Tangent ratio optimization across gemstone materials
| Material | RI | Original | Optimized | Ratio | Δ | |
|---|---|---|---|---|---|---|
| Moissanite | 2.650 | 0.196 | 0.284 | 0.5270 | +0.088 | |
| Tanzanite | 1.695 | 0.116 | 0.251 | 1.0838 | +0.136 | |
| Amethyst | 1.544 | 0.043 | 0.231 | 1.1532 | +0.187 | |
| Emerald | 1.577 | 0.064 | 0.221 | 1.0606 | +0.157 | |
| CZ | 2.150 | 0.208 | 0.220 | 0.7461 | +0.013 | |
| Aquamarine | 1.577 | 0.064 | 0.218 | 1.0606 | +0.154 | |
| Sapphire | 1.770 | 0.149 | 0.214 | 1.0157 | +0.065 | |
| Peridot | 1.670 | 0.119 | 0.203 | 1.0909 | +0.084 | |
| Tourmaline | 1.624 | 0.088 | 0.197 | 1.0791 | +0.109 | |
| Zircon | 1.930 | 0.322 | 0.195 | 0.7360 | -0.126 | |
| Topaz | 1.619 | 0.088 | 0.190 | 1.0655 | +0.102 | |
| Spinel | 1.718 | 0.104 | 0.188 | 0.9711 | +0.084 | |
| Quartz | 1.544 | 0.060 | 0.153 | 1.0327 | +0.093 | |
| Garnet (Almandine) | 1.760 | 0.163 | 0.120 | 0.8929 | -0.043 | |
| Garnet (Rhodolite) | 1.760 | 0.128 | 0.118 | 0.8929 | -0.010 | |
| Fluorite | 1.434 | 0.089 | 0.111 | 1.0588 | +0.021 |