Three-dimensional topography reconstruction method for non-uniform under-sampled vertical scanning...

Low-coherence scanning interferometry (LCSI) is a high-precision method for 3D surface topography measurement. However, the non-uniform spatial distribution of sampling points and the size of sampling intervals jointly constrain the measurement accuracy and efficiency of existing methods. To address this issue, this paper proposes an envelope centroid localization method based on sinc function interpolation (ECS). By exploiting the structural similarity between the sinc function and the distribution of low-coherence interference signals, the ECS method compensates for non-uniform and sparse vertical scan sampling points in the characteristic regions of the interference envelope via interpolation. This approach effectively mitigates information loss caused by insufficient sampling and variations in the sampling interval, thereby achieving a better balance between measurement accuracy and efficiency. Under conditions of extremely sparse sampling (sampling interval reaching 17 times the Nyquist interval) and non-uniform sampling intervals (sampling intervals difference up to ±0.2 µm), the proposed method improves measurement accuracy by more than 300% compared to the traditional center of mass (COM) method and peak fitting (PF) method. The reconstructed surface waviness is maintained at around 0.05 µm. These results verify the effectiveness of the proposed method in processing sparse and non-uniform sampling data in LCSI.