Three-Dimensional Digital Reconstruction Geometric Analysis for Fused Silica Microshell Resonators

This article reports, for the first time, a 3-D digital reconstruction method for the geometric characterization of fused silica microshell resonators (MSRs). 3-D digital geometric information of fused silica MSRs prepared by a chemical foaming process is acquired by an X-ray microscope (XRM). The surface points of the microshell are selected by pixel contrast to reconstruct the 3-D geometric model. The fourth harmonics distribution of spatial radius and thickness at different shell heights are successfully calculated with the reconstruction model. The finite-element method based on the reconstruction model is also established to analyze the resonant frequency and frequency split of the wineglass mode. Results show that the relative fourth radius harmonic decreases with the height increase, indicating that the chemical foaming process has the capability to restrain the asymmetry for fused silica MSRs. Besides, the wineglass frequency difference between the digital reconstruction model and the experiment is within 3%. The frequency splits from the digital model also correspond well with the experiments. This work provides new insights into 3-D shell information and may enable manufacturing precision improvement of 3-D MSRs.