High-precision reconstruction algorithm for scanning white light interferometry based on region-directed high-density interpolation

Scanning white light interferometry (SWLI), as a fundamental non-contact technique for three-dimensional surface topography measurement, is susceptible to accuracy degradation due to environmental vibrations and non-uniform sampling errors caused by scanning devices such as stepper motors. This paper proposes a vertical scanning algorithm based on region-directed high-density interpolation to effectively compensate for non-uniform sampling errors. The algorithm acquires the actual scanning position of the interference objective using a high-precision grating ruler, rearranging image frames into non-uniformly sampled signals with precise position labels. It employs the centroid method for coarse localization of the coherence peak to lock the effective region, followed by Fourier series fitting of the non-uniform data using the least-squares method to reconstruct continuous interference waveforms. Based on the coarse localization results, directed high-density interpolation is performed, and the zero optical path difference point is precisely determined through peak calculation, enabling fine reconstruction of the three-dimensional topography. For long signals, an adaptive segmentation strategy based on region of interest (ROI) is introduced to eliminate invalid data and reduce computational complexity. Experimental results demonstrate that the relative error for a 960 nm standard step measurement is 0.484%, with a standard deviation of 3.046 nm; for large-depth steps, the measurement error is controlled within −0.3%. The ROI segmentation improves computational efficiency by approximately 44 times compared to global fitting methods. The proposed algorithm combines high accuracy, strong robustness, and high efficiency under non-uniform sampling conditions, providing a feasible solution for high-precision batch measurement of surfaces with large-depth variations.