焦散线形成机理的几何分析

A GEOMETRICAL ANALYSIS ON THE PRINCIPLE OF CAUSTICS FORMATION

本文在论证形成焦散线解析条件的基础上,用微分几何理论导出裂纹尖端附近奇异场形成焦散线的几何条件,分析了奇异场变形曲面在光学映射过程中的几何关系与基本特性,从而从几何上更深入更形象地阐明焦散线的形成机理。

On the basis of the demonstrations on the analytic conditions of caustics formation, we deduced the geometric conditions of caustic formation in singular field near crack tip by differential geometry theory, analysed the geometric relations and basic characteristi(?)s of the deformed curve of singular field during optical image. Then the principles of caustics formation were elucidated thoroughly and visually in geometry.