RE-EXAMINATION OF OPTIMUM CUTTING ANGLES BETWEEN MAIN FACETS OF GEMSTONES BASED ON GEOMETRICAL OPTICS. : Summarized Translation of Journal of the Gemmological Society of Japan (Vol.9,No.1,3-17,June 1982)

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  • Main facetのCutting Angle : ファセッティングの再検討
  • Re-Examinination of Optimum Cutting Angles Between Main Facets of Gemstone Based on Geometrical Optics--Summarized Translation of Journal of the Gemmological Society of Japan(Vol.9, No.1, 3-17, June 1982)

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Abstract

Since angular relations in brilliant cuts according to Tolkowsky, Eppler or Scan.D.N. Standard, etc. and the procedures in evaluating these values involve some obscurities, the angular relations (cutting angles) are re-examined based on geometrical optics, using a round brilliant cut as a standard. Main focus in the present reexamination is paid to finding the conditions for the highest brilliancy. In evaluating brilliancy, first of all equations of i (angle between optical axis and incident ray) are derived for four cases (table → table, main → table, table → main, and main → main), followed by comparisons of brilliancy for different incident rays. Individual brilliancy coefficients are evaluated and are illustrated against different angular relations between a and β (see Figure 1,3,4). The best brilliancy is obtained when F_1 =F_2 (table entrance →table exit=main entrance → table exit). Such cut is called F-cut (Figure 5), in which β=8 (45°-α). This equation is applicable to any gemstones. The optimum main angles for diamond are 34°/40.75°. The effect of the following factors are also analyzed: Dispersion (Figure 8,9) Volume (Figure 10) Yield (Figure 11,12) Area of radiation including scintillation effect (Figure 13,14,15,16). Furthermore, selection of optimum cutting when F_1≠F_2 is analyzed (Figure 17,18,19) and lumpy and shallow stones are explained on the above consideration (Figure 20,21). Finally, the results obtained for brilliant cut diamonds are extended to other gemstones to obtain respective optimum cutting angles.

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