Demodulation of interferometry parameters with multiple-harmonic superposition based on the DTFT and semi-blind spectral analysis

The core issue of multi-surface wavelength-shifting interferometry at free cavity lengths is mainly centered on adaptively matching the tuning step. To avoid harmonic aliasing and undersampling, the discrete-time Fourier transform method with global spectrum densification is used to comprehensively analyze the spectral characteristics under different sampling cases and cavity lengths, then a composite multi-surface wavelength-shifting interferometry algorithm is proposed accordingly. The proposed method includes a preprocessing algorithm and three spectral criteria to identify and avoid undesirable sampling problems for in-situ measurements. The algorithm performance is quantitatively evaluated from several aspects of the simulation analysis. A flat plate with an average thickness of 20 mm was repeatedly measured using a Fizeau wavelength-shifting interferometer in the experiments, and the PVQ and RMS errors at different measurement distances were less than 5 mm and 1 mm, respectively.