Radial Hilbert transform for phase retrieval using two-wavelength three-frame phase-shifting interferometry

Abstract

Dual-wavelength interferometry (DWI) without phase unwrapping is widely applied in optical measurement and imaging. For improving measurement efficiency and increasing the range of applications, a method of retrieving a phase using fewer interferograms and shorter calculating time is proposed in this study. The proposed method requires only three multiplexed and phase-shifted interferograms. By subtracting the other two interferograms from the first frame image and using the Hilbert transform (HT), we first obtained the phase at each wavelength and then calculated the continuous phase at the synthetic wavelength. The method is applicable to open-loop fringes obtained in an off-axis interferometric system and closed-loop fringes obtained in an on-axis system. We used a combination of the radial HT and coordinate conversion method to solve the problem of having to use the conventional HT for closed-loop fringes. The feasibility and applicability of the method are verified using simulation and experimental results.