jewel sample is irradiated by incidence of straight and narrow-spread light (such as laser beam) which has sufficient width to cover the sample volume, (external and internal) reflection at the ridgelines divides the beam, and unidentified sequence of reflection makes the beam narrower.<br> Consequently, one straight incident beam to the polyhedrons is divided to scattered beams with various direction and much smaller widths. Or, the divided beams may be radiated (scattered) externally. If such beams scattered externally are detected by external some optical devices, that should just be “glare of jewels”.<br> Then, as the first step of our experiments with straight beam, the scattered beams are projected as “light spots” on a curved screen, and the scattered beams can be evaluated as the light spots with solid angles. And, the scattered light spots given by straight incidence are numerically evaluative through imaging analysis. Recognition of glare should be probability of scanning by the scattered light spots for region corresponded to virtual detectors; such probability is discussable with statistical distribution of number and size for the light spots.<br> Next, we can modify direction of incidence. When incidence moves with many enough steps as direction, it simulates “isotropic external lighting” approximately. Or, we can estimate emphasis of glare by anisotropic distribution in scattering. Then, data will be able to suggest what is more effective design for impressive glare under specific external lighting or what is better direction of observation for some designed jewels.<br> It is important that, in this discussion, we are not considering proportion of the sample; considered subjects are physical discussion: “how the beams are numerically divided when the sample is irradiated by a straight beam?” or “how projection of the scattered beams will change when incident direction is modified?”<br> As experimental equipment, we applied “parabolic (curved) screen” which had a focus adjusted to the measured sample. As straight incidence, laser beam or white LED light irradiated the sample through a slit equipped on the screen. “Light spots” from the sample projected on the screen were observed with a camera, and the images were analyzed as two-dimensional digital data.<br> And, for brilliant cut diamonds (58 facets) or ones with more or less facets, statistical distribution of solid angle (Ω) of scattered beams was analyzed. As a result; histogram of  showed “exponential rule” for numerical distribution in smaller Ω region: N(Ω)∝exp{-λΩ} (λ›0). However, since more impressive and intense glare may be attributed to light spots with larger Ω, we now suppose that deviation from the “exponential rule” may be important for jewel grading.