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.

Surface topography is an efficient tool for the understanding of physical phenomena, especially if multiscale roughness analysis is performed. However, the observable scale range in a topography measured with 3D optical profilometers is quite limited. Therefore, all scales linked to a physical phenomenon might not be measured, which impedes the correct analysis of the surface. Stitching of 3D topographies, a technique combining elementary topographic maps into a larger one, can be used to increase the scale range for an objective lens. A high resolution over a large field of measurement topography is then generated. A literature review of 3D topography stitching algorithm highlights the stitching procedure, and detailed explanations on in-plane registration algorithms are provided. However, some existing 3D topography stitching algorithms are not sufficiently accurate for the registration of surface, especially at smaller scales. This paper proposes a new reflectance-based multimap 3D stitching algorithm and three of its variants. These algorithm variants are compared to three existing 3D stitching algorithms (geometric, cross-correlation and global optimization of differences) on four test cases, containing measured elementary topographic maps obtained on four surfaces and with four 3D optical profilometers (two focus variation microscopes and two interferometers). Five qualitative and quantitative criteria and indicators are proposed for the comparison of 3D topography stitching algorithms: visual inspection, run time, memory usage, mean repositioning error and stitching error estimator. Lastly, two quantitative indicators and criteria are new indicators proposed in this article. Overall, the new 3D stitching algorithms based on reflectance and multimaps have a lower mean repositioning error and stitching error estimator compared to other existing algorithms. This highlights the relevance of multimap stitching algorithms in the case of 3D topographies. A new decision-helping tool, the stitching gain lift plot (SGL plot), is described for the selection of the best stitching algorithm for a given test case. The SGL plot especially highlights the higher performance of two of the variants of the novel algorithm compared to the three existing 3D stitching algorithms.

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.

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.

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.

With a view to improve measurements, this paper presents a statistical approach for characterizing the behaviour of roughness parameters based on measurements performed on ground surface topographies (grit #080/#120). A S neox^TM (Sensofar^®, Terrassa, Spain), equipped with three optical instrument modes (Focus Variation (FV), Coherence Scanning Interferometry (CSI), and Confocal Microscopy (CM)), is used according to a specific measurement plan, called Morphomeca Monitoring, including topography representativeness and several time-based measurements. Previously applied to the Sa parameter, the statistical approach based here solely on the Quality Index (QI) has now been extended to a multi-parameter approach. Firstly, the study focuses on detecting and explaining parameter disturbances in raw data by identifying and quantifying outliers of the parameter’s values, as a new first indicator. This allows us to draw parallels between these outliers and the surface topography, providing reflection tracks. Secondly, the statistical approach is applied to highlight disturbed parameters concerning the instrument mode used and the concerned grit level with two other indicators computed from QI, named homogeneity and number of modes. The applied method shows that a cleaning of the data containing the parameters values is necessary to remove outlier values, and a set of roughness parameters could be determined according to the assessment of the indicators. The final aim is to provide a set of parameters which best describe the measurement conditions based on monitoring data, statistical indexes, and surface topographies. It is shown that the parameters Sal, Sz and Sci are the most reliable roughness parameters, unlike Sdq and S5p, which appear as the most unstable parameters. More globally, the volume roughness parameters appear as the most stable, differing from the form parameters. This investigated point of view offers thus a complementary framework for improving measurement processes. In addition, this method aims to provide a global and more generalizable alternative than traditional methods of uncertainty calculation, based on a thorough analysis of multi-parameter and statistical indexes.