Image-based roughness estimation for patinated bronze surfaces: a practical multivariate algorithm applied to benchtop and portable microscopy

Surface texture is a key functional property of metallic substrates and surface treatments. In industrial metrology, surface roughness is traditionally characterized by contact methods, such as stylus profilometry, standardized by ISO 4287. However, in cultural heritage applications, direct contact measurements may be unsuitable for delicate and heterogeneous surfaces, while non-contact optical profilometry is often not readily available for routine investigations. Based on the surface roughness (Ra) measured by portable stylus meter on foundry patinated bronze coupons, a non-contact image-based approach was developed to estimate roughness-related information from digital microscopy images acquired with both benchtop and portable devices. The proposed workflow combines statistical transformation of grayscale images and multivariate analysis to extract texture descriptors correlated with the reference Ra value. The method was designed to ensure robustness, reproducibility, and implementation using standard computational resources. As a proof of concept, bronze coupons with Ra values between 2 and 16 µm were analyzed using stylus measurements and grazing-light microscopy images. Results demonstrate the potential of microscopy-based image analysis for quantitative, non-invasive in situ surface roughness assessment, especially when portable profilometry is unavailable or contact measurements are unsuitable. The approach also allows surface information to be extracted from microscopy images acquired for documentation.