Two 3D Fractal-Based Approaches for Topographical Characterization: Richardson Patchwork versus Sdr.

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.

Height Fluctuations and Surface Gradients in Topographic Measurements.

Topographic maps are composed of pixels associated with coordinates (x, y, z) on a surface. Each pixel location (x, y) is linked with fluctuations in a measured height sample (z). Fluctuations here are uncertainties in heights estimated from multiple topographic measurements at the same position. Height samples (z) are measured at individual locations (x, y) 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 (z = z(x, y)). 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.

Top-down Determination of Fluctuations in Topographic Measurements.

A top-down method is presented and studied for quantifying topographic map height (z) fluctuations directly from measurements on surfaces of interest. Contrary to bottom-up methods used in dimensional metrology, this method does not require knowledge of transfer functions and fluctuations of an instrument. Fluctuations are considered here to be indicative of some kinds of uncertainties. Multiple (n), successive topographic measurements (z = z(x,y)) are made at one location without moving the measurand relative to the measurement instrument. The measured heights (z) at each position (x,y) are analyzed statistically. Fluctuation maps are generated from the calculated variances. Three surfaces were measured with two interferometric measuring microscopes (Bruker ContourGT™ and Zygo NewView™ 7300). These surfaces included an anisotropic, turned surface; an isotropic, sandblasted surface; and an abraded, heterogeneous, multilayer surface having different, complex, multiscale morphologies. In demonstrating the method, it was found that few non-measured points persisted for all 100 measurements at any location. The distributions of uncertainties are similar to those of certain features on topographic maps at the same locations, suggesting that topographic features can augment measurement fluctuations. This was especially observed on the abraded ophthalmic lens; a scratch divides the topographic map into two zones with different uncertainty values. The distributions of fluctuations can be non-Gaussian. Additionally, they can vary between regions within some measurements.

Surface Reflectance: an Optical Method for Multiscale Curvature Characterization of Wear on Ceramic-Metal Composites.

Surface gradient characterization by light reflectance (SGCLR) is used for the first time for multiscale curvature calculations and discrimination of worn surfaces on six damaged ceramic-metal composites. Measurements are made using reflectance transformation imaging (RTI). Slope and curvature maps, generated from RTI, are analyzed instead of heights. From multiscale decompositions, bootstrapping, and analysis of variance (ANOVA), a strong correlation (R² = 0.90) is found between the density of furrows of Mehlum curvatures, with a band pass filter at 5.4 µm, present in ceramic grains and their mechanical properties. A strong correlation is found between the mean curvatures of the metal and the ceramics, with a high pass filter at 1286 µm.

Assessment of promising agricultural management practices.

iSQAPER project - Interactive Soil Quality Assessment in Europe and China for Agricultural Productivity and Environmental Resilience - aims to develop an app to advise farmers on selecting the best Agriculture Management Practice (AMPs) to improve soil quality. For this purpose, a soil quality index has to be developed to account for the changes in soil quality as impacted by the implementation of the AMPs. Some promising AMPs have been suggested over the time to prevent soil degradation. These practices have been randomly adopted by farmers but which practices are most used by farmers and where they are mostly adopted remains unclear. This study is part of the iSQAPER project with the specific aims: 1) map the current distribution of previously selected 18 promising AMPs in several pedo-climatic regions and farming systems located in ten and four study site areas (SSA) along Europe and China, respectively; and 2) identify the soil threats occurring in those areas. In each SSA, farmers using promising AMP's were identified and questionnaires were used to assess farmer's perception on soil threats significance in the area. 138 plots/farms using 18 promising AMPs, were identified in Europe (112) and China (26).Results show that promising AMPs used in Europe are Crop rotation (15%), Manuring & Composting (15%) and Min-till (14%), whereas in China are Manuring & Composting (18%), Residue maintenance (18%) and Integrated pest and disease management (12%). In Europe, soil erosion is the main threat in agricultural Mediterranean areas while soil-borne pests and diseases is more frequent in the SSAs from France and The Netherlands. In China, soil erosion, SOM decline, compaction and poor soil structure are among the most significant. This work provides important information for policy makers and the development of strategies to support and promote agricultural management practices with benefits for soil quality.