中文摘要：

在表面下的损坏和表面粗糙之间的关系的一个理论模型被建立认识到扎根的光材料的表面下的损坏的快速、非破坏性的测量。模型的要求的状况是表面下的损坏深度和 peak-to-valley 表面粗糙等于在导致由的易碎的表面的光线、侧面的裂缝的深度小半径(半径≤ 2 00 μ m ) 球形的 indenter 分别地。并且到光线的裂缝繁殖的有弹性的压力地的贡献也在装载周期被考虑。地面 BK7 眼镜的表面下的损坏深度被完成点技术验证表面粗糙的表面下的损坏的理论比率的 magnetorheological 测量。结果证明比率是直接比例的磨料谷物和光材料的坚硬装载，当相反地比例时到磨料谷物的颗粒度和光材料的破裂坚韧。而且，负担的影响和比率上的破裂坚韧分别地比颗粒度和坚硬更重要。砂砾和 120 砂砾修理了 BK7 眼镜的粗糙的磨擦的 80 的测量比率分别地是 5.8 和 5.4。

英文摘要：

A theoretical model of relationship between subsurface damage and surface roughness was established to realize rapid and non-destructive measurement of subsurface damage of ground optical materials. Postulated condition of the model was that subsurface damage depth and peak-to-valley surface roughness are equal to depth of radial and lateral cracks in brittle surface induced by small-radius （radius≤200μm） spherical indenter, respectively. And contribution of elastic stress field to the radial cracks propagation was also considered in the loading cycle. Subsurface damage depth of ground BK7 glasses was measured by magnetorheological finishing spot technique to validate theoretical ratio of subsurface damage to surface roughness. The results show that the ratio is directly proportional to load of abrasive grains and hardness of optical materials, while inversely proportional to granularity of abrasive grains and fracture toughness of optical materials. Moreover, the influence of the load and fracture toughness on the ratio is more significant than the granularity and hardness, respectively. The measured ratios of 80 grit and 120 grit fixed abrasive grinding of BK7 glasses are 5.8 and 5.4, respectively.