Super-Gaussian surface characterization and predictive geometry modeling for femtosecond laser micromachining in epoxy composites

Femtosecond laser micromachining in transparent FR4 epoxy substrates was performed using a 515 nm green laser system, with nanometer-scale surface topography characterized via white light interferometry (WLI). A Super-Gaussian fitting methodology was applied to quantify ablation crater profiles, introducing a shape exponent parameter that simultaneously describes bottom flatness and sidewall steepness characteristics. This approach achieved 59.9 % reduction in normalized root-mean-square error (NRMSE) compared to conventional parabolic fitting techniques. Through systematic full factorial experimental design spanning laser powers from 3 to 18 W and pulse counts from 5 to 200, three semi-empirical predictive models were developed correlating laser processing parameters to Super-Gaussian geometric descriptors: depth ( D ), diameter ( W ), and shape exponent ( p ). These parameters have been predicted by the models with great accuracy, enabling sub-micron geometric control. This investigation establishes, for the first time, a comprehensive physics-informed modeling framework that enables predictive process control in femtosecond laser microfabrication, providing quantitative foundations for automated manufacturing systems and advancing industrial implementation of ultrafast laser technologies in precision polymer composite processing.