由于折射率椭球缺乏足够的数学分析,因而只能做为几何表示晶体光学性质的手段。本文弥补了这一不足,使折射率椭球对晶体光学性质的描述数学化。证明晶体的光轴不能多于2个,并确定其方向。将晶体折射率直接同传播方向联系起来,十分有利于实际应用。 Due to the lack of sufficient mathematical analysis of the index ellipsoid, it can only be used as a means of geometrically representing the optical properties of crystals. This paper makes up for this deficiency and makes the description of the optical properties of the crystal by the index ellipsoid mathematical. Prove that the optical axis of the crystal can not be more than 2, and determine its direction. The crystal refractive index directly linked with the direction of propagation, is very conducive to practical application.