Abstract: In order to improve the accuracy and efficiency of the phase solution of the grating fringe, this paper optimizes the multi-frequency heterodyne and phase shift method from the perspective of time series. According to the importance of the unfolding frequency, the phase shift of the asynchronous number is selected to solve the main value of the phase. The four-step phase shift is used for the main frequency, and the three-step phase shift is used for other frequencies. Finally, the heterodyne principle is used to expand the phase of the grating fringe. The experimental results prove the feasibility of the algorithm. Compared with the traditional Gray code expansion method, this optimization algorithm has higher accuracy and fewer projected images. Compared with the conventional multi-frequency heterodyne method, it can project fewer images without reducing the accuracy and improve the measurement efficiency.

Key words: Digital grating projection, Phase unwrapping, Multi-frequency heterodyne, Phase shift method