Robustness of Surface Roughness against Low Number of Picture Elements and Its Benefit for Scaling Analysis

Abstract

Surface roughness is widely used in the research of topography, and the scaling characteristics of roughness have been noticed in many fields. To rapidly obtain the relationship between root-mean-squared roughness (Rq) and measurement scale (L) could be helpful to achieve more understandings of the surface property, particularly the Rq-L curve could be fitted to calculate the fractal dimension (D). In this study, the robustness of Rq against low number of picture elements was investigated. Artificial surfaces and the surfaces of two actual samples (a silver thin film and a milled workpiece) were selected. When the number of picture elements was lowered, Rq was found to be stable within a large portion of the concerned scope. Such a robustness property could validate the feasibility of Rq-L curve obtained by segmenting a single morphological picture with roughness scaling extraction (RSE) method, which was proposed in our previous study. Since the traditional roughness (TR) method to obtain Rq-L curves was based on multiple pictures, which used a fixed number of picture elements at various L, RSE method could be significantly more rapid than TR method. Moreover, a direct comparison was carried out between RSE method and TR method in calculating the Rq-L curve and D, and the credibility and accuracy of RSE method with flatten order 1 and 2 was verified.