Surface roughness characterization using representative elementary area (REA) analysis

Abstract

We proposed the Representative Elementary Area (REA) analysis method and illustrated how it is needed to evaluate representative roughness parameters of surfaces. We used mean height (Sa) roughness to study how its variations converge to a steady state as we expanded the area of investigation (AOI) using combined scan tiles obtained through Confocal Laser Scanning Microscopy. We tested quartz and glass surfaces, subjecting them to various levels of polishing with grit sizes ranging between # 60 and #1200. The scan tiles revealed a multiscale roughness texture characterized by the dominance of valleys over peaks, lacking a fractal nature. REA analysis revealed Sa variations converged to a steady state as AOI increased, highlighting the necessity of the proposed method. The steady-state Sa, denoted as SaREA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{Sa}}}_{{\ ext{REA}}}$$\\end{document}, followed an inverse power law with polishing grit size, with its exponent dependent on the material hardness. The REA length representing SaREA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{Sa}}}_{{\ ext{REA}}}$$\\end{document} of glass surfaces, followed another inverse power law with polishing grit size and an indeterminate relationship for quartz surfaces. The multiscale characteristics and convergence to steady state were also evident in skewness, kurtosis, and autocorrelation length (Sal) parameters. Sal increased to a maximum value before decreasing linearly as AOI was linearly increased. The maximum Sal, termed as Salmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{Sal}}}_{{\ ext{max}}}$$\\end{document}, exhibited a linear relationship with REA. In the absence of REA analysis, the magnitude of uncertainty depended on the polishing grit size. Finely polished surfaces exhibited a 10–20% variability, which increased to up to 70% relative to the steady-state Sa with coarser polishing.