Scale-dependent roughness parameters for topography analysis

TL;DR

This paper introduces the Scale-Dependent Roughness Parameters (SDRP) framework, enabling multi-scale characterization of surface topography by analyzing derivatives at various scales, improving surface analysis and artifact detection.

Contribution

The paper presents a novel SDRP framework that captures scale-dependent surface features, linking it with existing methods and allowing detailed multi-scale surface analysis from single measurements.

Findings

SDRP provides new metrics for surface characterization across scales.

SDRP can detect measurement artifacts.

SDRP relates to ACF, VBM, and PSD methods.

Abstract

The failure of roughness parameters to predict surface properties stems from their inherent scale-dependence; in other words, the measured value depends on the way it was measured. Here we take advantage of this scale-dependence to develop a new framework for characterizing rough surfaces: the Scale-Dependent Roughness Parameters (SDRP) analysis that yields slope, curvature and higher-order derivatives of surface topography at many scales, even on a single topography measurement. We demonstrate the relationship between SDRP and other common statistical methods for analyzing surfaces: the height-difference autocorrelation function (ACF), variable bandwidth methods (VBMs) and the power spectral density (PSD). We use computer-generated and measured topographies to demonstrate the benefits of SDRP analysis, including: novel metrics for characterizing surfaces across scales, and the detection of measurement artifacts. The SDRP is a generalized framework for scale-dependent analysis of surface topography that yields metrics that are intuitively understandable.