Research on fractal behavior of surface topography in precision grinding of monocrystal sapphire

At present, how to evaluate the quality of precision ground surface of optical crystals reasonably and effectively is an important problem for the field of optical element processing and its application. A three dimension (3D) and two dimension (2D) box-counting fractal analysis methods are used to analyze ground monocrystal sapphire surface topography. The results obtained show that the 3D fractal dimension D_s shows a negative correlation with the surface roughness parameter R_a. As the D_s are higher, its topography is more exquisite. For the ground surface with smaller D_s, the pronounced surface defects are exhibited in ground surface. The change of material removal mode can be implied from the distribution of 2D cross-sectional profile fractal dimension D_L. When the 2D fractal dimension is highly symmetry along the grinding direction, the material removal mode is ductile. When the 2D fractal dimension is weakly asymmetry or irregular distribution, the material removal mode is brittle. This study indicates that the fractal method can not only be used for comprehensive characterization of ground monocrystal sapphire, but also be used to reveal the material removal mechanism of ground monocrystal sapphire.