Two-step gradient-assisted phase-shifting demodulation algorithm for fast 3D reconstruction

The conventional multi-frequency heterodyne method is one of the most widely used methods in non-contact 3D measurement. However, it needs to project different phase-shifting patterns with different frequencies, so a large number of patterns are required. For most conventional methods, the fringe period number of the projected patterns is usually small due to its limited noise tolerance, though a larger fringe period number always means higher accuracy. We propose a two-step phase-shifting demodulation algorithm based on an intensitygradient. In this method, only two patterns for each frequency are required. With the intensity gradient of the two patterns, we obtain the wrapped phase of each frequency. Next, the absolute phase is retrieved from the three wrapped phases with the heterodyne algorithm. Because only two patterns are required for each frequency, the proposed method is more robust and has higher measuring speed compared with the traditional three-frequency four-step heterodyne method. Simulations and experiments prove the feasibility and effectiveness of the method, and demonstrate that the proposed method extends the noise tolerance and achieves highprecision with only half of the patterns required by the traditional three-frequency four-step method.