Cross-period sub-nyquist sampling method for efficient 3D surface profiling in low-coherence scanning interferometry

Low-coherence scanning interferometry (LCSI) serves as a highly accurate methodology for three-dimensional surface profilometry. However, to preserve the characteristic information embedded in the interferometry signals, the sampling interval in this technique is strictly governed by the Nyquist sampling criterion, which limits the measurement efficiency. To solve the problem, this paper proposes a cross-period sub-Nyquist sampling method that significantly enhances the sampling interval while preserving the essential signal characteristics. This method can keep the spatial and frequency information of the signal at the same time by measuring with a specific sampling interval, which is based on the Nyquist sampling step size and multiple n whole wavelength cycles. Compared to conventional random sub-sampling, the proposed method enhances the measurement accuracy by over 90% and improves the roughness from 0.9259<i>µm</i> to 0.7003<i>µm</i>, while enabling a sampling interval 25 times larger than the Nyquist limit.