3D micromorphological reconstruction and roughness measurement based on shape from focus and error propagation analysis

Abstract

This study introduces a unified metrological model to enhance SFF-based 3D roughness measurement accuracy in the presence of depth, tilt, and random errors. A novel aspect of this research is the development of a unified error propagation model that quantitatively maps and integrates depth, tilt-induced deviations, and random uncertainties, marking a significant departure from traditional SFF methods. The method includes an adaptive depth estimation strategy based on curve morphology perception and gradient profile analysis, ensuring robust peak localization even under challenging conditions such as multi-peak and offset focus curves. Furthermore, an adaptive smoothing filter, guided by the gradient field of the all-in-focus image, strikes an optimal balance between noise suppression and detail preservation. Tilt correction is addressed through a method combining least-squares plane fitting with Rodrigues’ rotation theory, supplemented by a quadratic polynomial fitting approach to effectively compensate for residual errors. These integrated techniques substantially enhance the accuracy and stability of 3D surface roughness measurements. Extensive simulations and physical experiments validate the method, maintaining a consistent relative error of Sa between 0.23 % and 0.63 % across three types of laser-processed surfaces. For step surfaces with heights of 50 µm, 100 µm, and 150 µm, the relative error remains below 1.5 %. The proposed method offers a cost-effective, reliable solution suitable for applications including additive manufacturing, semiconductor packaging, and tool wear monitoring.