Double Hilbert transform based nonlinear harmonics correction for fringe projection profilometry

Fringe projection profilometry (FPP) has the advantages of large field of view, high precision and resolution, and is widely used in industrial inspection, medical treatment, aerospace and other fields. The nonlinear response between the camera and the projector in the system will affect the sinusoidal intensity of the captured fringe images, produce periodic phase errors, and affect the final reconstruction accuracy. Traditional double N-step phase shift (NPS) and Hilbert transform (HT) methods only correct the fundamental harmonic part of the phase nonlinear errors, and ignore the rest of the higher harmonic. Therefore, a double HTs based nonlinear phase error correction method is proposed, taking the higher order nonlinear harmonics into account. The artificial sinusoidal fringe images without background term are constructed using the wrapped phase calculated by captured fringe images. Then the HT is performed to convert the phase error to multiplication from addition, which can realize error balance in phase calculation. After obtaining the new phase, reoperation of artificial fringe generation and HT (AHT) is carried out to effectively remove the high order harmonic part of nonlinear harmonics. In proposed method, the wrapped phase calculated by captured fringe images is directly used to generate the artificial fringe images, which does not require additional projection patterns and realize real-time correction of phase nonlinear errors with high accuracy. Furthermore, direct artificial fringe generation also can efficiently avoids the effect of background intensity to the HT. Theoretical analysis, simulation analysis and experimental verification all prove the feasibility and superiority of the proposed method.