Performance Analysis of Surface Reconstruction Algorithms in Vertical Scanning Interferometry Based on Coherence Envelope Detection

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.