Fourier Analysis with Gini Coefficient: A New Approach to Assess Surface T opography in Direct Laser Interference Patterning

Direct Laser Interference Patterning (DLIP) is an emerging manufacturing technology for creating functional surfaces. To integrate DLIP into industrial processes, reliable and rapid methods for determining the quality of the produced microstructures are essential. Surface roughness evaluation methods are typically designed to quantify variations in surface morphology relative to an ideal uniform surface. As a result, these methods are inadequate for assessing the quality of periodic structures generated by DLIP, requiring the implementation of additional algorithms to mitigate their influence. Recently, a method that uses Gini analysis on surface topographical parameters was established for this purpose. It first divides the surface into a series of decomposed parts according to the period and then uses the Gini coefficient to statistically describe the roughness parameters obtained from each part to evaluate the homogeneity. However, the resulting value is strongly dependent on the type and number of parameters selected. This work introduces a novel approach that employs Gini analysis of two-dimensional Fast Fourier Transform (2D FFT) on topography images, providing both qualitative and quantitative assessments of texture homogeneity. The comparison of those two methods indicates that the FFT Gini method correlates well with homogeneity measurements directly taken from the surface topography and demonstrates the advantage of evaluating the structuring process at high proceeding speed.