Hilbert transform–assisted phase-shifting profilometry resistant to motion-induced errors

The phase-shifting method is widely used for phase calculation in fringe projection profilometry but suffers from motion-induced phase errors (MIPEs) in dynamic measurements due to motion-induced phase shifts (MIPSs). Existing methods for mitigating the MIPEs typically rely on assumptions such as temporally linear or spatially uniform MIPSs, limiting their applicability in practical scenarios. To overcome these limitations, this paper presents a novel method that reduces phase errors induced by various types of motion. The method first estimates the MIPSs from the background-removed and Hilbert-transformed fringe images. It then compensates for the MIPEs by incorporating the estimated MIPSs into the phase calculation. Finally, the phase is iteratively optimized using the updated fringe background. The boundary effect of the Hilbert transform is also mitigated in this method. By removing the restrictive assumptions of existing methods, the proposed method can handle objects with complex shapes and motions. Experimental results demonstrate its effectiveness, achieving up to 87.47% additional reduction in MIPEs under non-uniform motion compared with the state-of-the-art method, while maintaining similar performance under uniform motion. Overall, the proposed method is effective and robust in practical dynamic measurements.