Fractal-Inspired Multiscale Surface Topography Characterization via ISO 25178 Sdr

Surface topography characterization increasingly relies on areal parameters (ISO 25178) to relate manufacturing processes to functional performance (e.g., wettability, adhesion, tribology). Yet, most roughness parameters remain scale-dependent, making multiscale frameworks essential for describing complex, fractal-like surfaces. In this work, we introduce a standard-friendly multiscale approach based on the interfacial area ratio Sdr (ISO 25178-2) iterated across scales using low-pass Gaussian filtering (ISO 16610), yielding an area–scale curve that quantifies surface complexity through relative area development. This protocol provides a practical alternative to the well-established Richardson Patchwork (triangular tiling) area-scale method used in standards, while relying exclusively on widely implemented standardized operators (Gaussian filter + ISO parameter), enabling straightforward deployment in conventional surface metrology software.

We validate the approach on grit-blasted TA6V surfaces produced under controlled variations of blasting pressure and media, showing that the multiscale Sdr procedure reproduces Patchwork trends over the investigated scale ranges and remains discriminant with respect to process conditions.

To objectively identify the most informative observation scale, we further propose an uncertainty-based scale selection strategy using bootstrap regression, highlighting a relevant cut-off length around 120 µm for capturing the pressure–topography relationship across media.

Overall, this work bridges fractal-inspired area-scale analysis with ISO-compliant metrology practice, providing a robust and accessible route to multiscale characterization and to process–topography interaction studies.