Objective homogeneity quantification of a periodic surface using the Gini coefficient

Abstract

The significance of periodic surface structuring methods, such as direct laser interference patterning, is growing steadily. Thus, the ability to objectively and consistently evaluate these surfaces is increasingly important. Standard parameters such as surface roughness or the arithmetic average height are meant to quantify the deviation of a real surface from an ideally flat one. Periodically patterned surfaces, however, are an intentional deviation from that ideal. Therefore, their surface profile has to be separated into a periodic and a non-periodic part. The latter can then be analyzed using the established surface parameters and the periodic nature allows a quantification of structure homogeneity, e.g. based on Gini coefficient. This work presents a new combination of established methods to reliably and objectively evaluate periodic surface quality. For this purpose, the periodicity of a given surface is extracted by Fourier analysis, and its homogeneity with respect to a particular property is determined for the repeating element via a Gini analysis. The proposed method provides an objective and reliable instrument for evaluating the surface quality for the selected attribute regardless of the user. Additionally, this technique can potentially be used to both identify a suitable surface structuring technique and determine the optimal process parameters.