Main facetのCutting Angle : ファセッティングの再検討 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)

本論文は,宝石学会誌Vo1.9,No.1,P3-17,1982で発表した上記標題の英文,およびその後の同じ本題に関して1988年までに発表した一連の論文と宝石のファセッティング全般に関する主要文献についてのW.Funnel,F.G.A.Aのコメント及び主要文献の大要の紹介で構成されている。もともと上記論文が発表されてしばらくあと,オーストラリアの宝石学者W.Funnelより,編集長あて同論文の英訳の入手可能性について問い合わせがあった。Australian Gemmologistに掲載したいという趣旨であったので,抄訳の形で送稿したが,長文であるとの理由で,同誌上への掲載は見送られる結果となった。代わりに上記のようにFunnel氏が小論にNOTE以降を付加して小冊子を作製し,同氏より直接入手可能の旨がAustralian Gemmologist誌上に紹介された。ファセッテインクに関する同氏の付記は本誌読者にとっても有益だろうと判断し,これらをまとめてここに再録するものである。再録承認に対し同氏に改めて感謝する。なお現在同氏御夫妻とも老齢病躯にあり,心からご快癒を祈る。

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.