Characterization of 3D Surface Texture Directionality Using Multi-Scale Curvature Tensor Analysis

Anisotropy of surface texture can in many practical cases significantly affect the interaction between the surface and phenomena that influence or are influenced by the topography. Tribological contacts in sheet forming, wetting behavior or dental wear are good examples. This article introduces and exemplifies a method for quantification and visualization of anisotropy using the newly developed 3D multi-scale curvature tensor analysis. Examples of a milled steel surface, which exhibited an evident anisotropy, and a ruby contact probe surface, which was the example of isotropic surface, were measured by the confocal microscope. They were presented in the paper to support the proposed approach. In the method, the curvature tensor T is calculated using three proximate unit vectors normal to the surface. The multi-scale effect is achieved by changing the size of the sampling interval for the estimation of the normals. Normals are estimated from regular meshes by applying a covariance matrix method. Estimation of curvature tensor allows determination of two directions around which surface bends the most and the least (principal directions) and the bending radii (principal curvatures). The direction of the normal plane, where the curvature took its maximum, could be plotted for each analyzed region and scale. In addition, 2D and 3D distribution graphs could be provided to visualize anisotropic or isotropic characteristics. This helps to determine the dominant texture direction or directions for each scale. In contrast to commonly used surface isotropy/anisotropy determination techniques such as Fourier transform or autocorrelation, the presented method provides the analysis in 3D and for every region at each scale. Thus, different aspects of the studied surfaces could clearly be seen at different scales.