A novel dual-wavelength iterative method for generalized dual-wavelength phase-shifting interferometry with second-order harmonics

To address dual-wavelength interferograms with arbitrary phase shifts and second-order harmonics, a novel dual-wavelength iterative method (DWIM) based on the least-squares algorithm is proposed. In generalized dual-wavelength phase-shifting interferometry, to compensate for the phase-shift errors consisting of systematic and random phase-shift error, the wrapped phases of single-wavelength with high accuracy can be simultaneously obtained from generalized dual-wavelength interferograms without second-order harmonics. In addition, this method is also employed to deal with randomly phase-shifted dual-wavelength interferograms with the second-order harmonics, and then the effects of the fringe number in interferogram and the number of interferograms used on the accuracy of phase extraction are investigated by numerical simulations. Based on theoretical analysis and simulation results of DWIM, we present the basic relationship between the number of wavelengths, the second-order harmonics and the requirement of the minimum number of interferograms. Finally, the effectiveness of this method is proved by the simulation results of the spherical cap, and its applicability is verified with the results of the micro-sphere, the HeLa cell and the red blood cell, respectively.