Lemesle Julie, Moreau Clement, Deltombe Raphael, Martin Joseph, Blateyron François, Bigerelle Maxence, Brown Christopher A
U.R Concept, 59300 Valenciennes, France.
Valutec, Univ. Polytechnique Hauts-de-France, CEDEX 9, 59314 Valenciennes, France.
Materials (Basel). 2023 Aug 1;16(15):5408. doi: 10.3390/ma16155408.
Topographic maps are composed of pixels associated with coordinates (, , ) on a surface. Each pixel location (, ) is linked with fluctuations in a measured height sample (). Fluctuations here are uncertainties in heights estimated from multiple topographic measurements at the same position. Height samples () are measured at individual locations (, ) in topographic measurements and compared with gradients on topographies. Here, gradients are slopes on a surface calculated at the scale of the sampling interval from inclination angles of vectors that are normal to triangular facets formed by adjacent height samples ( = (, )). Similarities between maps of gradients logs and height fluctuations are apparent. This shows that the fluctuations are exponentially dependent on local surface gradients. The highest fluctuations correspond to tool/material interactions for turned surfaces and to regions of maximum plastic deformation for sandblasted surfaces. Finally, for abraded, heterogeneous, multilayer surfaces, fluctuations are dependent on both abrasion and light/sub-layer interactions. It appears that the natures of irregular surface topographies govern fluctuation regimes, and that regions which are indicative of surface functionality, or integrity, can have the highest fluctuations.
地形图由与表面上的坐标（x, y, z）相关联的像素组成。每个像素位置（x, y）与测量高度样本（z）中的波动相关联。这里的波动是在同一位置从多个地形测量中估计出的高度的不确定性。高度样本（z）在地形测量中的各个位置（x, y）进行测量，并与地形上的梯度进行比较。这里，梯度是在采样间隔尺度上根据与由相邻高度样本（z = (x, y)）形成的三角形小平面垂直的向量的倾斜角计算出的表面斜率。梯度对数图和高度波动图之间的相似性很明显。这表明波动与局部表面梯度呈指数关系。最高的波动对应于车削表面的刀具/材料相互作用以及喷砂表面的最大塑性变形区域。最后，对于磨损的、异质的、多层表面，波动取决于磨损以及光/子层相互作用。似乎不规则表面地形的性质决定了波动状态，并且表明表面功能或完整性的区域可能具有最高的波动。
