High-resolution microscopic fringe projection profilometry using Nyquist frequency fringe

Abstract

Vertical resolution is a crucial property in microscopic fringe projection profilometry (MFPP) systems. The challenge in improving vertical resolution lies not only in enhancing height-sensing sensitivity but also in reducing the gain of phase-shifting algorithms (PSA) against dominant noise in the fringe signal. This study uses an optical flat for continuous phase shifting, achieving phase demodulation for fringe with Nyquist frequency. To mitigate the inherent disturbances caused by continuous phase shifting during phase demodulation, a transfer relation between phase-shift error and 1/f noise is established using spectral analysis and the frequency transfer function framework. Based on this transfer relation, we propose a novel PSA with high signal noise ratio and sensitivity. Experiments validate the proposed PSA, indicating that the vertical resolution of a telecentric MFPP system using the proposed PSA is 73 nm. The reconstruction results of wafer-level 3D structures are consistent with those from confocal microscopy.