X+1+1: A fast three-frequency heterodyne absolute phase measurement method integrating modified Fourier transform

The three-frequency heterodyne phase shift profilometry is widely used in high-precision 3D reconstruction. However, the high accuracy comes at the cost of requiring many projected frames, which increases measurement time and decreases measurement efficiency. To address this challenge, we propose a rapid, high-precision absolute phase acquisition method called X+1+1, which fully integrates the accuracy advantages of the multi-frequency n-step heterodyne phase-shifting method and the speed advantages of the Modified Fourier transform profilometry (MFTP). The highest frequency gratings use the standard X-step phase-shifting method to determine the wrapped phase, ensuring high unwrapping accuracy and obtaining background light intensity. For intermediate and low frequencies, a single-frame grating and the Backgroundgenerated Modified Fourier transform profilometry (BGMFTP) are used to solve each wrapped phase to reduce the measurement time. Finally, the heterodyne method processes these three-frequency wrapped phases to obtain the absolute phase. Experimental results demonstrated the high accuracy and speed of this method in the 3D measurement process. Compared to traditional Fourier transform profilometry, the X+1+1 method has a 53% improvement in accuracy, while maintains the same level of performance as the three-frequency four-step heterodyne method in continuous non-marginal flat areas and the projection time was reduced by approximately 50%. The proposed X+1+1 method provides a new solution for balancing speed and accuracy in the application and promotion of structured-light 3D measurement.