There is a growing interest in cultural heritage preservation. The notion of HyperHeritage highlights the creation of new means of communication for the perception and data processing in cultural heritage. This article presents the Digital Surface HyperHeritage approach, an academic project to identify the topography of art painting surfaces at the scale at which the elementary information of sensorial rendering is contained. High-resolution roughness and imaging measurement tools are then required. The high-resolution digital model of painted surfaces provides a solid foundation for artwork-related information and is a source of many potential opportunities in the fields of identification, conservation, and restoration. It can facilitate the determination of the operations used by the artist in the creative process and allow art historians to define, for instance, the meaning, provenance, or authorship of a masterpiece. The Digital Surface HyperHeritage approach also includes the development of a database for archiving and sharing the topographic signature of a painting.

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.

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.

Roping or ridging is a visual defect affecting the surface of ferritic stainless steels, assessed using visual inspection of the surfaces. The aim of this study was to quantify the morphological signature of roping to link roughness results with five levels of roping identified with visual inspection. First, the multiscale analysis of roughness showed that the texture aspect ratio S_tr computed with a low-pass filter of 32 µm gave a clear separation between the acceptable levels of roping and the non-acceptable levels (rejected sheets). To obtain a gradation description of roping instead of a binary description, a methodology based on the use of the autocorrelation function was created. It consisted of several steps: a low-pass filtering of the autocorrelation function at 150 µm, the segmentation of the autocorrelation into four stabilized portions, and finally, the computation of isotropy and the root-mean-square roughness S_q on the obtained quarters of function. The use of the isotropy combined with the root-mean-square roughness S_q led to a clear separation of the five levels of roping: the acceptable levels of roping corresponded to strong isotropy (values larger than 10%) coupled with low root-mean-square roughness S_q. Both methodologies can be used to quantitatively describe surface morphology of roping in order to improve our understanding of the roping phenomenon.

This study presents a robust methodology for analyzing 3D roughness parameters to characterize sandblasted surfaces, identifying the most relevant descriptors for process optimization. Sandblasting with irregularly shaped corundum particles is performed using five grit sizes (25, 50, 90, 125, and 250 µm) and three pressure levels (2, 3, and 4 bar). The resulting surfaces are characterized through eight 3D roughness parameters: Sa, Spc, Sal, Sfd, Sdq, Sdr, Spd, and Str. A linear model of the form Q = a + b.D + d.D.P, where Q represents the roughness parameter, D is the average grit size, and P is the sandblasting pressure, is employed. For Spd, a nonlinear model, Spd = (a + b.D + d.D.P)², yields a significantly improved determination coefficient, demonstrating the model’s enhanced ability to capture the complexity of the Spd parameter. The double-bootstrap analysis validates the statistical significance of all models, providing confidence intervals for each parameter. This approach emphasizes the importance of advanced 3D roughness descriptors for accurately analyzing surface textures in sandblasting processes, offering a reliable framework for surface characterization and industrial optimization.