Wavelength-tuning phase-shifting interferometry of transparent plates using sub-signal frequency correction

Abstract

The difficulty of measurements on transparent flats comes from that the measured surfaces contribute corresponding sub-signals to the captured interferograms. As the cornerstone of phase demodulation, the frequency solution of the inter-harmonics is significant. The frequency solution accuracy is not satisfactory in traditional algorithms since the unavoidable frequency leakage. To overcome the problem above, a Fourier transform-based frequency correction algorithm with a narrower spectrum interval (FT-FCA) is proposed. By the developed algorithm, reliable multi-surface measurements can be ensured by the obtained sub-signal frequencies and the designed sampling weight functions. In the comparative studies, the robustness of the proposed FT-FCA to the random wavelength-tuning error and phase-shifting error is verified. In the experiments, two transparent flats with thicknesses of 20 mm and 43 mm were measured using a Fizeau wavelength-shifting interferometer, and the wavefronts were reconstructed by the developed algorithm. The comparative experimental analysis verifies the effectiveness of the FT-FCA.