Recovery of absolute phases for the fringe patterns of three selected wavelengths with improved anti-error capability

In a recent published work, we proposed a technique to recover the absolute phase maps of fringe patterns with two selected fringe wavelengths. To achieve higher anti-error capability, the proposed method requires employing the fringe patterns with longer wavelengths; however, longer wavelength may lead to the degradation of the signal-to-noise ratio (SNR) in the surface measurement. In this paper, we propose a new approach to unwrap the phase maps from their wrapped versions based on the use of fringes with three different wavelengths which is characterized by improved anti-error capability and SNR. Therefore, while the previous method works on the two-phase maps obtained from six-step phase-shifting profilometry (PSP) (thus 12 fringe patterns are needed), the proposed technique performs very well on three-phase maps from three steps PSP, requiring only nine fringe patterns and hence more efficient. Moreover, the advantages of the two-wavelength method in simple implementation and flexibility in the use of fringe patterns are also reserved. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.