Spatial pattern-shifting method for complete two-wavelength fringe projection profilometry.

Two-wavelength fringe projection profilometry (FPP) unwraps a phase with the unambiguous phase range (UPR) of the least common multiple (LCM) of the two wavelengths. It is accurate, convenient, and robust, and thus plays an important role in shape measurement. However, when two non-coprime wavelengths are used, only a small UPR can be generated, and the unwrapping performance is compromised. In this Letter, a spatial pattern-shifting method (SPSM) is proposed to generate the maximum UPR (i.e., the product of the two wavelengths) from two non-coprime wavelengths. For the first time, to the best of our knowledge, the SPSM breaks the constraint of wavelength selection and enables a complete (i.e., either coprime or non-coprime) two-wavelength FPP. The SPSM, on the other hand, only requires spatially shift of the low-frequency pattern with the designed amounts and accordingly adjusting the fringe order determination, which is extremely convenient in implementation. Both numerical and experimental analyses verify its flexibility and correctness.

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